The document contains information about various finance formulae, including simple interest, compound interest, depreciation, and investing money through regular instalments. It provides the formulae and examples of how to calculate things like interest earned, future value, depreciation over time, and total superannuation value from regular annual contributions invested at compound interest.
The document discusses various finance formulae including:
- Simple interest formula where interest (I) equals the principal (P) multiplied by the interest rate (R) as a decimal multiplied by the number of time periods (T).
- Compound interest formula where the amount (A) after n time periods equals the principal multiplied by (1 plus the interest rate) to the power of n, with examples of compounding annually and monthly.
- Depreciation formula which is similar to the compound interest formula but uses 1 minus the depreciation rate instead of 1 plus the interest rate, with an example calculating depreciation over 9 years.
- A calculation showing the year an asset's value drops
The document discusses various topics related to corporate finance and ratio analysis. It covers time value of money concepts like compounding, discounting, and annuities. It also discusses bond valuation and the yield to maturity formula. Additionally, it outlines numerous ratios used in ratio analysis including liquidity, turnover, profitability, leverage, coverage, dividend, returns and valuation ratios. The DuPont chart and extended DuPont chart are also explained. Other topics covered include risk and return, beta, the capital asset pricing model formula, and the security market line.
Daily Agenda Unit 02 Business CommunicationsAngela Edel
This document outlines the daily agenda and activities for a business communications class over the course of a school week. The week focuses on different topics each day, including business letters, telephone and email etiquette, and public speaking. Students will complete readings, activities, and homework assignments related to each topic, including drafting a business letter and practicing a short speech. Quizzes and tests are also scheduled to assess comprehension of key concepts.
This document outlines the revised 2013 syllabus for CAPE Accounting. It introduces the examination and provides the rationale, aims, skills assessed, prerequisites, and structure of the two-unit syllabus. The syllabus is designed to provide certification in accounting and develop skills like critical thinking, decision-making, and communicating financial information. It consists of two independent units - Financial Accounting and Cost and Management Accounting. Financial Accounting focuses on recording transactions, preparing financial statements, and financial reporting and interpretation. Cost and Management Accounting examines costing principles, systems, and planning and decision making. The syllabus aims to foster understanding of accounting principles and practices.
GAAP and accounting standards form the theory base of accounting and describe rules for preparing financial statements. Accounting conventions emerge from commonly used accounting principles and practices, though they do not need universal application. Key accounting concepts include the entity, money measurement, periodicity, accrual, matching, going concern, cost, and realization concepts. Accounting principles should be based on assumptions, simple to understand, consistently followed, reflect future predictions, and be informative for users.
The document summarizes key concepts from chapters 6-14 of a finance textbook relating to risk and return, time value of money, bonds, stock valuation, cost of capital, capital budgeting, and cash flow estimation. It defines terms like expected rate of return, risk measures like standard deviation and beta, bond and stock valuation methods, weighted average cost of capital (WACC), net present value (NPV), internal rate of return (IRR), modified IRR, payback period, and cash flow items like net operating working capital, operating cash flow, and free cash flow. Formulas and calculator instructions are provided for computing many of these concepts.
This document provides notes on Caribbean society and culture. It discusses the location of the Caribbean region and defines it geographically, geologically, politically, and in terms of European colonialism. The notes cover population characteristics, social behavior, social institutions, cultural influences, and social change as the major factors that determine the general social conditions of Caribbean societies.
The document discusses various finance formulae including:
- Simple interest formula where interest (I) equals the principal (P) multiplied by the interest rate (R) as a decimal multiplied by the number of time periods (T).
- Compound interest formula where the amount (A) after n time periods equals the principal multiplied by (1 plus the interest rate) to the power of n, with examples of compounding annually and monthly.
- Depreciation formula which is similar to the compound interest formula but uses 1 minus the depreciation rate instead of 1 plus the interest rate, with an example calculating depreciation over 9 years.
- A calculation showing the year an asset's value drops
The document discusses various topics related to corporate finance and ratio analysis. It covers time value of money concepts like compounding, discounting, and annuities. It also discusses bond valuation and the yield to maturity formula. Additionally, it outlines numerous ratios used in ratio analysis including liquidity, turnover, profitability, leverage, coverage, dividend, returns and valuation ratios. The DuPont chart and extended DuPont chart are also explained. Other topics covered include risk and return, beta, the capital asset pricing model formula, and the security market line.
Daily Agenda Unit 02 Business CommunicationsAngela Edel
This document outlines the daily agenda and activities for a business communications class over the course of a school week. The week focuses on different topics each day, including business letters, telephone and email etiquette, and public speaking. Students will complete readings, activities, and homework assignments related to each topic, including drafting a business letter and practicing a short speech. Quizzes and tests are also scheduled to assess comprehension of key concepts.
This document outlines the revised 2013 syllabus for CAPE Accounting. It introduces the examination and provides the rationale, aims, skills assessed, prerequisites, and structure of the two-unit syllabus. The syllabus is designed to provide certification in accounting and develop skills like critical thinking, decision-making, and communicating financial information. It consists of two independent units - Financial Accounting and Cost and Management Accounting. Financial Accounting focuses on recording transactions, preparing financial statements, and financial reporting and interpretation. Cost and Management Accounting examines costing principles, systems, and planning and decision making. The syllabus aims to foster understanding of accounting principles and practices.
GAAP and accounting standards form the theory base of accounting and describe rules for preparing financial statements. Accounting conventions emerge from commonly used accounting principles and practices, though they do not need universal application. Key accounting concepts include the entity, money measurement, periodicity, accrual, matching, going concern, cost, and realization concepts. Accounting principles should be based on assumptions, simple to understand, consistently followed, reflect future predictions, and be informative for users.
The document summarizes key concepts from chapters 6-14 of a finance textbook relating to risk and return, time value of money, bonds, stock valuation, cost of capital, capital budgeting, and cash flow estimation. It defines terms like expected rate of return, risk measures like standard deviation and beta, bond and stock valuation methods, weighted average cost of capital (WACC), net present value (NPV), internal rate of return (IRR), modified IRR, payback period, and cash flow items like net operating working capital, operating cash flow, and free cash flow. Formulas and calculator instructions are provided for computing many of these concepts.
This document provides notes on Caribbean society and culture. It discusses the location of the Caribbean region and defines it geographically, geologically, politically, and in terms of European colonialism. The notes cover population characteristics, social behavior, social institutions, cultural influences, and social change as the major factors that determine the general social conditions of Caribbean societies.
The document provides formulae for simple interest, compound interest, depreciation, and investing money by regular instalments. It includes examples of calculating simple interest, compound interest compounded annually and monthly, depreciation rates, and the total value of investments made annually over 21 years at 8.75% interest compounded annually. It finds the total value is $299,604.86 and the year the fund first exceeds $200,000.
1. Simple interest is interest paid on the principal amount only and not on accumulated interest. The simple interest formula is I=PRT, where I is interest, P is principal, R is interest rate, and T is time.
2. Compound interest is interest paid on the principal as well as on previously accumulated interest. The amount of compound interest is calculated using the formula A=P(1+R/n)^(n*t), where A is total amount, P is principal, R is annual interest rate, n is number of compounding periods per year, and t is time in years.
3. An annuity is a series of regular payments made at fixed time intervals. The
This document discusses economics and interest factors that are important for engineering decisions. It covers topics such as interest, present and future worth factors, bonds, taxes, and depreciation. Equations are provided for calculating interest on lump sums, uniform series of amounts, and non-uniform amounts. Examples show how to apply these concepts to problems involving loans, investments, and evaluating potential projects.
time value of money,Simple interest and compound interestJunaidHabib8
The document discusses several key concepts related to the time value of money including:
1) Money available now is worth more than the same amount in the future due to its earning potential through interest or other investments.
2) Simple and compound interest are explained as well as how to calculate future and present value using interest rates and time periods.
3) Various cash flow patterns are introduced including uniform series, gradient series, sinking funds, and capital recovery amounts.
4) The effective interest rate and rule of 72 for approximating doubling time are also covered.
The document defines and describes simple annuities. A simple annuity is an annuity where the payment interval is the same as the interest period. It provides examples of calculating the future value and present value of annuity payments using formulas. The key variables in the formulas are the periodic payment amount, interest rate per period, and number of periods. The future value is the sum of all payments accumulated with interest over the term, while the present value discounts each payment back to the start of the term.
