https://passrealestate.toay/ These slides overview interest rate covers, constant payment mortgages, how to calculate outstanding balances as well as accelerated Bi-Weekly payments. Principal & Interest splits are also covered in detail.
As an example, Finding the "Interest Rate"
Example
A private investor expects to receive $281.72 per month for a period of 17 years as a result of a mortgage loan she has just advanced. Calculate the investor’s expected yield (expressed as a nominal rate with semi-annual compounding) on her investment if the loan was for $23,250.
Amortization Period
Example
Ex. A Mortgage in the amount of $150,000 requires the buyer to make payments of $1,250 per month for as long as necessary to fully amortize the loan at 8% per annum, compounded semi-annually. How many full payments of $1,250 will be required?
Outstanding Balances & Introducing Terms
Example
While mortgage payments are calculated using the amortization period, the actual length of the mortgage contract may be different than the amortization period
The Length of a mortgage contract is referred to as a “Term”. The life of the mortgage loan is split up into “Terms” because of the sometimes long Amortization Periods that come with Mortgage Loans.
Due to these Terms, it is important to be able to calculate an Outstanding Balance, as even though the Term is over, it does not mean that the loan is paid in full - or in other words “Fully Amortized”
Course Details
This course has been created by Alisha Ilaender and Shane Toews, with www.passrealestate.today to assist with Mortgage Broker licensing designation.
This document provides an overview of basic long-term financial concepts including compound and simple interest, present and future value of money, annuities, loan amortization, net present value, and risk-return tradeoff. Examples are provided to demonstrate calculations for interest, present and future value, annuities, loan payments, and net present value analysis. The key relationships between risk and return are explained.
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.
This chapter discusses long-term liabilities, including the issuance and accounting treatment of bonds and notes payable. It covers topics such as bond types, valuation at issuance, discount and premium amortization methods, extinguishment of debt, and off-balance sheet financing arrangements. The goal is for students to understand how to account for long-term debt and present it in financial statements.
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
Here are the key steps to solve this problem:
1) The monthly interest rate (i) is given as 0.287% per month. To convert to a decimal, we divide by 100: i = 0.00287
2) To find the equivalent annual rate (EAR), we use the compound interest formula:
(1 + i)^12 - 1 = EAR
(1 + 0.00287)^12 - 1 = 0.0347 = 3.47%
So the equivalent annual rate for an interest rate of 0.287% per month, compounded monthly, is 3.47%.
3) To find the future value (FV) of €100 after 1 year:
Mathcad seven common financial computationsJulio Banks
The most important factor in a marital relationship is the wise management of the family income. I strongly recommend that dating or married couples consider mastering the simple financial calculations in this document. I have transcribed the reference document verbatim to the level allowed by Mathcad. The numerical results exactly match all of the examples provided in the reference article given included at the end of the Mathcad calculations. This last method is useful when borrowing or lending and need to know the interest
rate of return (ROR) being paid or collected, respectively. Henceforth, let us refer to i simply, as ROR.
The document discusses time value of money concepts including present and future value, compound interest, annuities, loans, mortgages, and other applications. Key equations for present value, future value, and annuities are presented along with examples showing how to apply the equations and use a financial calculator to solve time value of money problems.
This document provides an overview of basic long-term financial concepts including compound and simple interest, present and future value of money, annuities, loan amortization, net present value, and risk-return tradeoff. Examples are provided to demonstrate calculations for interest, present and future value, annuities, loan payments, and net present value analysis. The key relationships between risk and return are explained.
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.
This chapter discusses long-term liabilities, including the issuance and accounting treatment of bonds and notes payable. It covers topics such as bond types, valuation at issuance, discount and premium amortization methods, extinguishment of debt, and off-balance sheet financing arrangements. The goal is for students to understand how to account for long-term debt and present it in financial statements.
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
Here are the key steps to solve this problem:
1) The monthly interest rate (i) is given as 0.287% per month. To convert to a decimal, we divide by 100: i = 0.00287
2) To find the equivalent annual rate (EAR), we use the compound interest formula:
(1 + i)^12 - 1 = EAR
(1 + 0.00287)^12 - 1 = 0.0347 = 3.47%
So the equivalent annual rate for an interest rate of 0.287% per month, compounded monthly, is 3.47%.
3) To find the future value (FV) of €100 after 1 year:
Mathcad seven common financial computationsJulio Banks
The most important factor in a marital relationship is the wise management of the family income. I strongly recommend that dating or married couples consider mastering the simple financial calculations in this document. I have transcribed the reference document verbatim to the level allowed by Mathcad. The numerical results exactly match all of the examples provided in the reference article given included at the end of the Mathcad calculations. This last method is useful when borrowing or lending and need to know the interest
rate of return (ROR) being paid or collected, respectively. Henceforth, let us refer to i simply, as ROR.
The document discusses time value of money concepts including present and future value, compound interest, annuities, loans, mortgages, and other applications. Key equations for present value, future value, and annuities are presented along with examples showing how to apply the equations and use a financial calculator to solve time value of money problems.
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.
