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Chapter 4 nominal & effective interest rates

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.

Annuity

This document defines and explains different types of annuities, including ordinary annuity, annuity due, and deferred annuity. It provides formulas to calculate the present value and regular payments of each type of annuity. Key details include that ordinary annuity payments are made at the end of each interval, annuity due payments are made at the beginning of each interval, and deferred annuity payments begin at a later time.

Present value

There are three main reasons why a dollar in the future is worth less than a dollar today:
1. People prefer present consumption over future consumption
2. Inflation decreases the value of currency over time
3. Uncertainty associated with future cash flows decreases their value
The discount rate incorporates these factors and is used to discount future cash flows to their present value. A higher discount rate leads to a lower present value for future cash flows. Discounting future cash flows converts them to present value dollars.

Ordinary annuity and annuity due

- An annuity is a series of payments made at regular intervals, typically to provide income for retirement. It can be ordinary (payments made at the end of each period) or due (payments made at the beginning of each period).
- The amount (sum) of an annuity is the total value of all payments over the term. Formulas are provided to calculate the amount based on the payment amount, interest rate, number of periods.
- The present value is the current worth of a future sum or series of sums. Formulas are also provided to calculate the present value of ordinary and due annuities.
- Several examples are provided to demonstrate calculating amounts and present values of ordinary and due annu

Time value of money

time value of money
,
concept of time value of money
,
significance of time value of money
,
present value vs future value
,
solve for the present value
,
simple vs compound interest rate
,
nominal vs effective annual interest rates
,
future value of a lump sum
,
solve for the future value
,
present value of a lump sum
,
types of annuity
,
future value of an annuity

Chapter 6 annuity

The document provides an overview of annuities and time value of money concepts. It discusses ordinary annuities, including how to calculate future value, payment amount, interest rate, and number of periods for an ordinary annuity. It also covers present value of annuities, amortized loans including loan payments and schedules, and annuities due. Examples are provided for each topic and how to solve them using a financial calculator or Excel spreadsheet.

The Time Value of Money

The document discusses the time value of money concept. It defines time value of money as the principle that a dollar received today is worth more than a dollar received tomorrow due to interest earnings. It then provides examples of simple and compound interest calculations to illustrate the difference. Finally, it outlines the key formulas used in present value, future value, and annuity calculations including variables like present value, future value, interest rate, and time periods.

Mathematics of Finance

The document provides an overview of key concepts in mathematics of finance, including:
1) It defines interest as the extra amount paid for borrowing money or using money, with the original amount being called the principal.
2) It describes the two main types of interest as simple interest, which is paid only on the principal, and compound interest, which is calculated on both the principal and accumulated interest over time.
3) Key formulas are presented for calculating simple interest, compound interest, effective annual interest rates, future and present values of annuities, and sinking funds. Real-world examples are provided to demonstrate how to apply the formulas.

Chapter 4 nominal & effective interest rates

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.

Annuity

This document defines and explains different types of annuities, including ordinary annuity, annuity due, and deferred annuity. It provides formulas to calculate the present value and regular payments of each type of annuity. Key details include that ordinary annuity payments are made at the end of each interval, annuity due payments are made at the beginning of each interval, and deferred annuity payments begin at a later time.

Present value

There are three main reasons why a dollar in the future is worth less than a dollar today:
1. People prefer present consumption over future consumption
2. Inflation decreases the value of currency over time
3. Uncertainty associated with future cash flows decreases their value
The discount rate incorporates these factors and is used to discount future cash flows to their present value. A higher discount rate leads to a lower present value for future cash flows. Discounting future cash flows converts them to present value dollars.

Ordinary annuity and annuity due

- An annuity is a series of payments made at regular intervals, typically to provide income for retirement. It can be ordinary (payments made at the end of each period) or due (payments made at the beginning of each period).
- The amount (sum) of an annuity is the total value of all payments over the term. Formulas are provided to calculate the amount based on the payment amount, interest rate, number of periods.
- The present value is the current worth of a future sum or series of sums. Formulas are also provided to calculate the present value of ordinary and due annuities.
- Several examples are provided to demonstrate calculating amounts and present values of ordinary and due annu

Time value of money

time value of money
,
concept of time value of money
,
significance of time value of money
,
present value vs future value
,
solve for the present value
,
simple vs compound interest rate
,
nominal vs effective annual interest rates
,
future value of a lump sum
,
solve for the future value
,
present value of a lump sum
,
types of annuity
,
future value of an annuity

Chapter 6 annuity

The document provides an overview of annuities and time value of money concepts. It discusses ordinary annuities, including how to calculate future value, payment amount, interest rate, and number of periods for an ordinary annuity. It also covers present value of annuities, amortized loans including loan payments and schedules, and annuities due. Examples are provided for each topic and how to solve them using a financial calculator or Excel spreadsheet.

The Time Value of Money

The document discusses the time value of money concept. It defines time value of money as the principle that a dollar received today is worth more than a dollar received tomorrow due to interest earnings. It then provides examples of simple and compound interest calculations to illustrate the difference. Finally, it outlines the key formulas used in present value, future value, and annuity calculations including variables like present value, future value, interest rate, and time periods.