This document defines and provides examples of simple annuities. It begins by defining an annuity as a sequence of equal payments made at regular intervals. It then classifies annuities as either simple or general, ordinary or annuity due, and annuity certain or contingent based on payment intervals, time of payment, and duration. The document provides formulas for calculating the future value, present value, and periodic payment of ordinary annuities. It includes examples demonstrating how to use the formulas to solve simple annuity problems involving interest compounded monthly, quarterly, annually, or semi-annually.
This document provides information about basic business mathematics concepts related to annuities. It defines different types of annuities such as simple annuities, general annuities, ordinary annuities, and annuity due. Formulas are presented for calculating the future value, present value, and periodic payment of a simple ordinary annuity. Examples are included to demonstrate calculating amounts for various annuity scenarios involving deposits, loans, and savings plans.
This document defines and provides examples of simple annuities. It begins by defining an annuity as a sequence of equal payments made at regular intervals. It then classifies annuities as either simple or general, depending on whether the payment interval matches the interest period. The document provides time diagrams and formulas for calculating the future and present value of ordinary annuities. It includes four examples that demonstrate calculating future values, present values, and periodic payments for simple annuities using the provided formulas.
This document defines terms related to simple and compound interest such as principal, interest rate, time period, and discusses how to calculate simple interest, compound interest, maturity value, and present value. It provides examples of calculating simple interest, compound interest annually and for periods of less than 1 year. It also discusses how to find equivalent interest rates, effective rates, and the number of compounding periods or time required to reach a given future value.
This document provides an overview of topics in mathematics of finance including compound interest, future and present value of annuities, and exponential and logistic functions. It includes examples of calculating interest compounded at different time periods, annual percentage yield, and using exponential functions to model growth. The document concludes with a sample chapter test covering these financial mathematics topics.
The document discusses various topics related to mathematics in finance including simple and compound interest, nominal and effective interest rates, present value, annuities, and sinking funds. It provides formulas to calculate interest, principal amounts, present value of annuities, and sinking fund amounts. Examples are given to demonstrate calculating interest compounded annually, semiannually, quarterly, and monthly. The key differences between annuities and sinking funds are that annuities involve making deposits over time into an account, while sinking funds involve periodic withdrawals from an account.
Aptitude Training - SIMPLE AND COMPOUND INTERESTAjay Chimmani
I have taken coaching from NARESH INSTITUTE for CRT (Campus Recruitment Training). In these videos, I have explained all the questions with answer and how to approach for the question etc, in the same manner how they have taught to me at the time of training. Hope u like it.
Aptitude training playlist link :
https://www.youtube.com/playlist?list=PL3v9ipJOEEPfumKHa02HWjCfPvGQiPZiG
For full playlist of Interview puzzles videos :
https://www.youtube.com/playlist?list=PL3v9ipJOEEPfI4zt4ExamGJwndkvg0SFc
24 standard interview puzzles:
https://www.youtube.com/playlist?list=PL3v9ipJOEEPefIF4nscYOobim1iRBJTjw
for C and C++ questions, that are asked in the interviews, go through the posts in the link : http://comsciguide.blogspot.com/
for more videos, my youtube channel :
https://www.youtube.com/channel/UCvMy2V7gYW7VR2WgyvLj3-A
- Cash flow diagrams (CFDs) illustrate the size, timing, and direction (positive or negative) of cash flows from engineering projects over time.
- A CFD is created by drawing a segmented time line and adding vertical arrows to represent cash inflows or outflows at each time period.
- Common categories of cash flows include first costs, operating/maintenance costs, salvage value, revenues, and overhauls.
The document discusses concepts related to the time value of money, including formulas for calculating future value and present value. Specifically, it provides formulas for calculating the future and present value of single amounts, annuities, perpetuities, and growing annuities. It also discusses concepts like effective interest rates, loan amortization schedules, and the relationship between nominal and effective rates for different compounding periods.
The document discusses the concepts of time value of money including future value, present value, and annuity calculations. It provides formulas for determining the future and present value of single amounts and annuities given interest rates. Examples are shown for calculating future values, present values, loan payments, and other time value of money problems. Key concepts covered include compound interest, effective interest rates, and using time value of money formulas to solve financial problems.
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest. It is the result of reinvesting interest, or adding it to the loaned capital rather than paying it out, or requiring payment from borrower, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. Compound interest is standard in finance and economics.
Compound interest is contrasted with simple interest, where previously accumulated interest is not added to the principal amount of the current period, so there is no compounding. The simple annual interest rate is the interest amount per period, multiplied by the number of periods per year. The simple annual interest rate is also known as the nominal interest rate (not to be confused with the interest rate not adjusted for inflation, which goes by the same name).Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest. It is the result of reinvesting interest, or adding it to the loaned capital rather than paying it out, or requiring payment from borrower, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. Compound interest is standard in finance and economics.
Compound interest is contrasted with simple interest, where previously accumulated interest is not added to the principal amount of the current period, so there is no compounding. The simple annual interest rate is the interest amount per period, multiplied by the number of periods per year. The simple annual interest rate is also known as the nominal interest rate (not to be confused with the interest rate not adjusted for inflation, which goes by the same name).Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest. It is the result of reinvesting interest, or adding it to the loaned capital rather than paying it out, or requiring payment from borrower, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. Compound interest is standard in finance and economics.
Compound interest is contrasted with simple interest, where previously accumulated interest is not added to the principal amount of the current period, so there is no compounding. The simple annual interest rate is the interest amount per period, multiplied by the number of periods per year. The simple annual interest rate is also known as the nominal interest rate (not to be confused with the interest rate not adjusted for inflation, which goes by the same name).
INVESTMENT CHOICE “COMPARISON AND SELECTION AMONG ALTERNATIVES”georgemalak922
This document provides information about nominal and effective interest rates:
1. It defines key terms like nominal interest rate, effective interest rate, compounding period, and payment period.
2. It explains how to calculate effective interest rates for different compounding periods like monthly, quarterly, or annually from a given nominal interest rate.
3. It provides examples of calculating future values and accumulated balances for single amounts and series cash flows using both nominal and effective interest rates when the payment period is greater than or less than the compounding period.
The document discusses compound interest, which is interest earned on both the principal amount invested as well as on any accumulated interest. It provides examples of how an investment of $1000 at 5% annual interest grows over 10 years with simple versus compound interest. Using the compound interest formula A=P(1+r/n)nt, it demonstrates how to calculate the accumulated amount for various compounding periods and interest rates. The key benefits of compound interest over long periods of time are highlighted.
The document discusses key concepts related to nominal and effective interest rates, including:
1) Definitions of interest period, compounding period, and compounding frequency.
2) Formulas for converting between nominal and effective interest rates for different time periods.
3) Procedures for performing interest calculations for single amounts, series cash flows, and situations where the payment period relates to the compounding period.
4) How to handle cases of continuous compounding and varying interest rates over time.
This document discusses nominal and effective interest rates. It begins by defining key terms like nominal rate, effective rate, compounding period, and payment period. It then explains how to convert between nominal and effective rates for different compounding frequencies. The document provides examples of calculating future values for single payments and series of payments when the payment period is greater than or less than the compounding period. It also covers calculations for continuous compounding and situations when interest rates vary over time.
Slideshare is discontinuing its Slidecast feature as of February 28, 2014. Existing Slidecasts will be converted to static presentations without audio by April 30, 2014. The document informs users that new slidecasts can be found on myPlick.com or the author's blog starting in 2014. However, myPlick proved unreliable, so future slidecasts will instead be hosted on the author's YouTube channel.
The document provides formulae for simple interest, compound interest, depreciation, and investing money by regular instalments. It includes examples of calculating simple interest, compound interest compounded annually and monthly, depreciation rates, and the total value of investments made annually over 21 years at 8.75% interest compounded annually. It finds the total value is $299,604.86 and the year the fund first exceeds $200,000.
1. Simple interest is interest paid on the principal amount only and not on accumulated interest. The simple interest formula is I=PRT, where I is interest, P is principal, R is interest rate, and T is time.
