Jeremy is in the process of purchasing a car. The list price of the car is €36,000. If Jeremy pays cash for the car, the dealer will reduce the price by 10%. Otherwise, the dealer will provide financing where Jeremy must pay €7,705 at the end of each of the next five years. Compute the effective interest rate to the nearest percent that Jeremy would pay if he chooses to make the five annual payments?

Question

Quizplus · Accepted Answer

If Jeremy pays cash for the car, he will get a 10% discount. Therefore, he will pay 90% of the list price which is:

0.9 x €36,000 = €32,400

If he chooses financing, he will pay €7,705 per year for five years, which makes the total cost:

€7,705 x 5 = €38,525

To find the effective interest rate, we can use the following formula:

Total cost = Principal x (1 + r)n

Where:

- Principal = €32,400 
- Total cost = €38,525 
- n = 5 (since there are five payments)

Solving for r, we get:

r = [(Total cost / Principal)1/n - 1] x 100%

r = [(€38,525 / €32,400)1/5 - 1] x 100%

r = 6.04%

Therefore, the effective interest rate is approximately 6%, which is lower than the 10% discount offered by paying cash. Hence, financing seems to be the better choice.

Jeremy Is in the Process of Purchasing a Car