Mathematics of Finance

The document provides an overview of key concepts in mathematics of finance, including:
1) It defines interest as the extra amount paid for borrowing money or using money, with the original amount being called the principal.
2) It describes the two main types of interest as simple interest, which is paid only on the principal, and compound interest, which is calculated on both the principal and accumulated interest over time.
3) Key formulas are presented for calculating simple interest, compound interest, effective annual interest rates, future and present values of annuities, and sinking funds. Real-world examples are provided to demonstrate how to apply the formulas.

Present Value and Future Value of a Single Sum Problem

This is a presentation on the time value of money using single sum problem for different periods. The computation of the present value and future value is presented using the formula approach, the financial calculator approach, and the spreadsheet approach.

Amortizing Loan | Finance

This document discusses two methods for calculating the outstanding principal on an amortizing loan: the prospective method and the retrospective method. It also provides examples of calculating outstanding principal using each method. Additionally, it reviews the formulas for calculating interest paid and unpaid balance on a loan over time. It concludes by explaining the steps for creating an amortization schedule, including calculating the interest and principal portions of each payment and updating the outstanding balance.

Bonds & Bond Pricing

1) The document discusses bonds and bond pricing, including the basic concepts of bonds, how bonds are evaluated and priced, and how to construct bond amortization schedules.
2) Key formulas are presented for pricing a bond using the basic price formula and constructing bond premium or discount amortization schedules using the effective interest method.
3) Examples are provided to illustrate bond pricing, including pricing between coupon dates, and constructing bond premium and discount amortization schedules.

Valuation of bonds

Bonds and shares can be valued using various approaches such as book value, replacement value, liquidation value, and market value. Bond values are determined by factors like face value, interest rate, maturity, redemption value, and market yield. The yield to maturity considers interest payments and capital gains/losses, while current yield only considers annual interest. Duration measures a bond's price sensitivity to interest rate changes. The term structure of interest rates, as shown by the yield curve, can be normal upward sloping or inverted. The expectation, liquidity premium, and segmented markets theories seek to explain the typical upward sloping yield curve. Credit ratings factor in default risk.

Interest

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

time value of money

The document discusses the concepts of time value of money, interest, and annuities. It defines key terms like present value, future value, simple interest, compound interest, and ordinary annuity. It provides examples of calculating simple interest, compound interest, future value, present value, and future value of annuities using standard formulas. Various questions and solutions are given to illustrate time value of money calculations.

Depreciation

This document discusses various concepts and methods of depreciation. It defines depreciation as a measure of the wearing out or loss of value of an asset due to use over time. The objectives and causes of depreciation are also outlined. Several methods for calculating depreciation are explained, including straight-line, diminishing balance, and sum of years digits. Specific formulas and examples are provided to illustrate how to apply these depreciation methods. The document also discusses unit production and depletion methods which are used to allocate depreciation based on units produced or extracted.

Financial maths

Introduction to financial maths. 6th Years please use in conjunction with the questions given on Friday.

Rules of debit and credit

The document is a chapter from an accounting textbook that discusses analyzing transactions and the basics of double-entry accounting. It introduces accounts, the rules of debit and credit, and how transactions are recorded in journals and T-accounts to update the balances of asset, liability, equity, revenue and expense accounts. It provides examples of common transactions recorded, such as cash deposits and withdrawals, purchases, expenses and revenue. The overall purpose is to teach students the fundamental principles and mechanics of double-entry accounting.

Time value of money

What is time value of money? Annuities, simple interest, compound interests, present value, future value, etc.

Annuity

An annuity is a series of fixed payments made over a specified period of time, with common payment frequencies being yearly, semi-annually, quarterly, and monthly. The present value of an annuity is the current worth of future cash flows discounted at a given interest rate, with a higher discount rate resulting in a lower present value. The future value is the amount one would have in the future given a specified interest rate, with a higher discount rate yielding a higher future value. Annuities can be ordinary, with payments at the end of each period, or annuities due, with payments at the beginning of each period.

Interest and its types

The document discusses different types of interest. It defines interest as a payment made by a borrower to a lender for the use of borrowed money. There are two main types of interest - simple interest, which is calculated only on the original principal amount, and compound interest, which calculates interest on both the principal and previously accumulated interest. The document provides examples to illustrate how to calculate simple interest and compound interest over time. It explains that compound interest results in higher total interest paid compared to simple interest due to interest being added to the principal each compounding period.

Bonds, preferred stocks and common stocks

The document discusses various types of bonds, preferred stocks, and common stocks. It begins by defining basic bond terms like principal amount, coupon rate, maturity date, and bond ratings. It then describes different types of bonds such as secured bonds (mortgage, equipment trust), unsecured bonds (debentures, subordinated), and bonds classified by coupon payments (zero coupon, fixed-rate, floating-rate) or issuer (government, municipal, corporate). The document also discusses bond retirement methods like sinking funds, serial bonds, and call provisions.

Net present Value, Internal Rate Of Return, Profitability Index, Payback, dis...

This document discusses various capital budgeting techniques used to evaluate investment projects, including:
1. Discounted cash flow methods like net present value (NPV), internal rate of return (IRR), and profitability index (PI).
2. Non-discounted cash flow methods like payback period, discounted payback period, and accounting rate of return (ARR).
It provides formulas, examples, and decision rules for calculating each method and comparing investment opportunities.