2. Compound interest is interest paid on the principal as well as on previously accumulated interest. The amount of compound interest is calculated using the formula A=P(1+R/n)^(n*t), where A is total amount, P is principal, R is annual interest rate, n is number of compounding periods per year, and t is time in years.
3. An annuity is a series of regular payments made at fixed time intervals. The
This document discusses economics and interest factors that are important for engineering decisions. It covers topics such as interest, present and future worth factors, bonds, taxes, and depreciation. Equations are provided for calculating interest on lump sums, uniform series of amounts, and non-uniform amounts. Examples show how to apply these concepts to problems involving loans, investments, and evaluating potential projects.
time value of money,Simple interest and compound interestJunaidHabib8
The document discusses several key concepts related to the time value of money including:
1) Money available now is worth more than the same amount in the future due to its earning potential through interest or other investments.
2) Simple and compound interest are explained as well as how to calculate future and present value using interest rates and time periods.
3) Various cash flow patterns are introduced including uniform series, gradient series, sinking funds, and capital recovery amounts.
4) The effective interest rate and rule of 72 for approximating doubling time are also covered.
The document defines and describes simple annuities. A simple annuity is an annuity where the payment interval is the same as the interest period. It provides examples of calculating the future value and present value of annuity payments using formulas. The key variables in the formulas are the periodic payment amount, interest rate per period, and number of periods. The future value is the sum of all payments accumulated with interest over the term, while the present value discounts each payment back to the start of the term.
This document defines and provides examples of simple annuities. It begins by defining an annuity as a sequence of equal payments made at regular intervals. It then classifies annuities as either simple or general, ordinary or annuity due, and annuity certain or contingent based on payment intervals, time of payment, and duration. The document provides formulas for calculating the future value, present value, and periodic payment of ordinary annuities. It includes examples demonstrating how to use the formulas to solve simple annuity problems involving interest compounded monthly, quarterly, annually, or semi-annually.
This document provides information about basic business mathematics concepts related to annuities. It defines different types of annuities such as simple annuities, general annuities, ordinary annuities, and annuity due. Formulas are presented for calculating the future value, present value, and periodic payment of a simple ordinary annuity. Examples are included to demonstrate calculating amounts for various annuity scenarios involving deposits, loans, and savings plans.
This document defines and provides examples of simple annuities. It begins by defining an annuity as a sequence of equal payments made at regular intervals. It then classifies annuities as either simple or general, depending on whether the payment interval matches the interest period. The document provides time diagrams and formulas for calculating the future and present value of ordinary annuities. It includes four examples that demonstrate calculating future values, present values, and periodic payments for simple annuities using the provided formulas.
This document defines terms related to simple and compound interest such as principal, interest rate, time period, and discusses how to calculate simple interest, compound interest, maturity value, and present value. It provides examples of calculating simple interest, compound interest annually and for periods of less than 1 year. It also discusses how to find equivalent interest rates, effective rates, and the number of compounding periods or time required to reach a given future value.
This document provides an overview of topics in mathematics of finance including compound interest, future and present value of annuities, and exponential and logistic functions. It includes examples of calculating interest compounded at different time periods, annual percentage yield, and using exponential functions to model growth. The document concludes with a sample chapter test covering these financial mathematics topics.
The document discusses various topics related to mathematics in finance including simple and compound interest, nominal and effective interest rates, present value, annuities, and sinking funds. It provides formulas to calculate interest, principal amounts, present value of annuities, and sinking fund amounts. Examples are given to demonstrate calculating interest compounded annually, semiannually, quarterly, and monthly. The key differences between annuities and sinking funds are that annuities involve making deposits over time into an account, while sinking funds involve periodic withdrawals from an account.
Aptitude Training - SIMPLE AND COMPOUND INTERESTAjay Chimmani
I have taken coaching from NARESH INSTITUTE for CRT (Campus Recruitment Training). In these videos, I have explained all the questions with answer and how to approach for the question etc, in the same manner how they have taught to me at the time of training. Hope u like it.
Aptitude training playlist link :
https://www.youtube.com/playlist?list=PL3v9ipJOEEPfumKHa02HWjCfPvGQiPZiG
For full playlist of Interview puzzles videos :
https://www.youtube.com/playlist?list=PL3v9ipJOEEPfI4zt4ExamGJwndkvg0SFc
24 standard interview puzzles:
https://www.youtube.com/playlist?list=PL3v9ipJOEEPefIF4nscYOobim1iRBJTjw
for C and C++ questions, that are asked in the interviews, go through the posts in the link : http://comsciguide.blogspot.com/
for more videos, my youtube channel :
https://www.youtube.com/channel/UCvMy2V7gYW7VR2WgyvLj3-A
- Cash flow diagrams (CFDs) illustrate the size, timing, and direction (positive or negative) of cash flows from engineering projects over time.
- A CFD is created by drawing a segmented time line and adding vertical arrows to represent cash inflows or outflows at each time period.
- Common categories of cash flows include first costs, operating/maintenance costs, salvage value, revenues, and overhauls.
The document discusses concepts related to the time value of money, including formulas for calculating future value and present value. Specifically, it provides formulas for calculating the future and present value of single amounts, annuities, perpetuities, and growing annuities. It also discusses concepts like effective interest rates, loan amortization schedules, and the relationship between nominal and effective rates for different compounding periods.
The document discusses the concepts of time value of money including future value, present value, and annuity calculations. It provides formulas for determining the future and present value of single amounts and annuities given interest rates. Examples are shown for calculating future values, present values, loan payments, and other time value of money problems. Key concepts covered include compound interest, effective interest rates, and using time value of money formulas to solve financial problems.
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest. It is the result of reinvesting interest, or adding it to the loaned capital rather than paying it out, or requiring payment from borrower, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. Compound interest is standard in finance and economics.
Compound interest is contrasted with simple interest, where previously accumulated interest is not added to the principal amount of the current period, so there is no compounding. The simple annual interest rate is the interest amount per period, multiplied by the number of periods per year. The simple annual interest rate is also known as the nominal interest rate (not to be confused with the interest rate not adjusted for inflation, which goes by the same name).Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest. It is the result of reinvesting interest, or adding it to the loaned capital rather than paying it out, or requiring payment from borrower, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. Compound interest is standard in finance and economics.
Compound interest is contrasted with simple interest, where previously accumulated interest is not added to the principal amount of the current period, so there is no compounding. The simple annual interest rate is the interest amount per period, multiplied by the number of periods per year. The simple annual interest rate is also known as the nominal interest rate (not to be confused with the interest rate not adjusted for inflation, which goes by the same name).Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest. It is the result of reinvesting interest, or adding it to the loaned capital rather than paying it out, or requiring payment from borrower, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. Compound interest is standard in finance and economics.
Compound interest is contrasted with simple interest, where previously accumulated interest is not added to the principal amount of the current period, so there is no compounding. The simple annual interest rate is the interest amount per period, multiplied by the number of periods per year. The simple annual interest rate is also known as the nominal interest rate (not to be confused with the interest rate not adjusted for inflation, which goes by the same name).
INVESTMENT CHOICE “COMPARISON AND SELECTION AMONG ALTERNATIVES”georgemalak922
This document provides information about nominal and effective interest rates:
1. It defines key terms like nominal interest rate, effective interest rate, compounding period, and payment period.
2. It explains how to calculate effective interest rates for different compounding periods like monthly, quarterly, or annually from a given nominal interest rate.
3. It provides examples of calculating future values and accumulated balances for single amounts and series cash flows using both nominal and effective interest rates when the payment period is greater than or less than the compounding period.
The document discusses compound interest, which is interest earned on both the principal amount invested as well as on any accumulated interest. It provides examples of how an investment of $1000 at 5% annual interest grows over 10 years with simple versus compound interest. Using the compound interest formula A=P(1+r/n)nt, it demonstrates how to calculate the accumulated amount for various compounding periods and interest rates. The key benefits of compound interest over long periods of time are highlighted.
The document discusses key concepts related to nominal and effective interest rates, including:
1) Definitions of interest period, compounding period, and compounding frequency.
2) Formulas for converting between nominal and effective interest rates for different time periods.
3) Procedures for performing interest calculations for single amounts, series cash flows, and situations where the payment period relates to the compounding period.
4) How to handle cases of continuous compounding and varying interest rates over time.
