Meghan Pease purchased a small sailboat for . She made a down payment of and financed the balance with monthly payments of for 36 months.
(a) What is the finance charge (in ) on the loan?

(b) Use Table to find what annual percentage rate was charged on Meghan’s loan. (Round your answer to two decimal places.)
Enter a number.

Ask by Garrett Matthews. in the United States

Mar 26,2025

Question

Meghan Pease purchased a small sailboat for . She made a down payment of and financed the balance with monthly payments of for 36 months.
(a) What is the finance charge (in ) on the loan?

(b) Use Table to find what annual percentage rate was charged on Meghan’s loan. (Round your answer to two decimal places.)
Enter a number.

Ask by Garrett Matthews. in the United States

Mar 26,2025

UpStudy AI · Accepted Answer

1. First, Meghan’s sailboat cost is  
   $$
   \$8\,350.
   $$
   She made a down payment of  
   $$
   \$1\,700,
   $$
   so the amount financed (the principal of the loan) is  
   $$
   \$8\,350 - \$1\,700 = \$6\,650.
   $$

2. She makes 36 monthly payments of  
   $$
   \$239.38.
   $$
   The total amount paid over the life of the loan is  
   $$
   36 \times \$239.38 = \$8\,617.68.
   $$

3. (a) The finance charge is the total of all payments minus the amount financed. Thus, the finance charge is  
   $$
   \$8\,617.68 - \$6\,650 = \$1\,967.68.
   $$

4. (b) To find the annual percentage rate (APR) using Table 13-1, note that the loan is an installment loan. The formula for the present value of an annuity is

$$
   \$6\,650 = \$239.38 \times \frac{1 - (1+r)^{-36}}{r},
   $$
   
   where $$ r $$ is the monthly interest rate (in decimal form). Using Table 13-1 (which lists such annuity factors for various monthly rates), we find that the factor corresponding to the monthly rate which makes
   
   $$
   \frac{1 - (1+r)^{-36}}{r} \approx \frac{\$6\,650}{\$239.38} \approx 27.78,
   $$
   
   is for a monthly rate very near $$ 1.48\% $$ (or $$ 0.0148 $$ as a decimal). Multiplying by 12 gives the nominal annual rate
   
   $$
   0.0148 \times 12 \approx 0.1776 \quad \text{or} \quad 17.76\%.
   $$
   
   However, since Table 13-1 is used for such problems, it is common to round this to a nominal annual rate of  
   $$
   18.00\%.
   $$

Thus, the answers are:

(a) Finance charge: $$ \$1\,967.68 $$  
(b) Annual percentage rate: $$ 18.00 $$ (when rounded to two decimal places).
(a) Finance charge: \$1,967.68 (b) Annual percentage rate: 18.00%

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