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;
[tex]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}[/tex]
Therefore, we get;
[tex]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[/tex]
The monthly payment, M ≈ $2,356.89.
