Chapter 11.2, Problem 58PPE

To determine

Find the monthly payment on a loan of $3000 at 6 % annual interest paid over 24 months

Answer to Problem 58PPE

Monthly payment is $132.96

Explanation of Solution

Given:

The formula below gives the monthly payment m on a loan as a function of the amount borrowed A, the annual rate of interest r(expressed as a decimal) and the number of months n of the loan. Use this formula and a calculator.

  $m=\frac{\text{A}(\frac{r}{12}){(1+\frac{r}{12})}^n}{{(1+\frac{r}{12})}^n-1}$

Concept Used:

Substitute the value: A = $3000; r = 6% = 0.06 and n = 24.

Calculate for ‘m ‘

Calculation:

The formula: $m=\frac{\text{A}(\frac{r}{12}){(1+\frac{r}{12})}^n}{{(1+\frac{r}{12})}^n-1}$

  $\begin{array}{l}\text{A}\text{=}\text{\$3000;}\text{r=}\text{6\%}\text{=0}\text{.06}\text{,}\text{n}\text{=}\text{24}\text{month;}\text{Find }\text{m}\\ m=\frac{\text{A}(\frac{r}{12}){(1+\frac{r}{12})}^n}{{(1+\frac{r}{12})}^n-1}=\\ m=\frac{\text{3000}(\frac{0.06}{12}){(1+\frac{0.06}{12})}^{24}}{{(1+\frac{0.06}{12})}^{24}-1}\\ \\ m=\frac{(15)·\text{(1}\text{.1271597762053917)}}{\text{0}\text{.1271597762053917}}\\ \\ m=\frac{\text{16}\text{.9073966430808755}}{\text{0}\text{.127047936700411}}\approx 132.96\end{array}$

m = $132.96

Thus, monthly payment is $132.96