Question

Lina Martinez wants to buy a new high-end audio system for her car. The system is being sold by two dealers in town, both of whom sell the equipment for the same price of $2,000. Lina can buy the equipment from Dealer A, with no money down, by making payments of $118.28 a month for 18 months; she can buy the same equipment from Dealer B by making 36 monthly payments of $70.31 (again, with no money down). Lina is considering purchasing the system from Dealer B because of the lower payment.

Find the APR for Dealer A.
Use the financial calculator and Find the APR for Dealer B

Answer 1

To determine the best option for purchasing the high-end audio system, one must calculate the APR for both Dealer A and Dealer B, taking into account the total payments and the number of monthly payments for each.

Step-by-step explanation:

Lina Martinez is considering two options for purchasing a high-end audio system with differing finance terms. To calculate the Annual Percentage Rate (APR) for Dealer A and Dealer B, we need to use the formula for the APR of a loan which accounts for interest as well as the time frame of payments. Calculating the APR for Dealer A requires knowing the total amount paid to the dealer, the loan amount (the price of the system), and the number of monthly payments. In this case, the total payments would be 18 months times $118.28 per month. To find the APR, we would use a financial calculator or an equivalent online tool that allows for the input of these values to solve for the interest rate.

Similarly, for Dealer B, we would calculate the total amount paid over the 36 months at $70.31 per month and again use a financial calculator or online APR calculator to determine the APR.

When deciding between the two, Lina should consider not only the monthly payment amounts but also the total amount paid over time and the APR, as a lower monthly payment might end up costing more in the long run if the APR is higher.

Answer 2

dealer A:

total interest charged = ($118.28 x 18 months) - $2,000 = $129.04

APR = [($129.04 / $2,000) / 1.5 periods] x 100% = 4.3%

dealer B:

total interest charged = ($70.31 x 36 months) - $2,000 = $531.16

APR = [($531.16 / $2,000) / 3 periods] x 100% = 8.85%

The APR charged by dealer A is much lower than the APR charged by dealer B. Even thought the monthly payments are much lower for dealer B, the total amount of interest charged is much higher.