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 for financing the car for 60 months at 0% APR, you can use a loan payment calculator or a financial formula.
The formula to calculate the monthly payment for a loan is:
Monthly Payment = Loan Amount / Number of Months
In this case, the loan amount is the sticker price of the car minus the rebates, which is $42,100 - $5,100 = $37,000. The number of months is 60.
So, the monthly payment would be:
Monthly Payment = $37,000 / 60 = $616.67
Therefore, the monthly payment, rounded to the nearest cent, would be $616.67.
(b) To find the monthly payment for financing the car at 2.5% add-on interest for 60 months, you can use a similar formula to the one used in part (a), but with an additional component for the interest.
Monthly Payment = (Loan Amount + Interest Amount) / Number of Months
The interest amount can be calculated as:
Interest Amount = Loan Amount * Interest Rate
In this case, the loan amount is still $37,000 and the interest rate is 2.5%. To convert the add-on interest rate to a decimal, divide it by 100. So, the interest rate in decimal form would be 0.025.
Interest Amount = $37,000 * 0.025 = $925
Now, we can calculate the monthly payment:
Monthly Payment = ($37,000 + $925) / 60 = $621.25
Therefore, the monthly payment, rounded to the nearest cent, would be $621.25.
(c) To use the APR approximation formula to find the APR for the loan in part (b), you need to first determine the finance charge. The finance charge is the interest amount over the life of the loan.
Finance Charge = (Monthly Payment * Number of Months) - Loan Amount
In this case, the monthly payment is $621.25 and the number of months is 60.
Finance Charge = ($621.25 * 60) - $37,000 = $27,675
Now, you can use the APR approximation formula:
APR = (Finance Charge / Loan Amount) * (12 / Number of Months)
APR = ($27,675 / $37,000) * (12 / 60) = 0.996
Rounding to one decimal place, the APR would be 1.0%.
(d) Comparing the options, the 0% APR should be preferred because it means that there is no additional interest charge on the loan. The 2.5% add-on interest rate results in higher monthly payments and a finance charge, making the total cost of the loan higher compared to the 0% APR option.