The valuation of bonds ppt @ bec doms financeBabasab Patil
The document discusses the valuation and characteristics of bonds. It covers the basis of bond valuation using present value of expected cash flows. It also discusses bond terminology like maturity, coupon rate, and yield. Bond valuation considers factors like interest rates, time to maturity, coupon payments, and principal repayment. The price of a bond moves in the opposite direction of interest rates.
The document summarizes key concepts related to time value of money including:
1) Money today is worth more than money in the future due to factors like interest rates and inflation.
2) Compound interest means interest is earned on both the principal amount and any previous interest earned.
3) Present value calculations determine the current worth of future cash flows while future value calculates the future worth of present cash flows.
4) Annuities represent a stream of regular payments and their present and future values can be calculated using standard formulas.
This document discusses interest rates and time value of money concepts. It begins by defining simple and compound interest rates. Examples are provided to illustrate calculating interest and total amounts due using simple and compound interest formulas. The concept of economic equivalence is introduced, showing that different cash flows can be equivalent based on a common interest rate. The single payment compound interest formula is derived and used to solve examples of determining future or present values. Overall, the document provides an introduction to fundamental time value of money and interest rate concepts in engineering economics.
This document discusses interest rates and time value of money concepts. It begins by defining simple and compound interest rates. Examples are provided to illustrate calculating interest and total amounts due using simple and compound interest formulas. The concept of economic equivalence is introduced, showing that different cash flows can be equivalent based on a common interest rate. The single payment compound interest formula is derived and used to solve examples of determining future or present values. Overall, the document provides an introduction to fundamental time value of money and interest rate concepts in engineering economics.
The document discusses interest rates and their role in finance. It defines interest rates as the amount charged by a lender to a borrower for any form of debt, generally expressed as a percentage of the principal amount borrowed. It discusses different types of interest rates like simple interest, compound interest, and effective annual interest rate. It also discusses concepts like yield to maturity, risk-free rates of interest, and theories that determine interest rates like classical theory, loanable funds theory, and liquidity preference theory. Interest rates play an important role in finance by acting as the cost of borrowing money.
The document discusses the time value of money concepts. It defines key terms like future value, present value, interest rates, inflation premium, and liquidity premium. It provides examples of calculating future values, present values, interest rates, and loan payments using a financial calculator. The document demonstrates how to use time value of money principles to solve multi-step problems involving investments, loans, and retirement savings.
Lesson: Amortization and Sinking Fund.pptJayLagman3
This document discusses amortization and sinking funds for repaying loans. Amortization involves making regular installment payments that divide each payment into interest and principal portions, with the outstanding principal decreasing with each payment. A sinking fund allows keeping the loan principal constant while accumulating a separate fund with deposits and interest to repay the principal in a lump sum later. Examples are provided for calculating payment amounts under each method. Yield rates equalize the value of payment streams for investors.
- Bonds are used to finance a company's operations and are considered debt, while equity refers to funds from owners. There are advantages like tax deductibility of interest expense but also risks like bankruptcy if obligations cannot be met.
- Bonds have a principal amount, coupon/stated interest rate, and maturity date. They can be secured by assets or callable/convertible. An indenture contract specifies legal provisions.
- Bonds can be issued at par value, at a discount if below par, or at a premium if above par. Discounts/premiums are amortized over the bond term using straight-line or effective interest methods to calculate periodic interest expense.
This document provides an overview of key finance concepts for managers in a course on finance. It defines cash flows, rates of return, interest rates, time value of money, and timelines. It also explains future value and present value calculations for ordinary annuities and annuities due using relevant formulas. Compounding and discounting are shown to be related concepts for dealing with time value of money.
This document defines key terms related to bonds, including par value, coupon rate, coupon payments, maturity date, call price, required return, yield to maturity, and yield to call. It also discusses how the value of a bond changes over time based on its coupon rate and the required rate of return. Finally, it briefly covers default risk, bond ratings, and different types of bonds.
The document discusses the fundamentals of bond valuation and analysis. It defines key terms like nominal yield, current yield, promised yield to maturity, and realized (horizon) yield. It also covers how to compute these yields using present value models and formulas. The document also discusses how interest rates are determined based on supply and demand factors like inflation expectations, risk premiums, and economic conditions. Bond yields are influenced not just by broader interest rate determinants but also issue-specific characteristics that impact risk.
The document discusses accounting for non-current liabilities such as bonds payable and long-term notes payable. It covers topics such as issuing long-term debt, types of bond issues, valuation of bonds at issuance, accounting for bond discounts and premiums using the effective interest method, and accounting for extinguishment of non-current liabilities.
The document discusses interest and economic equivalence. It provides examples and formulas for calculating simple interest, including examples of calculating interest earned on investments and interest paid on loans. It also discusses establishing economic equivalence between cash flows of different amounts that have the same economic value when discounted at an appropriate interest rate. For example, depositing $2,042 today at 8% interest would be equivalent to having $3,000 in 5 years.
Chapter 06 Valuation & Characteristics Of BondsAlamgir Alwani
The document discusses various topics related to bond valuation and characteristics, including:
- Bonds are valued based on the present value of their expected future cash flows.
