jill mock wants to add a small hair salon to her home. the addition will cost $19,400. she will make a down…

jill mock wants to add a small hair salon to her home. the addition will cost $19,400. she will make a down - payment of $2000 and finance the balance at 18.6% 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 $19,400. she will make a down - payment of $2000 and finance the balance at 18.6% 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 $19400$ and the down - payment is $2000$. So the loan amount $P$ is $19400 - 2000=17400$.

Step2: Convert the annual interest rate to a monthly interest rate

The annual interest rate $r = 18.6%=0.186$. The monthly interest rate $i=\frac{0.186}{12}=0.0155$.

Step3: Determine the number of payments

The number of months $n = 60$.

Step4: Use the loan - payment formula

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 $P = 17400$, $i = 0.0155$, and $n = 60$ into the formula: First, calculate $(1 + 0.0155)^{60}$. Let $x=(1 + 0.0155)^{60}$. Using a calculator, $x\approx2.52847$. Then, calculate the numerator: $17400\times0.0155\times2.52847=17400\times0.039181385 = 680.756199$. Next, calculate the denominator: $2.52847-1 = 1.52847$. Finally, $M=\frac{680.756199}{1.52847}\approx445.38$.

Answer:

$445.38$