This document discusses nominal and effective interest rates. It begins by defining key terms like nominal rate, effective rate, compounding period, and payment period. It then explains how to convert between nominal and effective rates for different compounding frequencies. The document provides examples of calculating future values for single payments and series of payments when the payment period is greater than or less than the compounding period. It also covers calculations for continuous compounding and situations when interest rates vary over time.
Similar to 12X1 T04 02 Finance Formulas (2010) (20)
Slideshare is discontinuing its Slidecast feature as of February 28, 2014. Existing Slidecasts will be converted to static presentations without audio by April 30, 2014. The document informs users that new slidecasts can be found on myPlick.com or the author's blog starting in 2014. However, myPlick proved unreliable, so future slidecasts will instead be hosted on the author's YouTube channel.
The document discusses different methods for factorising expressions:
1) Looking for a common factor and dividing it out of all terms
2) Using the difference of two squares formula (a2 - b2 = (a - b)(a + b))
3) Factorising quadratic trinomials into two binomial factors by identifying the values that multiply to give the constant term and sum to give the coefficient of the linear term.
The document provides information on index laws and the meaning of indices in algebra:
- Index laws state that am × an = am+n, am ÷ an = am-n, and (am)n = amn. Exponents can be added or subtracted when multiplying or dividing terms with the same base.
- Positive exponents indicate a term is raised to a power. Negative exponents indicate a root is being taken. Terms with exponents are evaluated from left to right.
- Examples demonstrate how to simplify expressions using index laws and interpret different types of indices.
12 x1 t01 03 integrating derivative on function (2013)Nigel Simmons
The document discusses integrating derivatives of functions. It states that the integral of the derivative of a function f(x) is equal to the natural log of f(x) plus a constant. It then provides examples of integrating several derivatives: (i) ∫(1/(7-3x)) dx = -1/3 log(7-3x) + c, (ii) ∫(1/(8x+5)) dx = 1/8 log(8x+5) + c, and (iii) ∫(x5/(x-2)) dx = 1/6 log(x6-2) + c. It also discusses techniques for integrating fractions by polynomial long division and finds
The document discusses logarithms and their properties. Logarithms are defined as the inverse of exponentials. If y = ax, then x = loga y. The natural logarithm is log base e, written as ln. Properties of logarithms include: loga m + loga n = loga mn; loga m - loga n = loga(m/n); loga mn = n loga m; loga 1 = 0; loga a = 1. Examples of evaluating logarithmic expressions are provided.
The document discusses relationships between the coefficients and roots of polynomials. It states that for a polynomial P(x) = axn + bxn-1 + cxn-2 + ..., the sum of the roots equals -b/a, the sum of the roots taken two at a time equals c/a, and so on for higher order terms. It also provides examples of using these relationships to find the sums of roots for a given polynomial.
P
4
3
2
The document discusses properties of polynomials with multiple roots. It first proves that if a polynomial P(x) has a root x = a of multiplicity m, then the derivative of P(x), P'(x), will have a root x = a of multiplicity m-1. It then provides an example of solving a cubic equation given it has a double root. Finally, it examines a quartic polynomial and shows that its root α cannot be 0, 1, or -1, and that 1/
The document discusses factorizing complex expressions. The main points are:
- If a polynomial's coefficients are real, its roots will appear in complex conjugate pairs.
- Any polynomial of degree n can be factorized into a mixture of quadratic and linear factors over real numbers, or into n linear factors over complex numbers.
- Odd degree polynomials must have at least one real root.
- Examples of factorizing polynomials over both real and complex numbers are provided.
The document describes the Trapezoidal Rule for approximating the area under a curve between two points. It shows that the area A is estimated by dividing the region into trapezoids with height equal to the function values at the interval endpoints and bases equal to the intervals. In general, the area is approximated as the sum of the areas of each trapezoid, which is equal to the average of the endpoint function values multiplied by the interval length.
The document discusses methods for calculating the volumes of solids of revolution. It provides formulas for finding volumes when an area is revolved around either the x-axis or y-axis. Examples are given for finding volumes of common solids like cones, spheres, and others. Steps are shown for using the formulas to calculate volumes based on given functions and limits of revolution.
The document discusses different methods for calculating the area under a curve or between curves.
(1) The area below the x-axis is given by the integral of the function between the bounds, which can be positive or negative depending on whether the area is above or below the x-axis.
(2) To calculate the area on the y-axis, the function is solved for x in terms of y, then the bounds are substituted into the integral of this new function with respect to y.
(3) The area between two curves is calculated by taking the integral of the upper curve minus the integral of the lower curve, both between the same bounds on the x-axis.
The document discusses 8 properties of definite integrals:
1) Integrating polynomials results in a fraction.
2) Constants can be factored out of integrals.
3) Integrals of sums are equal to the sum of integrals.
4) Splitting an integral range results in the sum of the integrals.
5) Integrals of positive functions over a range are positive, and negative if the function is negative.
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7) Changing the limits of integration flips the sign of the integral.
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A Free 200-Page eBook ~ Brain and Mind Exercise.pptxOH TEIK BIN
(A Free eBook comprising 3 Sets of Presentation of a selection of Puzzles, Brain Teasers and Thinking Problems to exercise both the mind and the Right and Left Brain. To help keep the mind and brain fit and healthy. Good for both the young and old alike.
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(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
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𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
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This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
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2. Finance Formulae
Simple Interest
I PRT
I simple interest R interest rate as a decimal (or fraction)
P principal T time periods
3. Finance Formulae
Simple Interest
I PRT
I simple interest R interest rate as a decimal (or fraction)
P principal T time periods
e.g. If $3000 is invested for seven years at 6% p.a. simple interest, how
much will it be worth after seven years?
4. Finance Formulae
Simple Interest
I PRT
I simple interest R interest rate as a decimal (or fraction)
P principal T time periods
e.g. If $3000 is invested for seven years at 6% p.a. simple interest, how
much will it be worth after seven years?
I PRT
5. Finance Formulae
Simple Interest
I PRT
I simple interest R interest rate as a decimal (or fraction)
P principal T time periods
e.g. If $3000 is invested for seven years at 6% p.a. simple interest, how
much will it be worth after seven years?
I PRT
I 3000 0.06 7
1260
6. Finance Formulae
Simple Interest
I PRT
I simple interest R interest rate as a decimal (or fraction)
P principal T time periods
e.g. If $3000 is invested for seven years at 6% p.a. simple interest, how
much will it be worth after seven years?
I PRT
I 3000 0.06 7
1260
Investment is worth $4260 after 7 years
7. Compound Interest
An PR n
An amount after n time periods P principal
R 1 interest rate as a decimal(or fraction)
n time periods
8. Compound Interest
An PR n
An amount after n time periods P principal
R 1 interest rate as a decimal(or fraction)
n time periods
Note: interest rate and time periods must match the compounding time
9. Compound Interest
Note: general term of a
An PR n
geometric series
An amount after n time periods P principal
R 1 interest rate as a decimal(or fraction)
n time periods
Note: interest rate and time periods must match the compounding time
10. Compound Interest
Note: general term of a
An PR n
geometric series
An amount after n time periods P principal
R 1 interest rate as a decimal(or fraction)
n time periods
Note: interest rate and time periods must match the compounding time
e.g. If $3000 is invested for seven years at 6% p.a, how much will it be
worth after seven years if;
a) compounded annually?
11. Compound Interest
Note: general term of a
An PR n
geometric series
An amount after n time periods P principal
R 1 interest rate as a decimal(or fraction)
n time periods
Note: interest rate and time periods must match the compounding time
e.g. If $3000 is invested for seven years at 6% p.a, how much will it be
worth after seven years if;
a) compounded annually?
An PR n
12. Compound Interest
Note: general term of a
An PR n
geometric series
An amount after n time periods P principal
R 1 interest rate as a decimal(or fraction)
n time periods
Note: interest rate and time periods must match the compounding time
e.g. If $3000 is invested for seven years at 6% p.a, how much will it be
worth after seven years if;
a) compounded annually?
An PR n
A7 3000 1.06
7
A7 4510.89
13. Compound Interest
Note: general term of a
An PR n
geometric series
An amount after n time periods P principal
R 1 interest rate as a decimal(or fraction)
n time periods
Note: interest rate and time periods must match the compounding time
e.g. If $3000 is invested for seven years at 6% p.a, how much will it be
worth after seven years if;
a) compounded annually?
