Prepared by Johnny Howard 2015 South-Western, a part of Cengage Learning

Prepared by Johnny Howard

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T E R M S Annuities Annuity Present value of an annuity Sinking fund Future value of an annuity Ordinary annuity Beginning of the annuity End of the annuity 1 23 3

Figure 23.1 Diagram of an Ordinary Annuity 23 4

Figure 23.2 Future Value of an Ordinary Annuity 23 5

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 23 6

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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 23 8

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Figure 23.3 Present Value of an Ordinary Annuity 23 11

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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 23 13

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 23 14

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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 23 16

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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 23 18

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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 23 20

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 21

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 22

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 23

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 26

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 31

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 32

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 33

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 36

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. 23 40