Prepared by Johnny Howard

© 2015 South-Western, a part of Cengage Learning

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Annuities

• Annuity

• Present value of an annuity

• Sinking fund

• Future value of an annuity

• Ordinary annuity

• Beginning of the annuity

• End of the annuity

T E R M S

1

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Figure 23.1 Diagram of an Ordinary Annuity

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Figure 23.2 Future Value of an Ordinary Annuity

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to Compute the Future Value of an Annuity

and Total Interest Earned

1. Determine the annuity factor (FVAF) using either a

calculator with exponents or Table 23-1.

2. Multiply the payment amount by the annuity factor

(FVAF). The product is the future value of the

annuity (FVA), including interest.

3. Multiply the payment amount by the number of

payments. The product is the total payments.

4. Subtract the total payments from the future value

of the annuity (FVA). The difference is the total

interest earned.

1

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to Find the Size of the Payment in an Annuity,

Given Its Future Value

1. Determine the annuity factor (FVAF) using Table

23-1 or a calculator.

2. Divide the future value by the annuity factor. The

quotient is the amount of each payment in the

annuity.

2

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Figure 23.3 Present Value of an Ordinary Annuity

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to Compute the Present Value of an Annuity and

Total Interest Earned

1. Determine the annuity factor (PVAF) using either a

calculator with exponents or Table 23-2.

2. Multiply the payment amount by the annuity factor

(PVAF). The product is the present value of the

annuity (PVA).

3. Multiply the payment amount by the number of

payments. The product is the total of all

payments.

4. Subtract the present value of the annuity from the

total of all payments. The difference is the total

interest earned.

3

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to Find the Size of the Payment in an Annuity,

Given the Present Value

1. Determine the annuity factor (PVAF) using a

calculator or Table 23-2.

2. Divide the present value by the annuity factor

(PVAF). The quotient is the amount of the

payments in the annuity. As a formula, Step 2

could be written as Pmt = PVA ÷ PVAF.

4

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to Find the Size of the Payment to Amortize a Loan

1. Determine the annuity factor (PVAF) using

Table 23-2 or a calculator.

2. Divide the loan amount by the annuity factor

(PVAF). The quotient is the amount of the

monthly loan payments.

5

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to Create an Amortization Schedule

For each row except the last:

1. Interest payment = Unpaid balance × Monthly interest rate

2. Principal payment = Monthly payment – Interest payment

3. New unpaid balance = Old unpaid balance – Principal

payment

For the last row:

1. Interest payment = Unpaid balance × Monthly interest rate

2. (Then ADD) Monthly payment = Unpaid balance + Interest

payment

3. Principal payment = Unpaid balance

6

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Chapter Terms for Review

annuity

future value of an annuity

future value of an annuity factor (FVAF)

ordinary annuity

present value of an annuity

present value of an annuity factor (PVAF)

sinking fund

time line

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Assignment 23.1: Annuities—Future Value

A For each of the following annuities, find the future value or the amount of the periodic

payment. Round answers to the nearest cent.

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Assignment 23.1: Annuities—Future Value

A For each of the following annuities, find the future value or the amount of the periodic

payment. Round answers to the nearest cent.

23–23 © 2015 South-Western, a part of Cengage Learning

Assignment 23.1: Annuities—Future Value

B For each of the following annuities, find the future value, the amount of the periodic

payment, or the total amount of interest paid. Round answers to the nearest cent.

23–24 © 2015 South-Western, a part of Cengage Learning

Assignment 23.1: Annuities—Future Value

B For each of the following annuities, find the future value, the amount of the periodic

payment, or the total amount of interest paid. Round answers to the nearest cent.

23–25 © 2015 South-Western, a part of Cengage Learning

Assignment 23.1: Annuities—Future Value

B For each of the following annuities, find the future value, the amount of the periodic

payment, or the total amount of interest paid. Round answers to the nearest cent.

23–26 © 2015 South-Western, a part of Cengage Learning

Assignment 23.1: Annuities—Future Value

C In each of the following applications, find the future value of the annuity, the amount of

the periodic payment, or the total amount of interest earned. Round answers to the

nearest cent.

23–27 © 2015 South-Western, a part of Cengage Learning

Assignment 23.1: Annuities—Future Value

C In each of the following applications, find the future value of the annuity, the amount of

the periodic payment, or the total amount of interest earned. Round answers to the

nearest cent.

23–28 © 2015 South-Western, a part of Cengage Learning

Assignment 23.1: Annuities—Future Value

C In each of the following applications, find the future value of the annuity, the amount of

the periodic payment, or the total amount of interest earned. Round answers to the

nearest cent.

23–29 © 2015 South-Western, a part of Cengage Learning

Assignment 23.1: Annuities—Future Value

C In each of the following applications, find the future value of the annuity, the amount of

the periodic payment, or the total amount of interest earned. Round answers to the

nearest cent.

23–30 © 2015 South-Western, a part of Cengage Learning

Assignment 23.1: Annuities—Future Value

C In each of the following applications, find the future value of the annuity, the amount of

the periodic payment, or the total amount of interest earned. Round answers to the

nearest cent.

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Assignment 23.2: Annuities—Present Value

A For each of the following annuities, find the present value or the amount of the periodic

payment. Round answers to the nearest cent.

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Assignment 23.2: Annuities—Present Value

A For each of the following annuities, find the present value or the amount of the periodic

payment. Round answers to the nearest cent.

23–33 © 2015 South-Western, a part of Cengage Learning

Assignment 23.2: Annuities—Present Value

B For each of the following annuities, find the present value, the amount of the periodic

payment, or the total amount of interest paid. Round answers to the nearest cent.

23–34 © 2015 South-Western, a part of Cengage Learning

Assignment 23.2: Annuities—Present Value

B For each of the following annuities, find the present value, the amount of the periodic

payment, or the total amount of interest paid. Round answers to the nearest cent.

23–35 © 2015 South-Western, a part of Cengage Learning

Assignment 23.2: Annuities—Present Value

B For each of the following annuities, find the present value, the amount of the periodic

payment, or the total amount of interest paid. Round answers to the nearest cent.

23–36 © 2015 South-Western, a part of Cengage Learning

Assignment 23.2: Annuities—Present Value

C In each of the following applications, find the present value of the annuity, the amount of

the periodic payment, or the total amount of interest earned. Round answers to the

nearest cent.

23–37 © 2015 South-Western, a part of Cengage Learning

Assignment 23.2: Annuities—Present Value

C In each of the following applications, find the present value of the annuity, the amount of

the periodic payment, or the total amount of interest earned. Round answers to the

nearest cent.

23–38 © 2015 South-Western, a part of Cengage Learning

Assignment 23.2: Annuities—Present Value

C In each of the following applications, find the present value of the annuity, the amount of

the periodic payment, or the total amount of interest earned. Round answers to the

nearest cent.

23–39 © 2015 South-Western, a part of Cengage Learning

Assignment 23.2: Annuities—Present Value

C In each of the following applications, find the present value of the annuity, the amount of

the periodic payment, or the total amount of interest earned. Round answers to the

nearest cent.

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Assignment 23.2: Annuities—Present Value

D Gary Robinson purchased some new equipment and furniture for his office. Instead of

charging it on a credit card, which had an 18% interest rate, Gary negotiated financing

with the office supply dealer. The total purchase amount was $6,450 and it was amortized

over 4 months. The interest rate was 6% per year, or 0.5% per month. The first three

monthly payments were each $1,632.70. Complete the first three lines of the following

amortization schedule. Round answers to the nearest cent.