- Bond prices fluctuate as interest rates change, with bond prices falling when rates rise.
- Other factors like call provisions, convertibility, credit ratings, and bond indentures also impact bond valuation and risk.
- Diluted earnings per share calculations must account for potential share dilution from convertible bonds.
Fixed Income Securities Yield Measures.pptxanurag202001
Sources of Return
Yield Measures for Fixed-Rate Bonds
Yield to Call
Yield to Put
Yield to Worst
Cash Flow Yield
Yield Measures for Floating Rate Notes
Yield Measures for Money Market Instruments
Theoretical Spot rates (Bootstrapping)
Derivation of Forward Rates
Yield Spreads
Riding the Yield Curve
This document defines bonds and bond terminology. It discusses the different types of bonds, including treasury bonds, corporate bonds, municipal bonds, and more. Key bond concepts are explained such as par value, coupon rate, maturity date, bond ratings, and bond valuation. Bond valuation is calculated as the present value of expected future cash flows from interest payments and principal repayment. The relationships between bond values and interest rates are also summarized.
Management of funds is a critical aspect of financial management. Management of funds acts as the foremost concern whether it is in a business undertaking or in an educational institution. Financial management, which is simply meant dealing with management of money matters.
Financial Management is efficient use of economic resources namely capital funds. Financial management is concerned with the managerial decisions that result in the acquisition and financing of short term and long term credits for the firm. Here it deals with the situations that require selection of specific assets, or a combination of assets and the selection of specific problem of size and growth of an enterprise. Herein the analysis deals with the expected inflows and outflows of funds and their effect on managerial objectives. In short, Financial Management deals with Procurement of funds and their effective utilization in the business.Management of funds is a critical aspect of financial management. Management of funds acts as the foremost concern whether it is in a business undertaking or in an educational institution. Financial management, which is simply meant dealing with management of money matters.
Financial Management is efficient use of economic resources namely capital funds. Financial management is concerned with the managerial decisions that result in the acquisition and financing of short term and long term credits for the firm. Here it deals with the situations that require selection of specific assets, or a combination of assets and the selection of specific problem of size and growth of an enterprise. Herein the analysis deals with the expected inflows and outflows of funds and their effect on managerial objectives. In short, Financial Management deals with Procurement of funds and their effective utilization in the business.
Management of funds is a critical aspect of financial management. Management of funds acts as the foremost concern whether it is in a business undertaking or in an educational institution. Financial management, which is simply meant dealing with management of money matters.
Financial Management is efficient use of economic resources namely capital funds. Financial management is concerned with the managerial decisions that result in the acquisition and financing of short term and long term credits for the firm. Here it deals with the situations that require selection of specific assets, or a combination of assets and the selection of specific problem of size and growth of an enterprise. Herein the analysis deals with the expected inflows and outflows of funds and their effect on managerial objectives. In short, Financial Management deals with Procurement of funds and their effective utilization in the business.
Management of funds is a critical aspect of financial management. Management of funds acts as the foremost concern whether it is in a business undertaking or in an educational institution. Financial management, Management of fund
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
More Related Content
Similar to Introduction To Interest Rates And Mortgage Mathematical Calculations
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.
The valuation of bonds ppt @ bec doms financeBabasab Patil
The document discusses the valuation and characteristics of bonds. It covers the basis of bond valuation using present value of expected cash flows. It also discusses bond terminology like maturity, coupon rate, and yield. Bond valuation considers factors like interest rates, time to maturity, coupon payments, and principal repayment. The price of a bond moves in the opposite direction of interest rates.
The document summarizes key concepts related to time value of money including:
1) Money today is worth more than money in the future due to factors like interest rates and inflation.
2) Compound interest means interest is earned on both the principal amount and any previous interest earned.
3) Present value calculations determine the current worth of future cash flows while future value calculates the future worth of present cash flows.
4) Annuities represent a stream of regular payments and their present and future values can be calculated using standard formulas.
This document discusses interest rates and time value of money concepts. It begins by defining simple and compound interest rates. Examples are provided to illustrate calculating interest and total amounts due using simple and compound interest formulas. The concept of economic equivalence is introduced, showing that different cash flows can be equivalent based on a common interest rate. The single payment compound interest formula is derived and used to solve examples of determining future or present values. Overall, the document provides an introduction to fundamental time value of money and interest rate concepts in engineering economics.
This document discusses interest rates and time value of money concepts. It begins by defining simple and compound interest rates. Examples are provided to illustrate calculating interest and total amounts due using simple and compound interest formulas. The concept of economic equivalence is introduced, showing that different cash flows can be equivalent based on a common interest rate. The single payment compound interest formula is derived and used to solve examples of determining future or present values. Overall, the document provides an introduction to fundamental time value of money and interest rate concepts in engineering economics.
