Question

celia is enrolling in a trade school to become an electrician. she takes out a loan to purchase a set of tools for the program. the total cost of the tools is $900. the apr is 7% for a term of 18 months. what is celias monthly payment for this loan? round your answer to the nearest cent. monthly payment formula: ( m=\frac{p(r)(1 + r)^{12t}}{(1 + r)^{12t}-1} ), where ( p ) is the principal, ( r ) is the monthly rate, and ( t ) is the term in years. celias monthly payment is $

Explanation:

Step1: Calculate the monthly rate

The APR is \(7\%=0.07\). The monthly rate \(r=\frac{0.07}{12}\approx0.00583\).

Step2: Calculate the number of years

The term is \(18\) months. Since \(t=\frac{18}{12} = 1.5\) years.

Step3: Substitute values into the formula

We have \(P = 900\), \(r=\frac{0.07}{12}\), and \(t = 1.5\).

$$
LATEXBLOCK0
$$

First, calculate \((1+\frac{0.07}{12})^{12\times1.5}=(1 + 0.00583)^{18}\).
Using a calculator, \((1+0.00583)^{18}\approx1.1106\).
Then, \(900\times(\frac{0.07}{12})=900\times0.00583 = 5.247\).
The numerator is \(5.247\times1.1106\approx5.827\).
The denominator is \(1.1106- 1=0.1106\).
\(M=\frac{5.827}{0.1106}\approx52.69\)

Answer:

\(52.69\)