Question

You purchased a new car. The car had a list price of $41,070. You are paying 5.09% interest compounded monthly over a payment period of FIVE years. If you also had to pay 5.86% sales tax, a $384 vehicle registration fee, and an $89 documentation fee, what is your monthly payment?

Answer 1

The monthly payment is approximately $2,356.89

Explanation:

The list price of the car, P = $41,070

The interest rate payed, r = 5.09% compounded monthly

Therefore, the number of interest calculated per period, n = 1

The payment period, t = 5 years

The amount payed as sales tax = 5.86%

The amount paid as registration fee = $384

The amount paid as documentation fee = $89

The total amount to be paid, A = 41,070 + 41,070 × 0.0586 + 384 + 89 = 43,949.702

Therefore, the monthly payment, 'M', is given by the following formula;

`M = (P \cdot \left((r)/(n) \right) \cdot \left(1+(r)/(n) \right)^(n \cdot t) )/(\left(1+(r)/(n ) \right)^(n \cdot t) - 1)`

Therefore, we get;

`M = (43,949.702* \left((0.0509)/(1) \right) \cdot \left(1+(0.0509)/(1) \right)^(1 * 60) )/(\left(1+(0.0509)/(1 ) \right)^(1 * 60) - 1) \approx 2,356.89`

The monthly payment, M ≈ $2,356.89.