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 can apply the formula for calculating a loan payment. However, with 0% APR, there is no interest charged, making the formula simpler. The formula to calculate the monthly payment is:
Monthly Payment = Total Loan Amount / Number of Months
In this case, since there is no down payment, the total loan amount is equal to the sticker price minus the rebates:
Total Loan Amount = Sticker Price - Rebates
= $42,500 - $5,100
= $37,400
So, the monthly payment for a 0% APR loan for 60 months would be:
Monthly Payment = $37,400 / 60
= $623.33 (approximately)
Therefore, the monthly payment is approximately $623.33.
(b) To find the monthly payment if financed at 2.5% add-on interest for 60 months, we need to consider the interest added to the loan amount. The formula to calculate the monthly payment is:
Monthly Payment = (Total Loan Amount + Interest) / Number of Months
To calculate the interest, we need to find the interest amount and add it to the loan amount. The formula to calculate the interest amount for an add-on interest loan is:
Interest Amount = Total Loan Amount * Interest Rate * Loan Term
In this case, the interest rate is given as 2.5% and the loan term is 60 months. Thus, the interest amount would be:
Interest Amount = $37,400 * 0.025 * 60
= $56,100
Now, let's calculate the total loan amount by adding the interest amount:
Total Loan Amount = Initial Loan Amount + Interest
= $37,400 + $5,600
= $43,000
Finally, we can calculate the monthly payment using the formula mentioned earlier:
Monthly Payment = $43,000 / 60
= $716.67 (approximately)
Therefore, the monthly payment for a 2.5% add-on interest loan for 60 months would be approximately $716.67.
(c) To find the APR using the APR approximation formula, we can rearrange the formula to solve for the APR:
APR = ((Monthly Payment / Loan Amount) - 1) * (12 / Number of Months) * 100
In this case, the monthly payment is $716.67 and the loan amount is $37,400. The loan term is 60 months. Plugging these values into the formula, we get:
APR = (($716.67 / $37,400) - 1) * (12 / 60) * 100
= (0.019166 - 1) * 0.2 * 100
= -0.980833 * 0.2 * 100
= -19.617%
Therefore, the APR for the 2.5% add-on interest loan is approximately -19.6%.