Question

You want to buy a new sports coupe for $87,500, and the finance office at the dealership has quoted you an APR of 6.9 percent for a 48 month loan to buy the car.

What will your monthly payments be? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

To find the monthly payment on a $87,500 car loan at 6.9% APR for 48 months, use the annuity payment formula with the loan amount, the monthly interest rate (APR/12), and the number of payments.

Step-by-step explanation:

To calculate the monthly payment on a $87,500 car loan with a 6.9% APR over a 48-month period, we can use the formula for the annuity payment (PMT), which is derived from the present value of an annuity formula. The formula to find the monthly payment is PMT = P × (i / (1 - (1 + i)^{-n})), where P is the principal amount ($87,500), i is the monthly interest rate (APR divided by 12 months), and n is the total number of payments (48).

First, let's convert the APR to a monthly interest rate: 6.9% APR ÷ 12 months = 0.575% monthly rate, or 0.00575 expressed as a decimal.

Now, let's use the formula:

PMT = $87,500 × (0.00575 / (1 - (1 + 0.00575)^{-48}))

After performing the calculation, you'll find the monthly payment for the car loan.