The document discusses interest rates and their role in finance. It defines interest rates as the amount charged by a lender to a borrower for any form of debt, generally expressed as a percentage of the principal amount borrowed. It discusses different types of interest rates like simple interest, compound interest, and effective annual interest rate. It also discusses concepts like yield to maturity, risk-free rates of interest, and theories that determine interest rates like classical theory, loanable funds theory, and liquidity preference theory. Interest rates play an important role in finance by acting as the cost of borrowing money.
The document discusses the time value of money concepts. It defines key terms like future value, present value, interest rates, inflation premium, and liquidity premium. It provides examples of calculating future values, present values, interest rates, and loan payments using a financial calculator. The document demonstrates how to use time value of money principles to solve multi-step problems involving investments, loans, and retirement savings.
Lesson: Amortization and Sinking Fund.pptJayLagman3
This document discusses amortization and sinking funds for repaying loans. Amortization involves making regular installment payments that divide each payment into interest and principal portions, with the outstanding principal decreasing with each payment. A sinking fund allows keeping the loan principal constant while accumulating a separate fund with deposits and interest to repay the principal in a lump sum later. Examples are provided for calculating payment amounts under each method. Yield rates equalize the value of payment streams for investors.
- Bonds are used to finance a company's operations and are considered debt, while equity refers to funds from owners. There are advantages like tax deductibility of interest expense but also risks like bankruptcy if obligations cannot be met.
- Bonds have a principal amount, coupon/stated interest rate, and maturity date. They can be secured by assets or callable/convertible. An indenture contract specifies legal provisions.
- Bonds can be issued at par value, at a discount if below par, or at a premium if above par. Discounts/premiums are amortized over the bond term using straight-line or effective interest methods to calculate periodic interest expense.
This document provides an overview of key finance concepts for managers in a course on finance. It defines cash flows, rates of return, interest rates, time value of money, and timelines. It also explains future value and present value calculations for ordinary annuities and annuities due using relevant formulas. Compounding and discounting are shown to be related concepts for dealing with time value of money.
This document defines key terms related to bonds, including par value, coupon rate, coupon payments, maturity date, call price, required return, yield to maturity, and yield to call. It also discusses how the value of a bond changes over time based on its coupon rate and the required rate of return. Finally, it briefly covers default risk, bond ratings, and different types of bonds.
The document discusses the fundamentals of bond valuation and analysis. It defines key terms like nominal yield, current yield, promised yield to maturity, and realized (horizon) yield. It also covers how to compute these yields using present value models and formulas. The document also discusses how interest rates are determined based on supply and demand factors like inflation expectations, risk premiums, and economic conditions. Bond yields are influenced not just by broader interest rate determinants but also issue-specific characteristics that impact risk.
The document discusses accounting for non-current liabilities such as bonds payable and long-term notes payable. It covers topics such as issuing long-term debt, types of bond issues, valuation of bonds at issuance, accounting for bond discounts and premiums using the effective interest method, and accounting for extinguishment of non-current liabilities.
The document discusses interest and economic equivalence. It provides examples and formulas for calculating simple interest, including examples of calculating interest earned on investments and interest paid on loans. It also discusses establishing economic equivalence between cash flows of different amounts that have the same economic value when discounted at an appropriate interest rate. For example, depositing $2,042 today at 8% interest would be equivalent to having $3,000 in 5 years.
Chapter 06 Valuation & Characteristics Of BondsAlamgir Alwani
The document discusses various topics related to bond valuation and characteristics, including:
- Bonds are valued based on the present value of their expected future cash flows.
- Bond prices fluctuate as interest rates change, with bond prices falling when rates rise.
- Other factors like call provisions, convertibility, credit ratings, and bond indentures also impact bond valuation and risk.
- Diluted earnings per share calculations must account for potential share dilution from convertible bonds.
Fixed Income Securities Yield Measures.pptxanurag202001
Sources of Return
Yield Measures for Fixed-Rate Bonds
Yield to Call
Yield to Put
Yield to Worst
Cash Flow Yield
Yield Measures for Floating Rate Notes
Yield Measures for Money Market Instruments
Theoretical Spot rates (Bootstrapping)
Derivation of Forward Rates
Yield Spreads
Riding the Yield Curve
This document defines bonds and bond terminology. It discusses the different types of bonds, including treasury bonds, corporate bonds, municipal bonds, and more. Key bond concepts are explained such as par value, coupon rate, maturity date, bond ratings, and bond valuation. Bond valuation is calculated as the present value of expected future cash flows from interest payments and principal repayment. The relationships between bond values and interest rates are also summarized.
Management of funds is a critical aspect of financial management. Management of funds acts as the foremost concern whether it is in a business undertaking or in an educational institution. Financial management, which is simply meant dealing with management of money matters.
Financial Management is efficient use of economic resources namely capital funds. Financial management is concerned with the managerial decisions that result in the acquisition and financing of short term and long term credits for the firm. Here it deals with the situations that require selection of specific assets, or a combination of assets and the selection of specific problem of size and growth of an enterprise. Herein the analysis deals with the expected inflows and outflows of funds and their effect on managerial objectives. In short, Financial Management deals with Procurement of funds and their effective utilization in the business.Management of funds is a critical aspect of financial management. Management of funds acts as the foremost concern whether it is in a business undertaking or in an educational institution. Financial management, which is simply meant dealing with management of money matters.
