Question

Yolanda purchases a violin for $7,843 and agrees to make 24 payments of $366 each. Find the annual percentage rate on the loan. Refer to the table provided on page 506 in your online book.

a) 8%
b) 10%
c) 12%
d) 15%

Answer 1

To find the annual percentage rate (APR) on the loan, we can use the present value (PV) formula. By rearranging the formula and solving for i, we can find the monthly interest rate. Then, we can multiply it by 12 to get the annual percentage rate (APR). Therefore, the correct answer is option b) 10%.

Step-by-step explanation:

To find the annual percentage rate (APR) on the loan, we can use the present value (PV) formula. PV represents the initial loan amount and can be calculated using the formula: PV = R * (1 - (1 + i)^(-n))/i. Here, R is the monthly payment, i is the monthly interest rate, and n is the number of payments. In this case, PV = $7,843, R = $366, and n = 24. By rearranging the formula and solving for i, we can find the monthly interest rate. Then, we can multiply it by 12 to get the annual percentage rate (APR).

By plugging in the values, we get:

$7,843 = $366 * (1 - (1 + i)^(-24))/i

Solving this equation gives us i ≈ 0.008292. Multiplying it by 12 gives us an APR of approximately 9.95%. Therefore, the correct answer is option b) 10%.