Question

Michael wants to buy some new exercise equipment for his home gym for $363,000 financed at an annual interest rate of 15% using the add-on method. If Michael wants to pay off the loan in years, what will be his monthly payment?

Answer 1

Problem statement: Find the monthly payment

Method: The monthly payment formula is given by:

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

where

In our case

$\begin{gathered} P=\text{ \ 363,000} \\ n=5(years)\times12(\frac{months}{\text{year}})=60\text{months} \\ \\ r=\frac{\text{annual rate}}{n\nu mber\text{ of times componded per year}}=\frac{15\text{ \%}}{12}=\frac{15}{100\times12}=0.0125 \end{gathered}$

The next step will be to substitute the above values into the formula

$\begin{gathered} A=363,000\times\frac{0.0125(1+0.0125)^{60}}{(1+0.0125)^{60}-1} \\ A=363,000\times0.02379 \\ A=\text{ \ 8635.7}4 \end{gathered}$

Therefore, Michael's monthly payment will be $8635.74