Question

Maria secured a 6-year car loan at 5.90% compounded annually that required her to make payments of $889.15 at the beginning of each month. calculate the cost of the car if she made a downpayment of $2,250. $0.00 round to the nearest cent.

Answer 1

To calculate the cost of the car, we use the present value formula. The cost of the car is the sum of the down payment and the present value of the loan. The cost of the car is $40,791.73.

Step-by-step explanation:

To calculate the cost of the car, we need to find the present value of the loan. The monthly payments can be calculated using the annuity formula:

PMT = PV * (r/12) / (1 - (1 + r/12)^(-n))

Where PMT is the monthly payment, PV is the present value (loan amount), r is the annual interest rate, and n is the number of payments (number of years * 12). Rearranging the formula, we can solve for PV:

PV = PMT * (1 - (1 + r/12)^(-n)) / (r/12)

Substituting the given values, PV = $889.15 * (1 - (1 + 0.059 / 12)^(-6 * 12)) / (0.059 / 12) = $38,541.73.

The cost of the car is the sum of the down payment and the present value of the loan: $2,250 + $38,541.73 = $40,791.73.