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Thread: annuity present value problem: why is interest rate converted to monthly?

  1. #1
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    annuity present value problem: why is interest rate converted to monthly?

    Can anyone please explain why the interest rate (in the solution to the example at the bottom of this page) is converted into monthly while it already says 15% compounded monthly?



    Example 2.7

    . . .A principal of $50,000 is to be borrowed at an interest rate of 15% compounded monthly for 30 years. What will be the monthly payment to repay the loan?

    . . .Solution: Monthly interest i = 0.15/12 = 0.0125, or 1.25%. Since Appendix A does not contain a table for that interest rate, one must use the formulas.


    . . . . .[tex]A\, =\, P\, (A/P)_{i,n}\, =\, 50000\, (A/P)_{1.25, 360}[/tex]

    . . . .. . .[tex]=\, 50000\, \cdot\, \dfrac{(0.0125)\, (1\, +\, 0.0125)^{360}}{(1\, +\, 0.0125)\, -\, 1}[/tex]

    . . .. . . .[tex]=\, 50000\, (0.012644)\, =\, \$632[/tex]



    in my mind i have A = P(A/P,i,n); i = 15%, n = 360
    but solution is different here
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    Last edited by stapel; 12-05-2017 at 02:03 PM. Reason: Typing out the text in the graphic; creating useful subject line.

  2. #2
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    Quote Originally Posted by Tayeeba View Post
    Can anyone please explain why the interest rate (in the solution to the example at the bottom of this page) is converted into monthly while it already says 15% compounded monthly?



    Example 2.7

    . . .A principal of $50,000 is to be borrowed at an interest rate of 15% compounded monthly for 30 years. What will be the monthly payment to repay the loan?

    . . .Solution: Monthly interest i = 0.15/12 = 0.0125, or 1.25%. Since Appendix A does not contain a table for that interest rate, one must use the formulas.


    . . . . .[tex]A\, =\, P\, (A/P)_{i,n}\, =\, 50000\, (A/P)_{1.25, 360}[/tex]

    . . . .. . .[tex]=\, 50000\, \cdot\, \dfrac{(0.0125)\, (1\, +\, 0.0125)^{360}}{(1\, +\, 0.0125)\, -\, 1}[/tex]

    . . .. . . .[tex]=\, 50000\, (0.012644)\, =\, \$632[/tex]



    in my mind i have A = P(A/P,i,n); i = 15%, n = 360
    but solution is different here
    Not clear in the problem, but meant was 15% APR
    compounded monthly: so 15/1200 = .0125 = I

    Formula is P = Ai / [1 - 1/(1+i)^n]
    A = amount borrowed (50000)
    i = monthly interest factor (.0125)
    n = number months (360)
    P = monthly payment (?)
    Last edited by stapel; 12-05-2017 at 02:04 PM. Reason: Copying typed-out graphical content into reply.
    I'm just an imagination of your figment !

  3. #3
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    Quote Originally Posted by Denis View Post
    Not clear in the problem, but meant was 15% APR
    compounded monthly: so 15/1200 = .0125 = I

    Formula is P = Ai / [1 - 1/(1+i)^n]
    A = amount borrowed (50000)
    i = monthly interest factor (.0125)
    n = number months (360)
    P = monthly payment (?)
    Thanks Denis, got it

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