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Math Help - Present Value of an ordinary simple annuity

  1. #1
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    Present Value of an ordinary simple annuity

    A 20 year loan requires semiannual payments of $1073.33 including interest at 6.8% compounded semiannually.

    a) what was the original amount of the loan?

    FV = PMT ((( 1 + i)^n - 1)/i)

    i = 0.068 / 2

    1073.33 (1 + 0.034)^40 - 1 )
    _______________
    0.034

    FV = 85 704.59

    85,704.59 = pv ( 1 + 0.034 )^40

    Pv = 22,500

    B) What is the loan's balance 8.5 years later (just after the scheduled payment)

    22 500 ( 1 + 0.034)^17 or 85 704.59/(1+0.034)^40 - 1 )

    thats where i'm stuck
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  2. #2
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    Quote Originally Posted by diehardmath4 View Post
    A 20 year loan requires semiannual payments of $1073.33 including interest at 6.8% compounded semiannually.
    Check that 1073.33: doesn't "work"; typo?
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  3. #3
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    YEa it was a typo after i checked

    A 20 year loan requires semiannual payments of 1037.33 including interest at 6.8% compounded semiannually.

    a) what was the original amount of the loan?

    b) What is the loan's balance 8.5 years later ( just before the scheduled payment ) ?
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  4. #4
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    Quote Originally Posted by diehardmath4 View Post
    A 20 year loan requires semiannual payments of 1037.33 including interest at 6.8% compounded semiannually.

    a) what was the original amount of the loan?

    b) What is the loan's balance 8.5 years later ( just before the scheduled payment ) ?
    a) 22500 is correct. Simply get FV of the payments:
    1037.33(1 - 1/1.034^40) / .034 = 22500

    b) I'm assuming you mean "just after", as in your original post:
    x = FV of 22500 for n = 17
    y = FV of 1037.33 payment for n = 17
    owing 8.5 years later = x - y
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