Question

Calculate the monthly payment for a 5-year car loan of $23,570 at 10. 43% interest, compounded monthly. A. $247. 44 b. $337. 56 c. $433. 88 d. $505. 79.

Answer 1

The monthly payment for this car loan is equal to: D. $505. 79.

Given the following data:

• Time = 5 years

• Principal = $23,570

• Interest rate = 10.43%

To calculate the monthly payment for this car loan:

Mathematically, the monthly payment on a loan is given by this formula:

$M = \frac{P(\frac{r}{12})(1 \;+\; \frac{r}{12})^{12t}}{(1 \;+ \; \frac{r}{12})^{12t} -1}$

Where:

• P is the principal or amount borrowed.

• r is the interest rate.

• M is the monthly payment.

• t is the number of years.

Substituting the given parameters into the formula, we have;

$M = \frac{23570(\frac{0.1043}{12})(1 \;+\; \frac{0.1043}{12})^{12 \times 5}}{(1 \;+\; \frac{0.1043}{12})^{12 \times 5}\; -\;1}\\\\M = \frac{23570(0.008692)(1 \;+\; 0.008692)^{60}}{(1 \;+\; 0.008692)^{60}\; -\;1}\\\\M = \frac{23570(0.008692)(1.008692)^{60}}{(1.008692)^{60}\; -\;1}\\\\M = \frac{23570(0.008692)(1.6808)}{1.6808\; -\;1}\\\\M = \frac{344.34}{0.6808}$

Monthly payment, M = $505.79

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