Assume the car can be purchased for 0% down for 60 months (in lieu of rebate). A car with a sticker price of $42,500 with factory and dealer rebates of $5,100 (a) Find the monthly payment if financed for 60 months at 0% APR. (Round your answer to the nearest cent.) $ (b) Find the monthly payment if financed at 2.5% add-on interest for 60 months. (Round your answer to the nearest cent.) $ (c) Use the APR approximation formula to find the APR for part (b). (Round your answer to one decimal place.)

Question

Assume the car can be purchased for 0% down for 60 months (in lieu of rebate). A car with a sticker price of $42,500 with factory and dealer rebates of $5,100 (a) Find the monthly payment if financed for 60 months at 0% APR. (Round your answer to the nearest cent.) $ (b) Find the monthly payment if financed at 2.5% add-on interest for 60 months. (Round your answer to the nearest cent.) $ (c) Use the APR approximation formula to find the APR for part (b). (Round your answer to one decimal place.)

Answer 1

To find the monthly payment for a car financed with 0% APR for 60 months, we can simply divide the purchase price by the number of months.

(a) Monthly payment at 0% APR:
The purchase price of the car is $42,500, so the monthly payment would be $42,500 divided by 60 months, which is $708.33. Therefore, the monthly payment at 0% APR is $708.33.

To find the monthly payment for a car financed at 2.5% add-on interest for 60 months, we can use the following formula:

Monthly payment = (Purchase price + Total interest) / Number of months

(b) Monthly payment at 2.5% add-on interest:
The purchase price of the car is $42,500, and we need to calculate the total interest. Since the interest is added on top of the principal, we can calculate it by multiplying the purchase price by the interest rate (0.025 or 2.5%).

Total interest = Purchase price * Interest rate = $42,500 * 0.025 = $1,062.50

Now, we can calculate the monthly payment using the formula:

Monthly payment = ($42,500 + $1,062.50) / 60 = $43,562.50 / 60 = $726.04

Therefore, the monthly payment at 2.5% add-on interest is $726.04.

(c) APR approximation formula:
To find the APR for the loan with 2.5% add-on interest, we can use the following approximation formula:

APR = (Interest rate / Principal) * (1 + 1 / Number of payments) * 100

In this case, the interest rate is 2.5%, the principal is $42,500, and the number of payments is 60.

APR = (0.025 / $42,500) * (1 + 1 / 60) * 100

Simplifying this equation, we get:

APR = 59.5238

Therefore, the APR for the loan with 2.5% add-on interest is approximately 59.5%.