Financial Management is efficient use of economic resources namely capital funds. Financial management is concerned with the managerial decisions that result in the acquisition and financing of short term and long term credits for the firm. Here it deals with the situations that require selection of specific assets, or a combination of assets and the selection of specific problem of size and growth of an enterprise. Herein the analysis deals with the expected inflows and outflows of funds and their effect on managerial objectives. In short, Financial Management deals with Procurement of funds and their effective utilization in the business.
Management of funds is a critical aspect of financial management. Management of funds acts as the foremost concern whether it is in a business undertaking or in an educational institution. Financial management, which is simply meant dealing with management of money matters.
Financial Management is efficient use of economic resources namely capital funds. Financial management is concerned with the managerial decisions that result in the acquisition and financing of short term and long term credits for the firm. Here it deals with the situations that require selection of specific assets, or a combination of assets and the selection of specific problem of size and growth of an enterprise. Herein the analysis deals with the expected inflows and outflows of funds and their effect on managerial objectives. In short, Financial Management deals with Procurement of funds and their effective utilization in the business.
Management of funds is a critical aspect of financial management. Management of funds acts as the foremost concern whether it is in a business undertaking or in an educational institution. Financial management, Management of fund
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3. Constant Payment Mortgages
Constant payment mortgage calculations mainly are used in finding out, the size of
payments on a particular loan, the balance owing on an existing loan, or the amount
of a loan that a payment will support.
There are generally 4 financial components in constant payment mortgage loans:
1. Loan Amount
2. Amortization Period
3. Nominal Rate of Interest
4. Payment
4. CONSTANT PAYMENT MORTGAGES - Components
1. Loan Amount: The “Face Value” of the loan. The amount the borrower agrees to
repay. Otherwise known as the “Present Value” pertaining to the payment agreed
upon
2. Amortization Period: The “length” of the loan. What the payments are determined
upon
3. Nominal Rate of Interest: The interest rate the loan is written at - nominal interest
rate must match the frequency of the payments
4. Payment: The amount of principal and interest paid over the life of the loan or
“Amortization Period” that will eventually pay the loan off in full
5. Interest Rate Conversions
Does the compounding frequency given in the question match the payment frequency?
If NO, an Interest Rate Conversion is needed
This is common because of the Interest Act
- The Interest Act requires lenders to disclose the interest rates they charge as
a J1, or J2 which is a”yearly” or “semi annually” compounding
However - most people make payments in different ways. Most commonly
“monthly” especially when pertaining to mortgage payments
6. Rate Conversions - The Formula
1st - Input the amount of interest
2nd - Press “shift” NOM
3rd - Input the number of compounding periods
4th - Press “shift” P/YR
5th - Press “shift” EFF
6th - Input the new number of compounding periods
(must match the frequency they are paying, monthly, quarterly, etc.)
7th - Press "shift” P/YR
8th - Press “shift” NOM
8. Constant Payment Mortgages
- Formulas and Examples
Different examples to go through
➢ Finding the “Payment”
➢ Finding the “Present Value”
➢ Finding the “Interest Rate”
➢ Finding the “Amortization Period”
9. 1. Finding the “Payment”
Ex. Calculate the monthly payment required for the following mortgage:
Principal of $40,000; 14% Interest per annum, compounded semi-
annually;
amortization period of 20 years
Breakdown:
Loan (PV) = $40,000,
Interest J2 = 14%
Monthly Payments
Amortization 20 Yrs
Loan will full be paid off after 20
years
10. 1 . Finding the “Payment”
Ex. Calculate the monthly payment required for the following mortgage:
Principal of $40,000; 14% Interest per annum, compounded semi-
annually;
amortization period of 20 years
Breakdown:
Loan (PV) = $40,000,
Interest J2 = 14%
Monthly Payments
Amortization 20 Yrs
Loan will full be paid off after 20
years
Q. Does the payment frequency match the interest rate compounding frequency?
- If not we need to do a rate conversion
11. Rate Conversions - The Formula
1st - Input the amount of interest
2nd - Press “shift” NOM
3rd - Input the number of compounding periods
4th - Press “shift” P/YR
5th - Press “shift” EFF
6th - Input the new number of compounding periods
(must match the frequency they are paying, monthly, quarterly, etc.)
7th - Press "shift” P/YR
8th - Press “shift” NOM
12. 1. Finding the “Payment”
Ex. Calculate the monthly payment required for the following mortgage:
Principal of $40,000; 14% Interest per annum, compounded semi-annually;
amortization period of 20 years
Breakdown:
Loan (PV) = $40,000, Interest J2
= 14%
Monthly Payments
Amortization 20 Yrs
Loan will full be paid off after 20 years
Step 1. Rate Conversion: J2 to a J12
14 * NOM
2 * P/YR
* EFF%
12 *P/YR
*NOM
Step 2. Complete the Payment Calculation
40 000 PV
20 x 12 = 240 N
0
FV
13. 2. Finding the “Present Value”
EX. An investor wants to decide whether to buy a mortgage that calls for monthly
payments of $390 for 20 years. If the investor can earn j2 = 8%, at what price should
the mortgage be purchased?
