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.)
(a) To find the monthly payment if financed for 60 months at 0% APR, we need to know the financed amount. The financed amount can be calculated by subtracting the rebates from the sticker price:
Financed amount = Sticker price - Rebates
= $42,500 - $5,100
= $37,400
Since the interest rate is 0%, there will be no interest charges. Therefore, the monthly payment will be the financed amount divided by the number of months:
Monthly payment = Financed amount / Number of months
= $37,400 / 60
= $623.33
Therefore, the monthly payment if financed for 60 months at 0% APR is $623.33.
(b) To find the monthly payment if financed at 2.5% add-on interest for 60 months, we need to calculate the total amount paid over the loan term and then divide it by the number of months.
The total amount paid is calculated by adding the financed amount and the interest charges. The interest charges can be calculated using the add-on interest formula:
Interest charges = Financed amount * Interest rate
= $37,400 * 0.025
= $935
Total amount paid = Financed amount + Interest charges
= $37,400 + $935
= $38,335
The monthly payment is then calculated by dividing the total amount paid by the number of months:
Monthly payment = Total amount paid / Number of months
= $38,335 / 60
= $638.92
Therefore, the monthly payment if financed at 2.5% add-on interest for 60 months is $638.92.
(c) To find the APR using the APR approximation formula, we need to rearrange the formula to solve for the APR:
APR = (Interest charges / Financed amount) * (Number of months / 2) * (100 / 1)
Using the values calculated in part (b), we can substitute them into the formula:
APR = ($935 / $37,400) * (60 / 2) * (100 / 1)
= 0.025 * 30 * 100
= 75
Therefore, the APR for part (b) is 75%.