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The Petersons bought a $339,000 townhome. They made a down payment of $43,000 and took out a mortgage for the rest. Over the course of 30 years tmade monthly payments of $1774.68 on their mortgage until it was paid off.(a) What was the total amount they ended up paying for the townhome(including the down payment and monthly payments)?$0(b) How much interest did they pay on the mortgage?I need help with this math problem.

Sagot :

Explanation:

Step 1:

Calculate trge total amount of monthly repayment over 30 years, we will have

For each month he paid

[tex]\text{ \$}1774.68[/tex]

For 30 years, he will pay

[tex]\begin{gathered} 1774.68\times30\times12 \\ =\text{ \$}638,884.8 \end{gathered}[/tex]

The amoun of the down payment is

[tex]\text{ \$}43,000[/tex]

Hence,

The amount they ended up paying for the townhome

(including the down payment and monthly payments) will be

[tex]\begin{gathered} 638884.80+43000 \\ monthlyrepayments+downpayment \\ =\text{ \$}681,884.80 \end{gathered}[/tex]

Step 2:

To figure out the interst paid on the mortgage, we will substracted the total amount for the townhome from the total repayment including downpayment

[tex]\begin{gathered} interest=\text{ \$}681,884.80-\text{ \$}339,000 \\ interest=\text{ \$}342,884.80 \end{gathered}[/tex]

Hence,

The interest is

[tex]\imaginaryI nterest=\text{ \$}342,884.80[/tex]

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