Breakdown:
Interest J2 = 8%
Monthly Payments $390
Amortization 20 yrs
Loan will full be paid off after 20
years
14. 2. Finding the “Present Value”
EX. An investor wants to decide whether to buy a mortgage that calls for monthly
payments of $390 for 20 years. If the investor can earn j2 = 8%, at what price should
the mortgage be purchased?
Breakdown:
Interest J2 = 8%
Monthly Payments $390
Amortization 20 yrs
Loan will full be paid off after 20
years
Q. Does the payment frequency match the interest rate compounding frequency?
- If not we need to do a rate conversion
15. Rate Conversions - The Formula
1st - Input the amount of interest
2nd - Press “shift” NOM
3rd - Input the number of compounding periods
4th - Press “shift” P/YR
5th - Press “shift” EFF
6th - Input the new number of compounding periods
(must match the frequency they are paying, monthly, quarterly, etc.)
7th - Press "shift” P/YR
8th - Press “shift” NOM
16. 2. Finding the “Present Value”
EX. An investor wants to decide whether to buy a mortgage that calls for monthly payments of
$390 for 20 years. If the investor can earn j2 = 8%, at what price should the mortgage be
purchased?
Breakdown: Interest J2 = 8% Monthly
Payments $390
Amortization 20 yrs
Loan will full be paid off after 20
years
Step 1. Rate Conversion: J2 to a J12
8 * NOM
2 * P/YR
* EFF%
12 *P/YR
*NOM
Step 2. Complete the PV (Present Value) Calculation
20 x 12 = 240 N
0
FV
390 +/- PMT
47,081.1122383 PV
17. 3. Finding the “Interest Rate”
Ex. A private investor expects to receive $281.72 per month for a
period of 17 years as a result of a mortgage loan she has just advanced.
Calculate the investor’s expected yield (expressed as a nominal rate with
semi-annual compounding) on her investment if the loan was for $23,250.
Breakdown:
Loan (PV) = $23,250
Monthly Payments $281.72
Length of loan 17 Yrs
Loan will fully be paid after 17 years
Express yield with semi-annual
compounding
18. 3. Finding the “Interest Rate”
Ex. A private investor expects to receive $281.72 per month for a
period of 17 years as a result of a mortgage loan she has just advanced.
Calculate the investor’s expected yield (expressed as a nominal rate with
semi-annual compounding) on her investment if the loan was for $23,250.
Breakdown:
Loan (PV) = $23,250
Monthly Payments $281.72
Length of loan 17 Yrs
Loan will fully be paid after 17 years
Express yield with semi-annual
compounding
Q. Does the payment frequency match the interest rate compounding frequency?
- If not we need to do a rate conversion
19. Rate Conversions - The Formula
1st - Input the amount of interest
2nd - Press “shift” NOM
3rd - Input the number of compounding periods
4th - Press “shift” P/YR
5th - Press “shift” EFF
6th - Input the new number of compounding periods
(must match the frequency they are paying, monthly, quarterly, etc.)
7th - Press "shift” P/YR
8th - Press “shift” NOM
20. 3. Finding the “Interest Rate”
Ex. A private investor expects to receive $281.72 per month for a period of 17 years as
a result of a mortgage loan she has just advanced. Calculate the investor’s expected yield
(expressed as a nominal rate with semi-annual compounding) on her investment if the loan
was for $23,250.
Breakdown: Loan (PV) = $23,250 Monthly Payments
$281.72
Length of loan 17 Yrs Loan will fully
be paid off after 17 years
Express yield with semi-annual compounding
Step 1. Find the Nominal Interest rate
23 250 PV
0
FV
281.72 PMT
17 x 12 = 204 N
12
Step 2. Rate Conversion J12 to J2
12.898410 *NOM (already entered)
12 *
P/YR (already entered)
* EFF%
2 *P/YR
*NOM
21. 4. Finding the “Amortization Period”
Ex. A Mortgage in the amount of $150,000 requires the buyer to make
payments of $1,250 per month for as long as necessary to fully amortize
the loan at 8% per annum, compounded semi-annually. How many full
payments of $1,250 will be required?
Breakdown:
Loan (PV) = $150,000
Monthly Payments $1,250
J2 = 8% Loan will fully
be paid off at the end
22. 4. Finding the “Amortization Period”
Ex. A Mortgage in the amount of $150,000 requires the buyer to make
payments of $1,250 per month for as long as necessary to fully amortize
the loan at 8% per annum, compounded semi-annually. How many full
payments of $1,250 will be required?
Breakdown:
Loan (PV) = $150,000
Monthly Payments $1,250
J2 = 8% Loan will fully
be paid off at the end
Q. Does the payment frequency match the interest rate compounding frequency?
- If not we need to do a rate conversion
23. Rate Conversions - The Formula
1st - Input the amount of interest
2nd - Press “shift” NOM
3rd - Input the number of compounding periods
4th - Press “shift” P/YR
5th - Press “shift” EFF
6th - Input the new number of compounding periods
(must match the frequency they are paying, monthly, quarterly, etc.)