Capital asset pricing model

The Capital Asset Pricing Model (CAPM) was developed by William Sharpe in 1970 to calculate the expected return of an asset based on its risk. It distinguishes between systematic risk that cannot be diversified away, such as market risk, and unsystematic risk that can be reduced through diversification. The CAPM formula states that the expected return of an asset is equal to the risk-free rate plus a risk premium that is proportional to the asset's systematic risk or beta. Beta measures how volatile an asset's returns are relative to the overall market. The CAPM makes simplifying assumptions about investors and markets. While widely used, some argue it may not perfectly predict returns in practice.

Time Value of Money

The document summarizes key concepts about the time value of money including:
- Compound interest formulas to calculate future and present value over time.
- The parable of the talents discusses how servants invested their master's money and earned returns, teaching the lesson of investing money for growth.
- Examples are provided to illustrate compound vs simple interest calculations and applications to mortgages, loans, and retirement savings.
- Formulas are defined for simple interest, compounding, discounting, annuities, perpetuities and varying compound periods.

Amortization

This document discusses simple interest and simple discount calculations. It defines key terms like principal, interest rate, and time period. It presents the simple interest formula I=PRT and shows how to use it to calculate interest earned or owed on loans and investments. It also covers finding the maturity value of a loan, converting between months and fractional years, and determining principal, rate, or time when other factors are known. Finally, it discusses calculating interest using ordinary and exact time periods.

2 annuity and its types

This document discusses annuities and their types. It begins with defining an annuity as a series of regular payments made or received over time. The document then outlines five main types of annuities: ordinary annuity, annuity due, perpetuity, continuous annuity, and deferred annuity. For each type, it provides a definition and example. The document also includes formulas for calculating the future and present value of ordinary annuities and annuities due. It concludes with examples of how annuities can be used to calculate depreciation for accounting purposes.

Effective rate of interest

The effective rate of interest is the actual rate earned or paid on an investment when interest is compounded over time. It is usually higher than the nominal rate. The effective rate depends on both the nominal rate and the number of compounding periods. More compounding periods result in a higher effective rate. In the example given, a 6% nominal interest rate compounded semi-annually yields an effective rate of 6.09%, compounded quarterly yields 6.14%, and compounded monthly yields the highest rate of 6.17%.

Time value of money

This document provides an overview of time value of money concepts. It discusses that the value of money decreases over time, so money received today is worth more than the same amount in the future. There are four reasons for an individual's time preference for money: investment opportunities, risk, personal consumption preference, and inflation. The document then describes techniques for adjusting cash flows for time value, including compounding and discounting. It provides examples of simple and compound interest calculations. Finally, it discusses concepts such as present value, perpetuities, and effective interest rates.

Chapter 4 nominal & effective interest rates - students

No, in both cases the full interest is not earned/owed. When the payment period (PP) is less than the compounding period (CP), the interest is prorated based on the time elapsed within the CP. So in the savings account example, the interest earned on the first 2 monthly deposits would be less than the interest earned on the 3rd deposit. And for the credit card, paying early would reduce the interest owed for that period.

Nominal and Effective interest Rate fore

Nominal interest rates do not account for compounding, while effective interest rates do. Effective interest rates are calculated using the nominal rate and compounding period to determine the actual return. There are three key time units for any interest rate statement: the time period, compounding period, and compounding frequency. Effective rates are often higher than nominal rates due to the effects of compounding interest over time.

Present Value and Future Value of a Single Sum Problem

This is a presentation on the time value of money using single sum problem for different periods. The computation of the present value and future value is presented using the formula approach, the financial calculator approach, and the spreadsheet approach.

Amortizing Loan | Finance

This document discusses two methods for calculating the outstanding principal on an amortizing loan: the prospective method and the retrospective method. It also provides examples of calculating outstanding principal using each method. Additionally, it reviews the formulas for calculating interest paid and unpaid balance on a loan over time. It concludes by explaining the steps for creating an amortization schedule, including calculating the interest and principal portions of each payment and updating the outstanding balance.

Bonds & Bond Pricing

1) The document discusses bonds and bond pricing, including the basic concepts of bonds, how bonds are evaluated and priced, and how to construct bond amortization schedules.
2) Key formulas are presented for pricing a bond using the basic price formula and constructing bond premium or discount amortization schedules using the effective interest method.
3) Examples are provided to illustrate bond pricing, including pricing between coupon dates, and constructing bond premium and discount amortization schedules.

Valuation of bonds

Bonds and shares can be valued using various approaches such as book value, replacement value, liquidation value, and market value. Bond values are determined by factors like face value, interest rate, maturity, redemption value, and market yield. The yield to maturity considers interest payments and capital gains/losses, while current yield only considers annual interest. Duration measures a bond's price sensitivity to interest rate changes. The term structure of interest rates, as shown by the yield curve, can be normal upward sloping or inverted. The expectation, liquidity premium, and segmented markets theories seek to explain the typical upward sloping yield curve. Credit ratings factor in default risk.

Interest

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

time value of money

The document discusses the concepts of time value of money, interest, and annuities. It defines key terms like present value, future value, simple interest, compound interest, and ordinary annuity. It provides examples of calculating simple interest, compound interest, future value, present value, and future value of annuities using standard formulas. Various questions and solutions are given to illustrate time value of money calculations.

