Jeremy is in the process of purchasing a car.The list price of the car is $32,000.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 $6,850 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 pay $32,000 – 10% = $28,800.
If he chooses financing, he will pay $6,850 annually for five years, a total of $34,250.
To calculate the effective interest rate for the financing option, we need to find the interest rate that would make the total payments of $34,250 equivalent to the discounted cash price of $28,800.

Using the present value formula:
PV = PMT x [(1 – (1 + r)^-n) / r]
where PV is the present value, PMT is the payment, r is the interest rate, and n is the number of periods.

For the financing option:
PV = $34,250
PMT = $6,850
n = 5
We need to solve for r.
$34,250 = $6,850 x [(1 – (1 + r)^-5) / r]
5 x $6,850 = $6,850 x [(1 – (1 + r)^-5) / r]
5 = [(1 – (1 + r)^-5) / r]
5r = 1 – (1 + r)^-5
(1 + r)^-5 = 1 – 5r
Taking the fifth root of both sides:
1 + r = (1 – 5r)^(1/5)
r = (1 – (1 – 5r)^(1/5))

Using trial and error or a spreadsheet, we can find that r ≈ 0.0697.
Therefore, the effective interest rate to the nearest percent is 6.97%, which rounds up to 7%, or choice C.

Jeremy Is in the Process of Purchasing a Car