7th - Press "shift” P/YR
8th - Press “shift” NOM
24. 4. Finding the “Amortization Period”
Ex. A Mortgage in the amount of $150,000 requires the buyer to make payments of
$1,250 per month for as long as necessary to fully amortize the loan at 8% per
annum, compounded semi-annually. How many full payments of $1,250 will be
required?
Breakdown: Loan (PV) = $150,000 Monthly
Payments $1,250
J2 = 8% Loan will fully be
paid off at the end
Step 1. Rate Conversion: J2 to a J12
8 * NOM
2 * P/YR
* EFF%
12 *P/YR
*NOM
7.869836 = J (Monthly
Step 2. Complete the “N” (Amortization Period) Calculation
150 000 PV
0 FV
-1250 PMT
236.566775 N
236 Full Payments will be Required
25. Outstanding Balances & Introducing Terms
While mortgage payments are calculated using the amortization period, the actual
length of the mortgage contract may be different than the amortization period
The Length of a mortgage contract is referred to as a “Term”. The life of the
mortgage loan is split up into “Terms” because of the sometimes long
Amortization Periods that come with Mortgage Loans.
Due to these Terms, it is important to be able to calculate an Outstanding
Balance, as even though the Term is over, it does not mean that the loan is paid
in full - or in other words “Fully Amortized”
26. Outstanding Balances & Introducing Terms
The terminology we use is as follows;
Fully Amortized Loans: When the mortgage term and amortization period are
the same length of time, the mortgage is referred to as being Fully Amortized
Partially Amortized Loans: When the mortgage term is shorter than the
amortization period, the mortgage is referred to as being Partially Amortized
27. Calculating Outstanding Balances
When you see a Term in a question that is shorter than the amortization period,
we know we have to calculate the outstanding balance.
To Calculate the outstanding balance we first have to find the payments based
on the fully amortized loan and then re-entering the rounded payment back into
the calculator.
If the question tells you to round to a specific number, you must do that and re-
enter the payment. If no instruction to round is given, round to the nearest 2
decimal points, and re-enter. DON'T FORGET TO ENTER IN AS A NEGATIVE
28. Calculating Outstanding Balances - Example
Ex. A borrower is arranging a mortgage with Nicety Finance Company. The loan
amount is $175,000, the interest rate is 4.5% per annum, compounded semi-
annually, the amortization period is 20 years, and the contractual term is 2 years. If
payments are made monthly and rounded up to the next higher $10, calculate the
outstanding balance at the end of the loan term.
Breakdown:
Loan (PV) = $175,000,
Interest J2 = 4.5%
Monthly Payments (Nxt high$10)
Amortization 20 Yrs
29. Calculating Outstanding Balances - Example
Ex. A borrower is arranging a mortgage with Nicety Finance Company. The loan
amount is $175,000, the interest rate is 4.5% per annum, compounded semi-
annually, the amortization period is 20 years, and the contractual term is 2 years. If
payments are made monthly and rounded up to the next higher $10, calculate the
outstanding balance at the end of the loan term.
Breakdown:
Loan (PV) = $175,000,
Interest J2 = 4.5%
Monthly Payments (Nxt high$10)
Amortization 20 Yrs
Term 2 Yrs
30. Calculating Outstanding Balances - Example
Breakdown: Loan (PV) = $175,000, Interest J2
= 4.5%
Monthly Payments (Nxt high$10)
Amortization 20 Yrs
Term 2 Yrs
Step 1. Rate Conversion: J2 to a J12
4.5 * NOM
2 * P/YR
* EFF%
12 *P/YR
4.458383 *NOM
Step 2. Finish payment calculation
175 000 PV
20 x 12 N
0 FV
Step 3. Re-Enter Payment & Calculate Outstanding Balance
based on length of Term
1,110 +/- PMT
2 x 12= 24 Input shift AMORT
= = =
-163,479.729771 FV
Step 4. Round answer to the nearest 2 decimal places
31. Accelerated Bi-Weekly Payments
There are differences between payment options for mortgages
Constant Monthly Payments: Equal Payments that are paid once a month
Bi-Weekly Payments: Constant Payments that are paid every two weeks
Accelerated Bi-Weekly Payments: Constant Payments that are equal to half of the
regular monthly payment and are paid every two weeks
Accelerating payments is a very effective way to pay off a mortgage loan faster and to
reduce amount if interest paid. It also works with many peoples pay structure of
receiving income every 2 weeks
32. Accelerated Bi-Weekly Payments
Accelerated Bi-Weekly Payments: Constant Payments that are equal to half of the
regular monthly payment and are paid every two weeks
To calculate the Accelerated Bi-Weekly payment, you must first find the Constant
Monthly Payment based on the Fully Amortized Loan and divide it in half.