Depreciation

This document discusses various concepts and methods of depreciation. It defines depreciation as a measure of the wearing out or loss of value of an asset due to use over time. The objectives and causes of depreciation are also outlined. Several methods for calculating depreciation are explained, including straight-line, diminishing balance, and sum of years digits. Specific formulas and examples are provided to illustrate how to apply these depreciation methods. The document also discusses unit production and depletion methods which are used to allocate depreciation based on units produced or extracted.

Financial maths

Introduction to financial maths. 6th Years please use in conjunction with the questions given on Friday.

Rules of debit and credit

The document is a chapter from an accounting textbook that discusses analyzing transactions and the basics of double-entry accounting. It introduces accounts, the rules of debit and credit, and how transactions are recorded in journals and T-accounts to update the balances of asset, liability, equity, revenue and expense accounts. It provides examples of common transactions recorded, such as cash deposits and withdrawals, purchases, expenses and revenue. The overall purpose is to teach students the fundamental principles and mechanics of double-entry accounting.

Time value of money

What is time value of money? Annuities, simple interest, compound interests, present value, future value, etc.

Annuity

An annuity is a series of fixed payments made over a specified period of time, with common payment frequencies being yearly, semi-annually, quarterly, and monthly. The present value of an annuity is the current worth of future cash flows discounted at a given interest rate, with a higher discount rate resulting in a lower present value. The future value is the amount one would have in the future given a specified interest rate, with a higher discount rate yielding a higher future value. Annuities can be ordinary, with payments at the end of each period, or annuities due, with payments at the beginning of each period.

Interest and its types

The document discusses different types of interest. It defines interest as a payment made by a borrower to a lender for the use of borrowed money. There are two main types of interest - simple interest, which is calculated only on the original principal amount, and compound interest, which calculates interest on both the principal and previously accumulated interest. The document provides examples to illustrate how to calculate simple interest and compound interest over time. It explains that compound interest results in higher total interest paid compared to simple interest due to interest being added to the principal each compounding period.

Bonds, preferred stocks and common stocks

The document discusses various types of bonds, preferred stocks, and common stocks. It begins by defining basic bond terms like principal amount, coupon rate, maturity date, and bond ratings. It then describes different types of bonds such as secured bonds (mortgage, equipment trust), unsecured bonds (debentures, subordinated), and bonds classified by coupon payments (zero coupon, fixed-rate, floating-rate) or issuer (government, municipal, corporate). The document also discusses bond retirement methods like sinking funds, serial bonds, and call provisions.

Net present Value, Internal Rate Of Return, Profitability Index, Payback, dis...

This document discusses various capital budgeting techniques used to evaluate investment projects, including:
1. Discounted cash flow methods like net present value (NPV), internal rate of return (IRR), and profitability index (PI).
2. Non-discounted cash flow methods like payback period, discounted payback period, and accounting rate of return (ARR).
It provides formulas, examples, and decision rules for calculating each method and comparing investment opportunities.

Capital asset pricing model

The Capital Asset Pricing Model (CAPM) was developed by William Sharpe in 1970 to calculate the expected return of an asset based on its risk. It distinguishes between systematic risk that cannot be diversified away, such as market risk, and unsystematic risk that can be reduced through diversification. The CAPM formula states that the expected return of an asset is equal to the risk-free rate plus a risk premium that is proportional to the asset's systematic risk or beta. Beta measures how volatile an asset's returns are relative to the overall market. The CAPM makes simplifying assumptions about investors and markets. While widely used, some argue it may not perfectly predict returns in practice.

Time Value of Money

The document summarizes key concepts about the time value of money including:
- Compound interest formulas to calculate future and present value over time.
- The parable of the talents discusses how servants invested their master's money and earned returns, teaching the lesson of investing money for growth.
- Examples are provided to illustrate compound vs simple interest calculations and applications to mortgages, loans, and retirement savings.
- Formulas are defined for simple interest, compounding, discounting, annuities, perpetuities and varying compound periods.

Amortization

This document discusses simple interest and simple discount calculations. It defines key terms like principal, interest rate, and time period. It presents the simple interest formula I=PRT and shows how to use it to calculate interest earned or owed on loans and investments. It also covers finding the maturity value of a loan, converting between months and fractional years, and determining principal, rate, or time when other factors are known. Finally, it discusses calculating interest using ordinary and exact time periods.

2 annuity and its types

This document discusses annuities and their types. It begins with defining an annuity as a series of regular payments made or received over time. The document then outlines five main types of annuities: ordinary annuity, annuity due, perpetuity, continuous annuity, and deferred annuity. For each type, it provides a definition and example. The document also includes formulas for calculating the future and present value of ordinary annuities and annuities due. It concludes with examples of how annuities can be used to calculate depreciation for accounting purposes.

Effective rate of interest

The effective rate of interest is the actual rate earned or paid on an investment when interest is compounded over time. It is usually higher than the nominal rate. The effective rate depends on both the nominal rate and the number of compounding periods. More compounding periods result in a higher effective rate. In the example given, a 6% nominal interest rate compounded semi-annually yields an effective rate of 6.09%, compounded quarterly yields 6.14%, and compounded monthly yields the highest rate of 6.17%.