An PR n
A7 3000 1.06
7
A7 4510.89
Investment is worth
$4510.89 after 7 years
14. Compound Interest
Note: general term of a
An PR n
geometric series
An amount after n time periods P principal
R 1 interest rate as a decimal(or fraction)
n time periods
Note: interest rate and time periods must match the compounding time
e.g. If $3000 is invested for seven years at 6% p.a, how much will it be
worth after seven years if;
a) compounded annually? b) compounded monthly?
An PR n
A7 3000 1.06
7
A7 4510.89
Investment is worth
$4510.89 after 7 years
15. Compound Interest
Note: general term of a
An PR n
geometric series
An amount after n time periods P principal
R 1 interest rate as a decimal(or fraction)
n time periods
Note: interest rate and time periods must match the compounding time
e.g. If $3000 is invested for seven years at 6% p.a, how much will it be
worth after seven years if;
a) compounded annually? b) compounded monthly?
An PR n An PR n
A7 3000 1.06
7
A7 4510.89
Investment is worth
$4510.89 after 7 years
16. Compound Interest
Note: general term of a
An PR n
geometric series
An amount after n time periods P principal
R 1 interest rate as a decimal(or fraction)
n time periods
Note: interest rate and time periods must match the compounding time
e.g. If $3000 is invested for seven years at 6% p.a, how much will it be
worth after seven years if;
a) compounded annually? b) compounded monthly?
An PR n An PR n
A7 3000 1.06 A84 3000 1.005
7 84
A7 4510.89 A84 4561.11
Investment is worth
$4510.89 after 7 years
17. Compound Interest
Note: general term of a
An PR n
geometric series
An amount after n time periods P principal
R 1 interest rate as a decimal(or fraction)
n time periods
Note: interest rate and time periods must match the compounding time
e.g. If $3000 is invested for seven years at 6% p.a, how much will it be
worth after seven years if;
a) compounded annually? b) compounded monthly?
An PR n An PR n
A7 3000 1.06 A84 3000 1.005
7 84
A7 4510.89 A84 4561.11
Investment is worth Investment is worth
$4510.89 after 7 years $4561.11 after 7 years
18. Depreciation
An PR n
An amount after n time periods P principal
R 1 depreciation rate as a decimal(or fraction)
n time periods
19. Depreciation
An PR n
An amount after n time periods P principal
R 1 depreciation rate as a decimal(or fraction)
n time periods
Note: depreciation rate and time periods must match the depreciation time
20. Depreciation
An PR n
An amount after n time periods P principal
R 1 depreciation rate as a decimal(or fraction)
n time periods
Note: depreciation rate and time periods must match the depreciation time
e.g. An espresso machine bought for $15000 on 1st January 2001
depreciates at a rate of 12.5%p.a.
a) What will its value be on 1st January 2010?
21. Depreciation
An PR n
An amount after n time periods P principal
R 1 depreciation rate as a decimal(or fraction)
n time periods
Note: depreciation rate and time periods must match the depreciation time
e.g. An espresso machine bought for $15000 on 1st January 2001
depreciates at a rate of 12.5%p.a.
a) What will its value be on 1st January 2010?
An PR n
22. Depreciation
An PR n
An amount after n time periods P principal
R 1 depreciation rate as a decimal(or fraction)
n time periods
Note: depreciation rate and time periods must match the depreciation time
e.g. An espresso machine bought for $15000 on 1st January 2001
depreciates at a rate of 12.5%p.a.
a) What will its value be on 1st January 2010?
An PR n
A9 15000 0.875
9
A9 4509.87
23. Depreciation
An PR n
An amount after n time periods P principal
R 1 depreciation rate as a decimal(or fraction)
n time periods
Note: depreciation rate and time periods must match the depreciation time
e.g. An espresso machine bought for $15000 on 1st January 2001
depreciates at a rate of 12.5%p.a.
a) What will its value be on 1st January 2010?
An PR n
A9 15000 0.875
9
A9 4509.87
Machine is worth $4509.87 after 9 years
24. b) During which year will the value drop below 10% of the original
cost?
25. b) During which year will the value drop below 10% of the original
cost?
An PR n
26. b) During which year will the value drop below 10% of the original
cost?
An PR n
15000 0.875 1500
n
27. b) During which year will the value drop below 10% of the original
cost?
An PR n
15000 0.875 1500
n
0.875 0.1
n
log 0.875 log 0.1
n
n log 0.875 log 0.1
log 0.1
n
log 0.875
n 17.24377353
28. b) During which year will the value drop below 10% of the original
cost?
An PR n
15000 0.875 1500
n
0.875 0.1
n
log 0.875 log 0.1
n
n log 0.875 log 0.1
log 0.1
n
log 0.875
n 17.24377353
during the 18th year (i.e. 2018) its value will drop to
10% the original cost
30. Investing Money by Regular
2002 HSC Question 9b)
Instalments
A superannuation fund pays an interest rate of 8.75% p.a. which (4)
compounds annually. Stephanie decides to invest $5000 in the fund at
the beginning of each year, commencing on 1 January 2003.
What will be the value of Stephanie’s superannuation when she retires on
31 December 2023?
31. Investing Money by Regular
2002 HSC Question 9b)
Instalments
A superannuation fund pays an interest rate of 8.75% p.a. which (4)
compounds annually. Stephanie decides to invest $5000 in the fund at
the beginning of each year, commencing on 1 January 2003.
What will be the value of Stephanie’s superannuation when she retires on
31 December 2023?
A21 5000 1.0875
21
amount invested for 21 years
32. Investing Money by Regular
2002 HSC Question 9b)
Instalments
A superannuation fund pays an interest rate of 8.75% p.a. which (4)
compounds annually. Stephanie decides to invest $5000 in the fund at
the beginning of each year, commencing on 1 January 2003.
What will be the value of Stephanie’s superannuation when she retires on
31 December 2023?
A21 5000 1.0875
21
amount invested for 21 years
A20 5000 1.0875
20
amount invested for 20 years
33. Investing Money by Regular
2002 HSC Question 9b)
Instalments
A superannuation fund pays an interest rate of 8.75% p.a. which (4)
compounds annually. Stephanie decides to invest $5000 in the fund at
the beginning of each year, commencing on 1 January 2003.
What will be the value of Stephanie’s superannuation when she retires on
31 December 2023?
A21 5000 1.0875
21
amount invested for 21 years
A20 5000 1.0875
20
amount invested for 20 years
A19 5000 1.0875
19
amount invested for 19 years
34. Investing Money by Regular
2002 HSC Question 9b)
Instalments
A superannuation fund pays an interest rate of 8.75% p.a. which (4)
compounds annually. Stephanie decides to invest $5000 in the fund at
the beginning of each year, commencing on 1 January 2003.
What will be the value of Stephanie’s superannuation when she retires on
31 December 2023?
A21 5000 1.0875
21
amount invested for 21 years
A20 5000 1.0875
20
amount invested for 20 years
A19 5000 1.0875
19
amount invested for 19 years
A1 5000 1.0875
1
amount invested for 1 year
50. 5000 1.0875 1.0875n 1
200000
0.0875
1.0875n 1 280
87
367
1.0875
n
87
367
log 1.0875 log
n
87
367
n log 1.0875 log
87
367
log
n 87
log 1.0875
n 17.16056585
n 18
Thus 2021 is the first year when the fund exceeds $200000
51. d*) What annual instalment would have produced $1000000 by 31st
December 2020?
52. d*) What annual instalment would have produced $1000000 by 31st
December 2020?
Amount P 1.0875 P 1.0875 P 1.0875
18 17
53. d*) What annual instalment would have produced $1000000 by 31st
December 2020?
Amount P 1.0875 P 1.0875 P 1.0875
18 17
a P 1.0875 , r 1.0875, n 18
54. d*) What annual instalment would have produced $1000000 by 31st
December 2020?
Amount P 1.0875 P 1.0875 P 1.0875
18 17
a P 1.0875 , r 1.0875, n 18
i.e. S18 1000000
55. d*) What annual instalment would have produced $1000000 by 31st
December 2020?