33. Accelerated Bi-Weekly Payments - Example
Ex. A mortgage loan has a face value of $350,000, an interest rate of j2 = 5.5%,
an amortization period of 20 years, a term of 3 years, and an option to make
accelerated biweekly payments. What is the amount of the accelerated biweekly
payment rounded up to the next highest dollar?
Breakdown:
Loan (PV) = $350,000,
Interest J2 = 5.5%
Biweekly Payments
Amortization 20 Yrs
Term 3 Yrs
34. Accelerated Bi-Weekly Payments - Example
Ex. A mortgage loan has a face value of $350,000, an interest rate of j2 = 5.5%,
an amortization period of 20 years, a term of 3 years, and an option to make
accelerated biweekly payments. What is the amount of the accelerated biweekly
payment rounded up to the next highest dollar?
Breakdown:
Loan (PV) = $350,000,
Interest J2 = 5.5%
Biweekly Payments
Amortization 20 Yrs
Term 3 Yrs
Q. Does the payment frequency match the interest rate compounding frequency?
- If not we need to do a rate conversion
35. Accelerated Bi-Weekly Payments - Example
Ex. A mortgage loan has a face value of $350,000, an interest rate of j2 = 5.5%, an
amortization period of 20 years, a term of 3 years, and an option to make accelerated biweekly
payments. What is the amount of the accelerated biweekly payment rounded up to the next
highest dollar? Breakdown:
Loan (PV) = $350,000,
Interest J2 = 5.5%
Biweekly Payments (Nxt high$1)
Amortization 20 Yrs
Term 3 Yrs
NOTE: To calculate the Accelerated Bi-Weekly payment, you must first find the
Constant Monthly Payment based on the Fully Amortized Loan and divide it in half.
Step 1. Rate Conversion: J2 to a J12
5.5 * NOM
2 * P/YR
* EFF%
12 *P/YR
*NOM
Step 2. Complete the Payment Calculation
350,000 PV
20 x 12 = 240 N
0
FV
-2,395.36951 PMT
2,395.36951 ÷ 2 =
36. Principal and Interest Splits
It is sometimes necessary to calculate either the Interest or the Principal of a Constant
Payment Mortgage Loan at any given time during the life of the loan.
It is good information to know if thinking of re-signing the loan, looking to see just
where you are in regards of repayment, or because interest on payments can
sometimes be deducted as an expense for income tax purposes
- To find the Principal and Interest at any given time in the Mortgage Loan life, we
first have to find the Payments based on the fully amortized loan and then re-
entering the rounded payment back into the calculator.
- At that time we can then use our financial calculator to find the Principal/Interest
37. Principal and Interest Splits - Calculator Keys
SHIFT Key : To access the Orange keys needed
in our Financial Calculator
INPUT Key : To Input the value of time into our
AMORT key
AMORT Key : The key that calculates the
Amortization of each equation. - Calculates
Outstanding Balance, Interest and Principal
separately for our knowledge and use
38. Principal and Interest - Example
Ex. A borrower has arranged a $159,900 mortgage at j12 = 12% with a 25-year
amortization, 5-year term, and monthly payments. If all payments are paid when due,
how much principal was paid off during the 5-year term?
Breakdown:
Loan (PV) = $159,900,
Interest J12 = 12%
Monthly Pmys
Amortization 25 Yrs
Term 5 Yrs
39. Principal and Interest - Example
Ex. A borrower has arranged a $159,900 mortgage at j12 = 12% with a 25-year
amortization, 5-year term, and monthly payments. If all payments are paid when due,
how much principal was paid off during the 5-year term?
Breakdown:
Loan (PV) = $159,900,
Interest J12 = 12%
Monthly Pmts
Amortization 25 Yrs
Term 5 Yrs
Q. Does the payment frequency match the interest rate compounding frequency?
- If not we need to do a rate conversion
40. Principal and Interest - Example
Ex. A borrower has arranged a $159,900 mortgage at j12 = 12% with a 25-year
amortization, 5-year term, and monthly payments. If all payments are paid when due, how much
principal was paid off during the 5-year term?
Breakdown: Loan (PV) = $159,900, Interest
J12 = 12%
Monthly Pmts
Amortization 25 Yrs
Term 5 Yrs
Step 1. Find the Payment based on the Full Loan, round
and re-enter payment into PMT key
159,900 PV
25 x 12 = 300 N
0
FV
12 *
Step 2. Find the amount of principal that has been paid
off during the 5-year term
1
INPUT
60 *
AMORT
41. Principal and Interest - Example
Ex. A borrower has arranged a $159,900 mortgage at j12 = 12% with a 25-year
amortization, 5-year term, and monthly payments. If all payments are paid when due, how much
principal was paid off during the 5-year term?
Breakdown: Loan (PV) = $159,900, Interest
J12 = 12%
Monthly Pmts
Amortization 25 Yrs
Term 5 Yrs
Step 1. Find the Payment based on the Full Loan, round
and re-enter payment into PMT key
159,900 PV
25 x 12 = 300 N
0
FV
12 *
Step 2. Find the amount of principal that has been paid
off during the 5-year term
1
INPUT
60 *
AMORT