Time value of money

This document provides an overview of time value of money concepts. It discusses that the value of money decreases over time, so money received today is worth more than the same amount in the future. There are four reasons for an individual's time preference for money: investment opportunities, risk, personal consumption preference, and inflation. The document then describes techniques for adjusting cash flows for time value, including compounding and discounting. It provides examples of simple and compound interest calculations. Finally, it discusses concepts such as present value, perpetuities, and effective interest rates.

Present Value and Future Value of a Single Sum Problem

Present Value and Future Value of a Single Sum Problem

Amortizing Loan | Finance

Amortizing Loan | Finance

Bonds & Bond Pricing

Bonds & Bond Pricing

Valuation of bonds

Valuation of bonds

Interest

Interest

time value of money

time value of money

Depreciation

Depreciation

Financial maths

Financial maths

Rules of debit and credit

Rules of debit and credit

Time value of money

Time value of money

Annuity

Annuity

Interest and its types

Interest and its types

Bonds, preferred stocks and common stocks

Bonds, preferred stocks and common stocks

Net present Value, Internal Rate Of Return, Profitability Index, Payback, dis...

Net present Value, Internal Rate Of Return, Profitability Index, Payback, dis...

Capital asset pricing model

Capital asset pricing model

Time Value of Money

Time Value of Money

Amortization

Amortization

2 annuity and its types

2 annuity and its types

Effective rate of interest

Effective rate of interest

Time value of money

Time value of money

Chapter 4 nominal & effective interest rates - students

No, in both cases the full interest is not earned/owed. When the payment period (PP) is less than the compounding period (CP), the interest is prorated based on the time elapsed within the CP. So in the savings account example, the interest earned on the first 2 monthly deposits would be less than the interest earned on the 3rd deposit. And for the credit card, paying early would reduce the interest owed for that period.

Nominal and Effective interest Rate fore

Nominal interest rates do not account for compounding, while effective interest rates do. Effective interest rates are calculated using the nominal rate and compounding period to determine the actual return. There are three key time units for any interest rate statement: the time period, compounding period, and compounding frequency. Effective rates are often higher than nominal rates due to the effects of compounding interest over time.

important exam.pdf

This document summarizes key concepts from Chapter 4 of the textbook Engineering Economy. It begins with learning outcomes related to understanding different interest rate terms and calculations. It then defines nominal and effective interest rates, and provides the formula for calculating effective interest rates. Several examples are worked through, including calculations for single cash flows, series cash flows where the payment period is greater than or equal to the compounding period, and calculations involving continuous compounding. The summary emphasizes the important distinction between nominal and effective rates, and how to determine the appropriate interest rate and number of periods for time value of money calculations.

Ch4 nom&effective ir_rev2

This document discusses nominal and effective interest rates, including continuous compounding. It defines nominal and effective interest rates, and how to calculate effective rates for different compounding periods. It provides examples of calculating effective rates for annual, semi-annual, quarterly, and continuous compounding. It also discusses how to handle calculations when the payment period is equal to, longer than, or shorter than the compounding period. This includes using the appropriate effective rate and number of periods in calculations.

Chapter 4 nominal & effective interest rates

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.

Nominal And Effective Interest Rates.pptx

Here are the calculations for the 3 cases:
Case 1:
Interest rate = 12% p.a. compounded semi-annually
Effective interest rate = (1 + 0.12/2)^2 - 1 = 12.36%
Investment amount after 5 years = Rs. 6000 * [(1.1236)^10 - 1] / 0.1236 = Rs. 51,000
Case 2:
Interest rate = 12% p.a. compounded annually
Effective interest rate = 12%
Investment amount after 5 years = Rs. 6000 * [(1.12)^5 - 1] / 0.12 = Rs. 50,000
Case 3:

Leland_Tarquin_Engineering_Economy_Chapter_4_Nominal_Effective_Interest_Rates...

This document discusses interest rates and cash flow analysis. It covers:
1. Definitions of nominal and effective interest rates, compounding periods, and payment periods.
2. Formulas for converting between nominal and effective rates for different time periods.
3. Methods for analyzing single cash flows, series of cash flows, and varying interest rates when the payment period is greater than or less than the compounding period.
4. Continuous compounding and its effective interest rate formula.
5. An example of a cash flow problem with varying interest rates over time.

INVESTMENT CHOICE “COMPARISON AND SELECTION AMONG ALTERNATIVES”

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.

Nominal rate and effective rates primer

This document provides an overview of nominal and effective interest rates. It discusses how interest rates can be quoted in different ways, such as nominal rates that do not account for compounding frequency and effective rates that specify the compounding period. Effective annual interest rates are the true rates that apply over a one-year period and account for how many times interest is compounded within that year, such as monthly, quarterly, or annually. The document provides examples of calculating effective rates given nominal rates and compounding frequencies.

Nominal and effective interest rates

This document discusses nominal and effective interest rates and how to calculate them. It defines nominal interest rates as rates stated over a period less than a year, like 1% per month, while effective rates account for the time value of money and compounding frequency. To calculate the effective rate from the nominal rate, the formula is the nominal rate divided by the number of compounding periods. The document provides examples of calculating effective rates from nominal rates stated as percentages per month or quarter. It also addresses calculating effective rates for payment periods equal to or longer than compounding periods.

