Assume the car can be purchased for 0% down for 60 months (in lieu of rebate).
A car with a sticker price of $42,100 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.)
$ 1
(b) Find the monthly payment if financed at 2.5% add-on interest for 60 months. (Round your answer to the nearest cent.)
$ 2
(c) Use the APR approximation formula to find the APR for part (b). (Round your answer to one decimal place.)
3 %
(d) State whether the 0% APR or the 2.5% add-on rate should be preferred.
0% APR
2.5% add-on rate
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(a) To find the monthly payment when financing the car for 60 months at 0% APR, you can divide the total purchase price by the number of months. In this case, the car's sticker price is $42,100, and since there's no down payment, that's the total purchase price.
Monthly payment = Total purchase price / Number of months
Monthly payment = $42,100 / 60
Using a calculator, the monthly payment would be approximately $701.67.
Therefore, the monthly payment if financed for 60 months at 0% APR is $701.67.
(b) To find the monthly payment when financing the car at 2.5% add-on interest for 60 months, you need to calculate the interest amount and add it to the principal.
First, calculate the interest amount:
Interest amount = Principal x Interest rate
Principal = Sticker price - Rebates = $42,100 - $5,100 = $37,000 (this is the amount being financed)
Interest rate = 2.5% = 0.025
Interest amount = $37,000 x 0.025
Using a calculator, the interest amount would be $925.
Next, add the interest amount to the principal and divide by the number of months to get the monthly payment:
Monthly payment = (Principal + Interest amount) / Number of months
Monthly payment = ($37,000 + $925) / 60
Using a calculator, the monthly payment would be approximately $651.25.
Therefore, the monthly payment if financed at 2.5% add-on interest for 60 months is $651.25.
(c) To use the APR approximation formula to find the APR for the 2.5% add-on rate, we can use the following formula:
APR = (Add-on interest rate / Number of months) x 12 x 100
In this case, the add-on interest rate is 2.5% and the number of months is 60.
APR = (2.5 / 60) x 12 x 100
Using a calculator, the APR would be approximately 5%.
Therefore, the APR for the financing option with a 2.5% add-on rate is approximately 5%.
(d) Based on the calculations, the 0% APR option would be preferred because it has a lower monthly payment compared to the 2.5% add-on rate option. Additionally, the 0% APR means that no interest is being charged, making it the more favorable choice financially.