Question

An installment contract for the purchase of a car requires payments of $251.76 at the end of each month for 2.75 years. interest is 11% per annum compounded monthly. What is the amount financed?

Answer 1

To calculate the amount financed for the car purchase, use the annuity formula with the given monthly payment, interest rate, and payment period, then solve for the present value.

Step-by-step explanation:

The amount financed for a car purchase, with monthly installments of $251.76 over 2.75 years at an annual interest rate of 11% compounded monthly, can be determined using the formula for the present value of an annuity.

The annuity formula is: PV = PMT × [(1 - (1 + i)-n) / i], where PV is the present value or the amount financed, PMT is the monthly payment, i is the monthly interest rate (annual rate / 12), and n is the total number of payments (months).

First, convert the annual interest rate to monthly by dividing by 12: i = 0.11 / 12 = 0.0091667. The total number of payments for 2.75 years is: n = 2.75 × 12 = 33 months.

Now, plug these numbers into the formula to find the amount financed:

PV = 251.76 × [(1 - (1 + 0.0091667)-33) / 0.0091667]

Calculate the expression within the brackets and the complete multiplication to get the final amount financed.