Chapter 1 Engineering Economics.pptx

This document provides an overview of key concepts in engineering economy. It discusses:
1) Why engineering economy is important for engineers to make sound economic decisions when designing and selecting between alternatives.
2) The time value of money concept and how money has more value the sooner it is received.
3) The general steps engineers should follow in decision making processes, including understanding the problem, identifying alternatives, and selecting the best option.
4) Key terms used in engineering economy like interest, interest rates, cash flows, economic equivalence, and the difference between simple and compound interest calculations.

Futurum stated and effective interest rate

This document discusses stated and effective annual interest rates. It begins by explaining how corporate finance textbooks typically cover the calculation of stated and effective annual interest rates. However, it notes that textbooks often fail to provide important additional context and warnings. Specifically, textbooks usually assume interest is paid at the end of periods rather than upfront, and they don't address whether stated and effective rates using different compounding methods are truly equivalent given their different cash flows. The document then provides an expanded explanation of these issues and cautions the reader to think critically before applying formulas without consideration of these important factors.

Stated and effective interest rate

This document discusses stated and effective annual interest rates. It begins by explaining how corporate finance textbooks typically cover the calculation of stated and effective annual interest rates. However, it notes that textbooks often fail to provide additional important context. Specifically, textbooks do not clarify that interest is usually paid at the end of a period, not the beginning, and do not address whether rates with different compounding methods are truly equivalent. The document then provides an expanded explanation of these issues and cautions readers to think critically about interest rate conversions.

Jerome4 sample chap08

This document provides an overview of key concepts in compound interest, including calculating future value, present value, and using financial calculators. It discusses how compound interest works by periodically calculating interest and adding it to principal. This causes the investment to grow at an accelerating rate over time. The document defines important terms like nominal interest rate, periodic interest rate, and compounding frequency. It presents examples for calculating periodic interest rates from nominal rates and vice versa. The chapter outlines how to calculate future value, present value, and use financial calculators to solve compound interest problems.

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This document discusses key concepts related to engineering economics, including capital, interest, cash flow diagrams, present worth, future value, nominal interest rates, effective interest rates, and simple vs compound interest. It provides examples and formulas for calculating future value, present worth, nominal interest rates, and effective interest rates. The key points are:
- Interest rates are used to determine the time value of money and allow economic comparisons of cash flows over different time periods.
- Compound interest accounts for interest earned on both the principal amount and previously accumulated interest.
- More frequent compounding results in a higher effective interest rate than the nominal annual rate.
- Present worth and future value formulas allow determining the equivalent value

Nominal & effective Interest Rates

1. The document discusses nominal and effective interest rates, explaining that nominal rates do not account for compounding frequency while effective rates do.
2. It provides an example of a 12% nominal annual interest rate with monthly compounding being equivalent to a 1% interest rate per month.
3. Nominal rates are always lower than equivalent effective annual rates due to differences in compounding frequency, so effective rates provide a better comparison.

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This document discusses microeconomics versus macroeconomics and engineering economy concepts such as the time value of money, interest calculations, and annuities. It defines microeconomics as the study of individual markets and segments of the economy, while macroeconomics examines the whole economy and aggregate variables. The key difference is that microeconomics focuses on issues affecting individuals and companies, while macroeconomics analyzes a national economy. It also covers cash flow concepts, simple and effective interest rates, and defines annuities as plans that provide regular payments for life after an initial lump sum investment.

Actuarial Statistics

The document discusses various actuarial statistics concepts in 10 sections:
1. It defines the difference between simple and compound interest, and provides a table comparing key aspects.
2. It presents the formula for calculating the present value of an annuity.
3. It provides an example problem calculating the value of a college fund after making monthly deposits over 10 years.
4. It defines a sinking fund as periodic payments designed to produce a given sum in the future, such as to pay off a loan.
5. It continues with additional concepts including cash flow, simple vs compound interest calculations, and repayment of loans.
6. It discusses the relationship between effective and nominal interest rates.

unit three.pdf

Here are the key steps to solve this problem:
* Future sum (F) = Rs. 1,00,000
* Interest rate (i) = 15%
* Number of periods (n) = 10 years
* Interest is compounded annually
* To find the present worth (P):
* P = F / (1 + i)^n
* P = Rs. 1,00,000 / (1 + 0.15)^10
* P = Rs. 1,00,000 / 2.472
* P = Rs. Rs. 40,320
Therefore, the single payment that should be made now to receive Rs. 1,00,000 after 10 years at

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Chapter 4 nominal & effective interest rates - students

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Nominal rate and effective rates primer

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Nominal and effective interest rates

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Futurum stated and effective interest rate

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Stated and effective interest rate

Stated and effective interest rate

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unit three.pdf

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GSB711-Lecture-Note-03-The-Time-Value-of-Money

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Income tax

Taxes imposed on the earnings of organizations and individuals are income taxes. Marginal tax rate and flat tax rate. Marginal tax rates are harmful to the economy.

InterestWhy Engineers should know ?

