Assume the car can be purchased for 0% down for 60 months (in lieu of rebate).
A car with a sticker price of $42,200 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.)
(d) State whether the 0% APR or the 2.5% add-on rate should be preferred.
0% APR 2.5% add-on rate
To find the monthly payment in each scenario, we can use the following formula:
Monthly payment = Principal / Number of months
where Principal is the amount financed.
(a) Since the car can be purchased for 0% down for 60 months, the total amount financed is equal to the sticker price minus the rebates:
Principal = Sticker price - Rebates
= $42,200 - $5,100
= $37,100
Therefore, the monthly payment at 0% APR is:
Monthly payment = $37,100 / 60
= $618.33 (rounded to the nearest cent)
(b) To calculate the monthly payment at a 2.5% add-on interest rate, we need to find the total amount financed with interest, which is the principal plus the interest over the loan term.
Principal = $37,100
Interest = Principal * Interest rate = $37,100 * 2.5% = $927.50
Total amount financed = Principal + Interest = $37,100 + $927.50 = $38,027.50
Monthly payment = $38,027.50 / 60
= $633.79 (rounded to the nearest cent)
(c) To find the APR using the APR approximation formula, we first need to calculate the add-on interest rate equivalent to APR.
APR = (Add-on interest rate) / (1 - Add-on interest rate * Number of payments)
Given:
Add-on interest rate = 2.5%
Number of payments = 60
APR = 0.025 / (1 - 0.025 * 60)
= 1.5% (rounded to one decimal place)
(d) Comparing the 0% APR and the 2.5% add-on rate options, the 0% APR should be preferred as it does not involve any interest payment, making it a better deal for the borrower.