Amount P 1.0875 P 1.0875 P 1.0875
18 17
a P 1.0875 , r 1.0875, n 18
i.e. S18 1000000
P 1.0875 1.087518 1
1000000
0.0875
56. d*) What annual instalment would have produced $1000000 by 31st
December 2020?
Amount P 1.0875 P 1.0875 P 1.0875
18 17
a P 1.0875 , r 1.0875, n 18
i.e. S18 1000000
P 1.0875 1.087518 1
1000000
0.0875
P
1000000 0.0875
1.0875 1.087518 1
57. d*) What annual instalment would have produced $1000000 by 31st
December 2020?
Amount P 1.0875 P 1.0875 P 1.0875
18 17
a P 1.0875 , r 1.0875, n 18
i.e. S18 1000000
P 1.0875 1.087518 1
1000000
0.0875
P
1000000 0.0875
1.0875 1.087518 1
22818.16829
58. d*) What annual instalment would have produced $1000000 by 31st
December 2020?
Amount P 1.0875 P 1.0875 P 1.0875
18 17
a P 1.0875 , r 1.0875, n 18
i.e. S18 1000000
P 1.0875 1.087518 1
1000000
0.0875
P
1000000 0.0875
1.0875 1.087518 1
22818.16829
An annual instalment of $22818.17 will produce $1000000
61. Loan Repayments
The amount still owing after n time periods is;
An principal plus interest instalments plus interest
62. Loan Repayments
The amount still owing after n time periods is;
An principal plus interest instalments plus interest
e.g. (i) Richard and Kathy borrow $20000 from the bank to go on an
overseas holiday. Interest is charged at 12% p.a., compounded
monthly. They start repaying the loan one month after taking it
out, and their monthly instalments are $300.
63. Loan Repayments
The amount still owing after n time periods is;
An principal plus interest instalments plus interest
e.g. (i) Richard and Kathy borrow $20000 from the bank to go on an
overseas holiday. Interest is charged at 12% p.a., compounded
monthly. They start repaying the loan one month after taking it
out, and their monthly instalments are $300.
a) How much will they still owe the bank at the end of six years?
64. Loan Repayments
The amount still owing after n time periods is;
An principal plus interest instalments plus interest
e.g. (i) Richard and Kathy borrow $20000 from the bank to go on an
overseas holiday. Interest is charged at 12% p.a., compounded
monthly. They start repaying the loan one month after taking it
out, and their monthly instalments are $300.
a) How much will they still owe the bank at the end of six years?
Initial loan is borrowed for 72 months 20000 1.0172
65. Loan Repayments
The amount still owing after n time periods is;
An principal plus interest instalments plus interest
e.g. (i) Richard and Kathy borrow $20000 from the bank to go on an
overseas holiday. Interest is charged at 12% p.a., compounded
monthly. They start repaying the loan one month after taking it
out, and their monthly instalments are $300.
a) How much will they still owe the bank at the end of six years?
Initial loan is borrowed for 72 months 20000 1.0172
Repayments
are an
investment
in your loan
66. Loan Repayments
The amount still owing after n time periods is;
An principal plus interest instalments plus interest
e.g. (i) Richard and Kathy borrow $20000 from the bank to go on an
overseas holiday. Interest is charged at 12% p.a., compounded
monthly. They start repaying the loan one month after taking it
out, and their monthly instalments are $300.
a) How much will they still owe the bank at the end of six years?
Initial loan is borrowed for 72 months 20000 1.0172
Repayments
300 1.01
st repayment invested for 71 months 71
1
are an
investment
in your loan
67. Loan Repayments
The amount still owing after n time periods is;
An principal plus interest instalments plus interest
e.g. (i) Richard and Kathy borrow $20000 from the bank to go on an
overseas holiday. Interest is charged at 12% p.a., compounded
monthly. They start repaying the loan one month after taking it
out, and their monthly instalments are $300.
a) How much will they still owe the bank at the end of six years?
Initial loan is borrowed for 72 months 20000 1.0172
Repayments
300 1.01
st repayment invested for 71 months 71
1
are an
2nd repayment invested for 70 months 300 1.0170 investment
in your loan
68. Loan Repayments
The amount still owing after n time periods is;
An principal plus interest instalments plus interest
e.g. (i) Richard and Kathy borrow $20000 from the bank to go on an
overseas holiday. Interest is charged at 12% p.a., compounded
monthly. They start repaying the loan one month after taking it
out, and their monthly instalments are $300.
a) How much will they still owe the bank at the end of six years?
Initial loan is borrowed for 72 months 20000 1.0172
Repayments
300 1.01
st repayment invested for 71 months 71
1
are an
2nd repayment invested for 70 months 300 1.0170 investment
in your loan
2nd last repayment invested for 1 month 300 1.011
69. Loan Repayments
The amount still owing after n time periods is;
An principal plus interest instalments plus interest
e.g. (i) Richard and Kathy borrow $20000 from the bank to go on an
overseas holiday. Interest is charged at 12% p.a., compounded
monthly. They start repaying the loan one month after taking it
out, and their monthly instalments are $300.
a) How much will they still owe the bank at the end of six years?
Initial loan is borrowed for 72 months 20000 1.0172
Repayments
300 1.01
st repayment invested for 71 months 71
1
are an
2nd repayment invested for 70 months 300 1.0170 investment
in your loan
2nd last repayment invested for 1 month 300 1.011
last repayment invested for 0 months 300
70. An principal plus interest instalments plus interest
71. An principal plus interest instalments plus interest
72
A72 20000 1.01 300 300 1.01 300 1.01 300 1.01
70 71
72. An principal plus interest instalments plus interest
72
A72 20000 1.01 300 300 1.01 300 1.01 300 1.01
70 71
a 300, r 1.01, n 72
73. An principal plus interest instalments plus interest
72
A72 20000 1.01 300 300 1.01 300 1.01 300 1.01
70 71
a 300, r 1.01, n 72
a r n 1
20000 1.01
72
r 1
74. An principal plus interest instalments plus interest
72
A72 20000 1.01 300 300 1.01 300 1.01 300 1.01
70 71
a 300, r 1.01, n 72
a r n 1
20000 1.01
72
r 1
300 1.0172 1
20000 1.01
72
0.01
$9529.01
75. An principal plus interest instalments plus interest
72
A72 20000 1.01 300 300 1.01 300 1.01 300 1.01
70 71
a 300, r 1.01, n 72
a r n 1
20000 1.01
72
r 1
300 1.0172 1
20000 1.01
72
0.01
$9529.01
b) How much interest will they have paid in six years?
76. An principal plus interest instalments plus interest
72
A72 20000 1.01 300 300 1.01 300 1.01 300 1.01
70 71
a 300, r 1.01, n 72
a r n 1
20000 1.01
72
r 1
300 1.0172 1
20000 1.01
72
0.01
$9529.01
b) How much interest will they have paid in six years?
Total repayments = 300 72
$21600
77. An principal plus interest instalments plus interest
72
A72 20000 1.01 300 300 1.01 300 1.01 300 1.01
70 71
a 300, r 1.01, n 72
a r n 1
20000 1.01
72
r 1
300 1.0172 1
20000 1.01
72
0.01
$9529.01
b) How much interest will they have paid in six years?
Total repayments = 300 72
$21600
Loan reduction = 20000 9529.01
$10470.99
78. An principal plus interest instalments plus interest
72
A72 20000 1.01 300 300 1.01 300 1.01 300 1.01
70 71
a 300, r 1.01, n 72
a r n 1
20000 1.01
72
r 1
300 1.0172 1
20000 1.01
72
0.01
$9529.01
b) How much interest will they have paid in six years?
Total repayments = 300 72
$21600
Loan reduction = 20000 9529.01 Interest = 21600 10470.99
$10470.99 $11129.01
80. (ii) Finding the amount of each instalment
Yog borrows $30000 to buy a car. He will repay the loan in five
years, paying 60 equal monthly instalments, beginning one month
after he takes out the loan. Interest is charged at 9% p.a. compounded
monthly.
Find how much the monthly instalment shold be.
81. (ii) Finding the amount of each instalment
Yog borrows $30000 to buy a car. He will repay the loan in five
years, paying 60 equal monthly instalments, beginning one month
after he takes out the loan. Interest is charged at 9% p.a. compounded
monthly.
