Question

You agree to purchase a home for $230,000 and decide to make a 20% down payment on the home. You finance the rest of the home payment with a 15 year fixed rate mortgage with an annual interest rate of 5.00%. Assuming that you make regular monthly payments, determine your regular monthly payment amount. Provide just a numerical answer rounded to the nearest cent.

Answer 1

Step-by-step explanation

to find the regular monthly payment amount we need to use the formula:

`A=P(r(1+r)^(n))/((1+r)^(n)-1)`

so

Step 1

find the principal,

if you make a 20% down , it means the rest is 80 %, so the Principal will be 80 % of the total

`\begin{gathered} Principal=\text{ whole cost*80 \%} \\ P=230000*(80)/(100) \\ P=184000 \end{gathered}`

Step 2

now, find the regular monthly payments amount

a) let

`\begin{gathered} Principal\text{ = P=184000} \\ time=15\text{ years =}15\text{ years*}\frac{12\text{ months}}{1\text{ year}}=180\text{ months} \\ r=5\text{ \% = }(5)/(100)=0.05 \end{gathered}`

b) replace

`\begin{gathered} A=P(r(1+r)^n)/((1+r)^n-1) \\ A=184000(0.05(1+0.05)^(180))/((1+0.05)^(180)-1) \\ A=9201.41 \end{gathered}`

so, the answer is 9201.41