Question

Janet would like to purchase a car with a loan for $6,100. If annual interest is 2.9% compounded monthly and she would like to make monthly payments over the next 5 years, what will her monthly payment be? Give your answer to the nearest dollar. For example, if you calculate $33.27, write 33.

Answer 1

Given:

There are given that the initial payment is $6100 and the interest is 2.9% compounded monthly.

Explanation:

According to the question:

We need to find the monthly payment.

Then,

To find the monthly payment, we will use the compound interest monthly formula:

So,

From the formula:

$A=P(1+\frac{r}{n})^{nt}-P$

Where,

$\begin{gathered} P=6100 \\ r=2.9\%=0.029 \\ t=5 \\ n=12 \end{gathered}$

Then,

Put all the values into the above formula:

So,

$\begin{gathered} A=P(1+\frac{r}{n})^{nt}-P \\ A=6100(1+\frac{0.029}{12})^{12(5)}-6100 \end{gathered}$

So,

$\begin{gathered} A=6100(1+\frac{0.029}{12})^{12(5)}-6100 \\ A=6100(1+0.002)^{60}-6100 \\ A=6100(1.002)^{60}-6100 \\ A=6100(1.127)-6100 \\ A=6874.7-6100 \\ A=774.7 \end{gathered}$

Final answer:

Hence, the value of the monthly payment is $775.