Find how much the monthly instalment shold be.
Let the monthly instalment be $M
82. (ii) Finding the amount of each instalment
Yog borrows $30000 to buy a car. He will repay the loan in five
years, paying 60 equal monthly instalments, beginning one month
after he takes out the loan. Interest is charged at 9% p.a. compounded
monthly.
Find how much the monthly instalment shold be.
Let the monthly instalment be $M
Initial loan is borrowed for 60 months 30000 1.0075 60
83. (ii) Finding the amount of each instalment
Yog borrows $30000 to buy a car. He will repay the loan in five
years, paying 60 equal monthly instalments, beginning one month
after he takes out the loan. Interest is charged at 9% p.a. compounded
monthly.
Find how much the monthly instalment shold be.
Let the monthly instalment be $M
Initial loan is borrowed for 60 months 30000 1.0075 60
1st repayment invested for 59 months M 1.0075 59
84. (ii) Finding the amount of each instalment
Yog borrows $30000 to buy a car. He will repay the loan in five
years, paying 60 equal monthly instalments, beginning one month
after he takes out the loan. Interest is charged at 9% p.a. compounded
monthly.
Find how much the monthly instalment shold be.
Let the monthly instalment be $M
Initial loan is borrowed for 60 months 30000 1.0075 60
1st repayment invested for 59 months M 1.0075 59
2nd repayment invested for 58 months M 1.0075 58
85. (ii) Finding the amount of each instalment
Yog borrows $30000 to buy a car. He will repay the loan in five
years, paying 60 equal monthly instalments, beginning one month
after he takes out the loan. Interest is charged at 9% p.a. compounded
monthly.
Find how much the monthly instalment shold be.
Let the monthly instalment be $M
Initial loan is borrowed for 60 months 30000 1.0075 60
1st repayment invested for 59 months M 1.0075 59
2nd repayment invested for 58 months M 1.0075 58
2nd last repayment invested for 1 month M 1.0075 1
86. (ii) Finding the amount of each instalment
Yog borrows $30000 to buy a car. He will repay the loan in five
years, paying 60 equal monthly instalments, beginning one month
after he takes out the loan. Interest is charged at 9% p.a. compounded
monthly.
Find how much the monthly instalment shold be.
Let the monthly instalment be $M
Initial loan is borrowed for 60 months 30000 1.0075 60
1st repayment invested for 59 months M 1.0075 59
2nd repayment invested for 58 months M 1.0075 58
2nd last repayment invested for 1 month M 1.0075 1
last repayment invested for 0 months M
87. An principal plus interest instalments plus interest
88. An principal plus interest instalments plus interest
60
A60 30000 1.0075 M M 1.0075 M 1.0075 M 1.0075
58 59
89. An principal plus interest instalments plus interest
60
A60 30000 1.0075 M M 1.0075 M 1.0075 M 1.0075
58 59
a M , r 1.0075, n 60
90. An principal plus interest instalments plus interest
60
A60 30000 1.0075 M M 1.0075 M 1.0075 M 1.0075
58 59
a M , r 1.0075, n 60
a r n 1
30000 1.0075
60
r 1
91. An principal plus interest instalments plus interest
60
A60 30000 1.0075 M M 1.0075 M 1.0075 M 1.0075
58 59
a M , r 1.0075, n 60
a r n 1
30000 1.0075
60
r 1
M 1.007560 1
30000 1.0075
60
0.0075
92. An principal plus interest instalments plus interest
60
A60 30000 1.0075 M M 1.0075 M 1.0075 M 1.0075
58 59
a M , r 1.0075, n 60
a r n 1
30000 1.0075
60
r 1
M 1.007560 1
30000 1.0075
60
0.0075
But A60 0
93. An principal plus interest instalments plus interest
60
A60 30000 1.0075 M M 1.0075 M 1.0075 M 1.0075
58 59
a M , r 1.0075, n 60
a r n 1
30000 1.0075
60
r 1
M 1.007560 1
30000 1.0075
60
0.0075
But A60 0
M 1.007560 1
30000 1.0075 0
60
0.0075
94. An principal plus interest instalments plus interest
60
A60 30000 1.0075 M M 1.0075 M 1.0075 M 1.0075
58 59
a M , r 1.0075, n 60
a r n 1
30000 1.0075
60
r 1
M 1.007560 1
30000 1.0075
60
0.0075
But A60 0
M 1.007560 1
30000 1.0075 0
60
0.0075
1.007560 1
30000 1.0075
60
M
0.0075
95. An principal plus interest instalments plus interest
60
A60 30000 1.0075 M M 1.0075 M 1.0075 M 1.0075
58 59
a M , r 1.0075, n 60
a r n 1
30000 1.0075
60
r 1
M 1.007560 1
30000 1.0075
60
0.0075
But A60 0
M 1.007560 1
30000 1.0075 0
60
0.0075
1.007560 1
30000 1.0075
60
M
0.0075
30000 1.0075 0.0075
60
M
1.007560 1
96. An principal plus interest instalments plus interest
60
A60 30000 1.0075 M M 1.0075 M 1.0075 M 1.0075
58 59
a M , r 1.0075, n 60
a r n 1
30000 1.0075
60
r 1
M 1.007560 1
30000 1.0075
60
0.0075
But A60 0
M 1.007560 1
30000 1.0075 0
60
0.0075
1.007560 1
30000 1.0075
60
M
0.0075
30000 1.0075 0.0075
60
M M $622.75
1.007560 1
98. (iii) Finding the length of the loan
2005 HSC Question 8c)
Weelabarrabak Shire Council borrowed $3000000 at the beginning of
2005. The annual interest rate is 12%. Each year, interest is calculated
on the balance at the beginning of the year and added to the balance
owing. The debt is to be repaid by equal annual repayments of $480000,
with the first repayment being made at the end of 2005.
Let An be the balance owing after the nth repayment.
99. (iii) Finding the length of the loan
2005 HSC Question 8c)
Weelabarrabak Shire Council borrowed $3000000 at the beginning of
2005. The annual interest rate is 12%. Each year, interest is calculated
on the balance at the beginning of the year and added to the balance
owing. The debt is to be repaid by equal annual repayments of $480000,
with the first repayment being made at the end of 2005.
Let An be the balance owing after the nth repayment.
(i) Show that A2 3 106 1.12 4.8 105 1 1.12
2
100. (iii) Finding the length of the loan
2005 HSC Question 8c)
Weelabarrabak Shire Council borrowed $3000000 at the beginning of
2005. The annual interest rate is 12%. Each year, interest is calculated
on the balance at the beginning of the year and added to the balance
owing. The debt is to be repaid by equal annual repayments of $480000,
with the first repayment being made at the end of 2005.
Let An be the balance owing after the nth repayment.
(i) Show that A2 3 106 1.12 4.8 105 1 1.12
2
3000000 1.12
2
Initial loan is borrowed for 2 years
101. (iii) Finding the length of the loan
2005 HSC Question 8c)
Weelabarrabak Shire Council borrowed $3000000 at the beginning of
2005. The annual interest rate is 12%. Each year, interest is calculated
on the balance at the beginning of the year and added to the balance
owing. The debt is to be repaid by equal annual repayments of $480000,
with the first repayment being made at the end of 2005.
Let An be the balance owing after the nth repayment.
(i) Show that A2 3 106 1.12 4.8 105 1 1.12
2
3000000 1.12
2
Initial loan is borrowed for 2 years
480000 1.12
1
1st repayment invested for 1 year
102. (iii) Finding the length of the loan
2005 HSC Question 8c)
Weelabarrabak Shire Council borrowed $3000000 at the beginning of
2005. The annual interest rate is 12%. Each year, interest is calculated
on the balance at the beginning of the year and added to the balance
owing. The debt is to be repaid by equal annual repayments of $480000,
with the first repayment being made at the end of 2005.
Let An be the balance owing after the nth repayment.
(i) Show that A2 3 106 1.12 4.8 105 1 1.12
2
3000000 1.12
2
Initial loan is borrowed for 2 years
480000 1.12
1
1st repayment invested for 1 year
2nd repayment invested for 0 years 480000
103. (iii) Finding the length of the loan
2005 HSC Question 8c)
Weelabarrabak Shire Council borrowed $3000000 at the beginning of
2005. The annual interest rate is 12%. Each year, interest is calculated
on the balance at the beginning of the year and added to the balance
owing. The debt is to be repaid by equal annual repayments of $480000,
with the first repayment being made at the end of 2005.