The money returned to the owners of capital for use of their capital.
Compound interest is the result of reinvesting interest, rather than paying it out.
Quotation of interest rates

Projects, Investment, Profitability

This document discusses various methods for evaluating project profitability and investment decisions. It describes quantitative measures like return on investment, return on average investment, payback period, net present worth, and internal rate of return. It also discusses qualitative, intangible factors like employee morale, safety, corporate image, and management goals. The document provides definitions and limitations of different profitability measures. It categorizes project types and notes profitability is difficult to define but important for decision making and maximizing returns on investment.

Taxes and InsuranceEngineering point of view

Tax is a mandatory financial charge, Property taxes, Excise taxes, Income taxes. Capital-gains tax is levied on profits made from the sale of capital assets. Self-insurance is a risk management method

Estimation of Fixed Capital Cost

Operating labour, allow one extra man on days. It is unlikely
that one extra man per shift would be needed to operate
this small plant, and one extra per shift would give
a disproportionately high labour cost.

Summary of Production Costs

Evaluation of preliminary industrial design work . Purchase cost of miscellaneous equipment. Total purchase cost of major equipment items .

Purchase Cost of Miscellaneous Equipment

The document outlines various indirect costs associated with purchasing miscellaneous equipment, including design and engineering costs estimated at 20-30% of direct capital costs, contractor's fees of 5-10% of direct capital costs, and a contingency allowance of 5-10% for issues like labor disputes or weather. The total physical plant cost is the sum of direct costs and these indirect costs.

Mass Transfer Equipment Cost

The document summarizes the components and cost factors involved in purchasing plate and packed towers for mass transfer equipment. The purchased cost can be divided into the shell cost, internals cost like trays and packing, and auxiliary costs. The purchased cost is calculated as the bare cost from figures multiplied by a material factor and pressure factor. Figures are provided showing examples of tray types and cross-sectional views of plate and packed towers.

HEAT-TRANSFER EQUIPMENT COSTS

basic information that should be supplied to a fabricator in order to obtain a price estimate or firm quotation on a proposed heat exchanger (Process Information, Mechanical Information)

Gross Profit, Net Profit

Gross profit, net profitper capital investment. Total annual product cost equals the total annual sales.

Manufacturing Costs

Manufacturing costs per capital investment.Manufacturing costs are: Variable production costs, fixed charges, and plant-overhead.
Direct and indirect production cost. Plant overhead costs. Administrative costs. Distribution and marketing costs. Research and development costs

Capital Investment

Capital cost estimate classifications, Chemical industry. Turnover ratio.
Total product are manufacturing cost and general expenses. product costs are calculated on:
daily basis, unit-of-product basis, or, annual basis

Cost Indices for Industrial Application

Cost Indices, change in cost over time. Cost indexes are maintained in areas such as construction, chemical and mechanical industries. Lang’s method , Hand method.

Estimation of Capital Investments

Capital needed to supply the necessary manufacturing and
plant facilities. Estimation of capital investment.
Order-of-magnitude estimates, 6-10th's rule, Price indices,

Production Costs

Cash flow, cash flow diagram and industry. Cost estimation is required to provide reliable decisions.Price fluctuations, company policies, governmental regulations

Location of an industry

Why location is important for installing an industry, factors affecting plant location, Current trends in selection of a pant location

Fluctuation of money value with time

Time value of money is measured by interest rates. Money has time value because it can earn more over time through interest (earning power) and its purchasing power changes with inflation. The present value of a future amount can be calculated using the present value formula, which takes into account the discount rate and number of periods until receipt. As time passes, the value of assets invested in a project will change. Assets are items owned that have future economic benefit and are divided into tangible assets with physical form and intangible assets without physical form.

Economics for Engineers, Why ?

The document discusses engineering economics and its importance for chemical engineers. It provides three key objectives of engineering economics: 1) to assess the appropriateness of a given project, 2) to estimate its value, and 3) to justify it from an engineering standpoint. The document then analyzes several potential reaction processes for producing vinyl chloride and calculates the gross profit that could be made from each based on raw material and product prices. Reaction 3, which converts ethylene and chlorine into vinyl chloride and hydrogen chloride, is identified as the most profitable option.

Psychrometric chart, How to read

Dew point, Humidity, Dry Bulb temperature, Locate a point on the chart. Enthalpy changes. Tips and tricks for the psychrometric chart.

The Scientific Methods

The scientific method is a set of procedures used to develop explanations of natural phenomena and possibly to predict additional phenomena. For example,
The average temperature of seawater increases, the seawater will become less dense, its volume will increase, and sea level will rise even if no continental ice melts.

Income tax

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InterestWhy Engineers should know ?

InterestWhy Engineers should know ?

Projects, Investment, Profitability

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Taxes and InsuranceEngineering point of view

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Estimation of Fixed Capital Cost

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Summary of Production Costs

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Purchase Cost of Miscellaneous Equipment

Purchase Cost of Miscellaneous Equipment

Mass Transfer Equipment Cost

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HEAT-TRANSFER EQUIPMENT COSTS

HEAT-TRANSFER EQUIPMENT COSTS

Gross Profit, Net Profit

Gross Profit, Net Profit

Manufacturing Costs

Manufacturing Costs

Capital Investment

Capital Investment

Cost Indices for Industrial Application

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Estimation of Capital Investments

Estimation of Capital Investments

Production Costs

Production Costs

Location of an industry

Location of an industry

Fluctuation of money value with time

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Economics for Engineers, Why ?

