Final answer:
To determine the amount financed and the interest cost of a car on an installment contract with monthly payments, we use the present value of an annuity formula. The amount financed is the present value, while the interest cost is the difference between total payments made and the amount financed.
Step-by-step explanation:
The question involves solving for the amount financed and the interest cost of a car purchased through an installment contract with monthly payments. Given the monthly payment, interest rate, and duration, we can use the present value formula to determine the amount financed.
Calculation of the Amount Financed
We can use the present value of an annuity formula to calculate the amount financed:
PV = PMT × {(1 - (1 + r)^-n) / r}
Where:
- PV is the present value or the amount financed,
- PMT is the monthly payment amount,
- r is the monthly interest rate (annual rate divided by 12 months),
- n is the total number of payments (months).
In this case, PMT = $201.73, r = 7% per annum compounded monthly, which is r = 7%/12 = 0.00583333 per month, and n = 4.5 years × 12 months/year = 54 months. Substituting these values into the formula provides us with the amount financed.
Calculation of Interest Cost
Once we have the amount financed, we can calculate the total amount paid over 4.5 years by multiplying the monthly payment by the number of payments. The interest cost is the difference between the total amount paid and the amount financed.