Let An be the balance owing after the nth repayment.
(i) Show that A2 3 106 1.12 4.8 105 1 1.12
2
3000000 1.12
2
Initial loan is borrowed for 2 years
480000 1.12
1
1st repayment invested for 1 year
2nd repayment invested for 0 years 480000
An principal plus interest instalments plus interest
104. (iii) Finding the length of the loan
2005 HSC Question 8c)
Weelabarrabak Shire Council borrowed $3000000 at the beginning of
2005. The annual interest rate is 12%. Each year, interest is calculated
on the balance at the beginning of the year and added to the balance
owing. The debt is to be repaid by equal annual repayments of $480000,
with the first repayment being made at the end of 2005.
Let An be the balance owing after the nth repayment.
(i) Show that A2 3 106 1.12 4.8 105 1 1.12
2
3000000 1.12
2
Initial loan is borrowed for 2 years
480000 1.12
1
1st repayment invested for 1 year
2nd repayment invested for 0 years 480000
An principal plus interest instalments plus interest
A2 3000000 1.12 480000 480000 1.12
2
105. (iii) Finding the length of the loan
2005 HSC Question 8c)
Weelabarrabak Shire Council borrowed $3000000 at the beginning of
2005. The annual interest rate is 12%. Each year, interest is calculated
on the balance at the beginning of the year and added to the balance
owing. The debt is to be repaid by equal annual repayments of $480000,
with the first repayment being made at the end of 2005.
Let An be the balance owing after the nth repayment.
(i) Show that A2 3 106 1.12 4.8 105 1 1.12
2
3000000 1.12
2
Initial loan is borrowed for 2 years
480000 1.12
1
1st repayment invested for 1 year
2nd repayment invested for 0 years 480000
An principal plus interest instalments plus interest
A2 3000000 1.12 480000 480000 1.12
2
A2 3 10 1.12 4.8 10 1 1.12
6 2 5
107.
(ii) Show that An 106 4 1.12
n
3000000 1.12
n
Initial loan is borrowed for n years
108.
(ii) Show that An 106 4 1.12
n
3000000 1.12
n
Initial loan is borrowed for n years
480000 1.12
n 1
1st repayment invested for n – 1 years
109.
(ii) Show that An 106 4 1.12
n
3000000 1.12
n
Initial loan is borrowed for n years
480000 1.12
n 1
1st repayment invested for n – 1 years
480000 1.12
n2
2nd repayment invested for n – 2 years
110.
(ii) Show that An 106 4 1.12
n
3000000 1.12
n
Initial loan is borrowed for n years
480000 1.12
n 1
1st repayment invested for n – 1 years
2nd repayment invested for n – 2 years 480000 1.12 n2
2nd last repayment invested for 1 year 480000 1.12 1
111.
(ii) Show that An 106 4 1.12
n
3000000 1.12
n
Initial loan is borrowed for n years
480000 1.12
n 1
1st repayment invested for n – 1 years
2nd repayment invested for n – 2 years 480000 1.12 n2
2nd last repayment invested for 1 year 480000 1.12 1
last repayment invested for 0 years 480000
112.
(ii) Show that An 106 4 1.12
n
3000000 1.12
n
Initial loan is borrowed for n years
480000 1.12
n 1
1st repayment invested for n – 1 years
2nd repayment invested for n – 2 years 480000 1.12 n2
2nd last repayment invested for 1 year 480000 1.12 1
last repayment invested for 0 years 480000
An principal plus interest instalments plus interest
113.
(ii) Show that An 106 4 1.12
n
3000000 1.12
n
Initial loan is borrowed for n years
480000 1.12
n 1
1st repayment invested for n – 1 years
2nd repayment invested for n – 2 years 480000 1.12 n2
2nd last repayment invested for 1 year 480000 1.12 1
last repayment invested for 0 years 480000
An principal plus interest instalments plus interest
n
An 3000000 1.12 480000 1 1.12 1.12
n2
1.12
n 1
114.
(ii) Show that An 106 4 1.12
n
3000000 1.12
n
Initial loan is borrowed for n years
480000 1.12
n 1
1st repayment invested for n – 1 years
2nd repayment invested for n – 2 years 480000 1.12 n2
2nd last repayment invested for 1 year 480000 1.12 1
last repayment invested for 0 years 480000
An principal plus interest instalments plus interest
n
An 3000000 1.12 480000 1 1.12 1.12 1.12
n2 n 1
a 480000, r 1.12, n n
115.
(ii) Show that An 106 4 1.12
n
3000000 1.12
n
Initial loan is borrowed for n years
480000 1.12
n 1
1st repayment invested for n – 1 years
2nd repayment invested for n – 2 years 480000 1.12 n2
2nd last repayment invested for 1 year 480000 1.12 1
last repayment invested for 0 years 480000
An principal plus interest instalments plus interest
n
An 3000000 1.12 480000 1 1.12 1.12 1.12
n2 n 1
a 480000, r 1.12, n n
a r n 1
3000000 1.12
n
r 1
118. 480000 1.12n 1
An 3000000 1.12
n
0.12
3000000 1.12 4000000 1.12n 1
n
3000000 1.12 4000000 1.12 4000000
n n
119. 480000 1.12n 1
An 3000000 1.12
n
0.12
3000000 1.12 4000000 1.12n 1
n
3000000 1.12 4000000 1.12 4000000
n n
4000000 1000000 1.12
n
120. 480000 1.12n 1
An 3000000 1.12
n
0.12
3000000 1.12 4000000 1.12n 1
n
3000000 1.12 4000000 1.12 4000000
n n
4000000 1000000 1.12
n
106 4 1.12
n
121. 480000 1.12n 1
An 3000000 1.12
n
0.12
3000000 1.12 4000000 1.12n 1
n
3000000 1.12 4000000 1.12 4000000
n n
4000000 1000000 1.12
n
106 4 1.12
n
(iii) In which year will Weelabarrabak Shire Council make the final
repayment?
122. 480000 1.12n 1
An 3000000 1.12
n
0.12
3000000 1.12 4000000 1.12n 1
n
3000000 1.12 4000000 1.12 4000000
n n
4000000 1000000 1.12
n
106 4 1.12
n
(iii) In which year will Weelabarrabak Shire Council make the final
repayment?
An 0
123. 480000 1.12n 1
An 3000000 1.12
n
0.12
3000000 1.12 4000000 1.12n 1
n
3000000 1.12 4000000 1.12 4000000
n n
4000000 1000000 1.12
n
106 4 1.12
n
(iii) In which year will Weelabarrabak Shire Council make the final
repayment?
An 0
10 4 1.12
6 n
0
124. 480000 1.12n 1
An 3000000 1.12
n
0.12
3000000 1.12 4000000 1.12n 1
n
3000000 1.12 4000000 1.12 4000000
n n
4000000 1000000 1.12
n
106 4 1.12
n
(iii) In which year will Weelabarrabak Shire Council make the final
repayment?
An 0
10 4 1.12
6 n
0
4 1.12 0
n
125. 480000 1.12n 1
An 3000000 1.12
n
0.12
3000000 1.12 4000000 1.12n 1
n
3000000 1.12 4000000 1.12 4000000
n n
4000000 1000000 1.12
n
106 4 1.12
n
(iii) In which year will Weelabarrabak Shire Council make the final
repayment?
An 0
10 4 1.12
6 n
0
4 1.12 0
n
1.12 4
n
128. log 1.12 log 4
n
n log1.12 log 4
log 4
n
log1.12
n 12.2325075
129. log 1.12 log 4
n
n log1.12 log 4
log 4
n
log1.12
n 12.2325075
The thirteenth repayment is the final repayment which will occur at
the end of 2017
130. log 1.12 log 4
n
n log1.12 log 4
log 4
n
log1.12
n 12.2325075
The thirteenth repayment is the final repayment which will occur at
the end of 2017
Exercise 7B; 4, 6, 8, 10
Exercise 7C; 1, 4, 7, 9
Exercise 7D; 3, 4, 9, 11