jill mock wants to add a small hair salon to her home. the addition will cost $15,100. she will make a down…

jill mock wants to add a small hair salon to her home. the addition will cost $15,100. she will make a down - payment of $2500 and finance the balance at 6.75% interest for 5 years (60 months). find the monthly payment using a calculator. round your answer to the nearest cent. the monthly payment is $

jill mock wants to add a small hair salon to her home. the addition will cost $15,100. she will make a down - payment of $2500 and finance the balance at 6.75% interest for 5 years (60 months). find the monthly payment using a calculator. round your answer to the nearest cent. the monthly payment is $

Answer

Explanation:

Step1: Calculate the loan amount

The cost of the addition is $15100$ and the down - payment is $2500$. So the loan amount $P$ is $15100 - 2500=12600$.

Step2: Convert the annual interest rate to a monthly rate

The annual interest rate $r = 6.75%=0.0675$. The monthly interest rate $i=\frac{0.0675}{12}=0.005625$.

Step3: Determine the number of payments

The number of months $n = 60$.

Step4: Use the monthly - payment formula for a loan

The formula for the monthly payment $M$ of a loan is $M=\frac{P\times i\times(1 + i)^n}{(1 + i)^n-1}$. Substitute $P = 12600$, $i=0.005625$, and $n = 60$ into the formula: [ \begin{align*} M&=\frac{12600\times0.005625\times(1 + 0.005625)^{60}}{(1+ 0.005625)^{60}-1}\ \end{align*} ] First, calculate $(1 + 0.005625)^{60}$. Let $x=(1 + 0.005625)^{60}$. Using a calculator, $x\approx1.41803$. Then, $12600\times0.005625\times x=12600\times0.005625\times1.41803\approx100.67$. And $(1 + 0.005625)^{60}-1\approx1.41803 - 1=0.41803$. So, $M=\frac{100.67}{0.41803}\approx240.82$.

Answer:

$240.82$