10.4 Installment Buying 619 Microsoft Excel Read the Technology Tip on page 608. To determine the monthly payment using Excel, place the letters P, r, n, t, and m in cells A1 through E1, respectively. In cells A2 through D2, place the values 1500, 0.06, 12, and 2, respectively. In cell E2, use the formula box to add the formula = − + − (A2*(B2/C2))/(1 (1 B2/C2) ^ ( C2*D2)) After the Enter key is pressed, the result is as follows. 1 A B C D E 2 3 p r n t m 1500 0.06 12 2 66.48091538 Sheet2 Ready Sheet3 Sheet1 Example 4 Determining the APR Bob is purchasing a motorcycle that sells for $26,500, including taxes and fees. Bob decides to make a $5000 down payment and finance the balance, $21,500, through his bank. The loan officer informs him that his monthly payment will be $644.40 for 36 months. a) Determine the finance charge. b) Determine the APR. Solution a) To determine the finance charge, we first determine the total installment price. The total installment price is the down payment plus the total monthly installment payments. Total installment price $5000 (36 $644.40) $5000 $23,198.40 $28,198.40 = + × = + = The finance charge is the total installment price minus the selling price. Finance charge $28,198.40 $26,500 $1698.40 = − = Therefore, Bob will pay a finance charge of $1698.40 b) To determine the annual percentage rate, use Table 10.2. First divide the finance charge by the amount financed and multiply the quotient by 100. The result is the finance charge per $100 of the amount financed. Finance charge Amount financed 100 1698.40 21,500 100 0.07899535 100 7.90 × = × ≈ × ≈ Thus, Bob pays about $7.90 for each $100 being financed. To use Table 10.2, look for 36 in the far-left column under the heading Number of Payments. Next, move across the table to the right until you find the value that is closest to $7.90. The value closest to 7.90 is 7.8952, circled in blue. At the top of this column is the value of 5.0%. Therefore, the annual percentage rate is approximately 5.0%. 7 Now try Exercise 23 Much more complete APR tables similar to Table 10.2 are available at your local lending institution or on the Internet. Also available on the Internet and on smartphone apps are loan “calculators” that will calculate your payment for you if you provide the loan amount, the length of the loan, and the APR. One such loan calculator can be found at Bankrate.com. Learning Catalytics Keyword: Angel-SOM-10.4 (See Preface for additional details.)
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