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Psychrometric chart, How to read

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The Scientific Methods

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LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP

This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.

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𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.

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Event Link:- https://meetups.mulesoft.com/events/details/mulesoft-mysore-presents-mule-event-processing-models/
Agenda
● What is event processing in MuleSoft?
● Types of event processing models in Mule 4
● Distinction between the reactive, parallel, blocking & non-blocking processing
For Upcoming Meetups Join Mysore Meetup Group - https://meetups.mulesoft.com/mysore/YouTube:- youtube.com/@mulesoftmysore
Mysore WhatsApp group:- https://chat.whatsapp.com/EhqtHtCC75vCAX7gaO842N
Speaker:-
Shivani Yasaswi - https://www.linkedin.com/in/shivaniyasaswi/
Organizers:-
Shubham Chaurasia - https://www.linkedin.com/in/shubhamchaurasia1/
Giridhar Meka - https://www.linkedin.com/in/giridharmeka
Priya Shaw - https://www.linkedin.com/in/priya-shaw

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- 1. Nominal and Effective Interest Rate Dr. K. Shahzad Baig Memorial University of Newfoundland (MUN) Canada
- 2. Nominal and effective interest rate Nominal means, “in name only”, not the real rate in this case. A Nominal Interest Rate, is an interest Rate that does not include any consideration of compound interest r = (interest rate per period) (No. of Periods) In common industrial practice, the length of the discrete interest period is assumed to be 1 year and the fixed interest rate i is based on 1 year. There are cases where other time units are employed. Even though the actual interest period is not 1 year, the interest rate is often expressed on an annual basis.
- 3. Examples – Nominal Interest Rates • 1.5% per month for 24 months – Same as: (1.5%)(24) = 36% per 24 months • 1.5% per month for 12 months – Same as (1.5%)(12 months) = 18%/year • 1.5% per month for 6 months –Same as: (1.5%)(6 months) = 9%/6 months or semi-annual Period • 1% per week for 1 year –Same as: (1%)(52 weeks) = 52% per year
- 4. A nominal rate (so quoted) do not reference the frequency of compounding. They all have the format “ r% per time period” • Nominal rates can be misleading • We need an alternative way to quote interest rates.... • The true Effective Interest Rate is then applied The Effective Interest Rate (EIR) • It is a rate that applies for a stated period of time • It is conventional to use the year as the time standard • So, the EIR is often referred to as the Effective Annual Interest Rate (EAIR)
- 5. Nominal Rates:– Format: “r% per time period, t” – Ex: 5% per 6-months” • Effective Interest Rates:– Format: “r% per time period, compounded ‘m’times a year.– ‘m’ denotes or infers the number of times per year that interest is compounded. – Ex: 18% per year, compounded monthly The Differences • The Effective interest Rate per compounding period, CP is: 𝑖 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑝𝑒𝑟 𝐶𝑃 = 𝑟% / 𝑡𝑖𝑚𝑒 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡 𝑚 𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑖𝑛𝑔 𝑝𝑒𝑟𝑖𝑜𝑑𝑠/𝑡
- 6. Deriving the EAIR Invest $1 of principal at time t = 0 at interest rate i per year .$P = $1.00 $F=$P(1+ia) 1One year later, F = P(1+ia)1 Assume the one year is now divided into “m” compounding periods. Replace “i” with “ia” since m now > 1
- 8. Problem Statement Given interest is 8% per year compounded quarterly. What id the annual interest rate? Calculate
- 9. Problem Statement 18% per year compound monthly. What is true, effective annual interest rate
- 10. Two similar expressions for F •F = P(1 + ia); •F = P( 1 + i )m •Equate the two expressions; Solving ‘ia’ in terms of ‘I’
- 11. Continuous Compounding What happens if we let m approach infinity? –That means an infinite number of compounding periods within a year or, –The time between compounding approaches “0”. –We will see that a limiting value will be approached for a given value of “r”
- 12. From the calculus of limits there is an important limit
- 13. To find the equivalent nominal rate given the EAIR when interest is compounded continuously, apply:
- 14. Problem Statement An investor requires an effective return of at least 15% per year. • What is the minimum annual nominal rate that is acceptable if interest on his investment is compounded continuously? A rate of 13.98% per year, cc. generates the same as 15% true effective annual rate. Solution To start: er– 1 = 0.15
- 15. Following books were used in preparation of notes Blank, L., Tarquin. A. 2005. Engineering Economy. 6th Edition, McGraw-Hill. Eschenbach, T. G. 2003. Engineering Economy”, 2nd Edition, Oxford University Press Riggs, J. L., Bedworth, D. D., Randhawa, S. U. 1996. Engineering Economics”, 4th Edition, Tata McGraw-Hill. Riggs, J. L., West. T. M. 1986. Essentials of Engineering Economics”, 2nd Edition, McGraw-Hill. Peter, M. S., Timmerhaus, K. D. 1991. Plant Design and Economics for Chemical Engineers. 4th Edition, McGraw-Hill.

- Now, examine the impact of letting “m” approach infinity.