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

Answer:

The monthly payment is approximately $2,356.89

Step-by-step 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;

$M = \dfrac{P \cdot \left(\dfrac{r}{n} \right) \cdot \left(1+\dfrac{r}{n} \right)^{n \cdot t} }{\left(1+\dfrac{r}{n } \right)^{n \cdot t} - 1}$

Therefore, we get;

$M = \dfrac{43,949.702\times \left(\dfrac{0.0509}{1} \right) \cdot \left(1+\dfrac{0.0509}{1} \right)^{1 \times 60} }{\left(1+\dfrac{0.0509}{1 } \right)^{1 \times 60} - 1} \approx 2,356.89$

The monthly payment, M ≈ $2,356.89.