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)^{n}}{(1 + r)^{n}-1} ), where ( p ) is the principal, ( r ) is the monthly rate, and ( t ) is the terms in years
when putting values in the formula, make sure you are using the correct units. to find the monthly rate ( r ), write the annual rate of ( 7 % ) as a decimal and divide by 12. to find ( n ), the number of years, we need to write the given term of 18 months as 1.5 years.
celias monthly payment is $

Explanation:

Step1: Calculate the monthly rate \( r \)

The annual percentage rate (APR) is \( 7\%=0.07 \). The monthly rate \( r=\frac{0.07}{12}\approx0.005833 \)

Step2: Calculate the number of years \( t \)

The term is \( 18 \) months. Since \( 1 \) year has \( 12 \) months, \( t = \frac{18}{12}=1.5 \) years

Step3: Substitute values into the formula

The principal \( P = 900 \), \( r\approx0.005833 \), \( t = 1.5 \). The number of payments \( n=12t=12\times1.5 = 18 \)

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First, calculate \( (1 + 0.005833)^{18}\)
Let \( x=(1 + 0.005833)^{18}\)
Using the formula \( a^{b}=e^{b\ln(a)}\), \(a = 1.005833\), \(b = 18\)
\(\ln(1.005833)\approx0.00581\), \(b\ln(a)=18\times0.00581 = 0.10458\), \(x = e^{0.10458}\approx1.1103\)

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Answer:

\( 52.83 \)