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Math Help - [SOLVED] Mortgage Word Problem. HELP.

  1. #1
    math-impaired
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    Unhappy [SOLVED] Mortgage Word Problem. HELP.

    This is the question. I have no idea how to solve it and I am now in panic mode. I hope someone can help. How do I solve this word problem. What are the steps I need to know to correctly solve it. Please help!

    "A bank makes a home mortgage loan of $180,000 at 7.25% amortized in equal monthly payments over 30 years. What is the total amount paid in interest when the mortgage is paid off."
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  2. #2
    Super Member

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    Hello, math-impaired!

    A bank makes a home mortgage loan of $180,000 at 7.25%
    amortized in equal monthly payments over 30 years.
    What is the total amount paid in interest when the mortgage is paid off?

    If you are not familiar with the Amortization Formula, forget it!


    . . . A \;=\;P\frac{i(1 + i)^n}{(1+i)^n - 1} . where: . \begin{array}{cccc}A & = \\ P  & = \\ i & = \\ n & = \end{array}\,\begin{array}{cccc}\text{periodic payment} \\ \text{principal amount of loan} \\ \text{periodic interest rate} \\ \text{number of periods}\end{array}


    We have: . \begin{array}{ccc}P & = \\ i & = \\ n & =\end{array}\:\begin{array}{ccc}180,000 \\ \frac{0.0725}{12} \\ 360\end{array}

    Then: . A\;=\;180,000\frac{\left(\frac{0.0725}{12}\right)\  left(1 + \frac{0.0725}{12}\right)^{360}}{\left(1 + \frac{0.0725}{12}\right)^{360}-1} \;=\;1227.917298

    Hence, the monthly payments are: \$1227.92


    Can you finish the problem now?

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