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Math Help - Linear/Nonlinear Equations--compute for monthly repayments

  1. #1
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    Linear/Nonlinear Equations--compute for monthly repayments

    Please help with grade9 Math-Linear/NonLinear Equations on how to compute for loans, monthly repayments and interest rates.

    $10,000 loan to be paid over 4 years at various interest rates:
    Monthly Payments is $242.51 for interest rate of 8%
    $244.75 for interest rate of 8.5 %

    Question: Find the monthly payment when interest rate is 8.25%
    What interest rate would require a monthly payment of $255?

    Appreciate your kind help.
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  2. #2
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    Lexington, MA (USA)
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    Hello, noreen_cruz!


    I have issues with this problem.

    [1] You have been given the Amortization Formula?
    . . .And you're expected to manipulate it algebraically? . . . in Grade 9 ?

    [2] I don't agree with their numbers.


    $10,000 loan to be paid over 4 years.

    Monthly Payments is: . \begin{array}{c}\text{\$242.51 for interest rate of 8\%} \\<br />
\text{\$244.75 for interest rate of 8.5\%} \end{array}

    (a) Find the monthly payment when interest rate is 8.25%
    (b) What interest rate would require a monthly payment of $255?

    Amortization Formula: . A \;=\;P\,\frac{i(1+i)^n}{(1+i)^n-1}

    . . where: . \begin{Bmatrix}A &=&\text{periodic payment} \\ P &=& \text{principal} \\ i &=& \text{periodic interest rate} \\ n &=& \text{number of periods} \end{Bmatrix}



    For the 8% loan, we have: . P = 10,\!000,\;\;i = \tfrac{0.08}{12}.\;\;n = 48

    Then: . A \;=\;10,\!000\,\frac{\left(\frac{0.08}{12}\right)\  left(1+\frac{0.08}{12}\right)^{48}} {\left(1 +\frac{0.08}{12}\right)^{48} -1} \;=\;244.1292263 \;\approx\;\boxed{\$244.13}\;\hdots\;\text{ not }\$242.51


    So I don't trust the author(s) of this problem . . .

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