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Math Help - calculating the number of compounding periods

  1. #1
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    calculating the number of compounding periods

    $7500 was borrowed for a 4 year term at 9% compounded quarterly.The terms of the loan allow prepayment of the loan based on discounting the loan's maturity value at 7% compounded quarterly How long ( to the nearest day ) before the maturity date was the loan prepaid if the payout amount was $9380.24 including accrued interest ? for the puropese of determining the number of days in a partial calendar quarter, assume that a full quarter has 91 days.

    FV = 9380.24
    PV = 7500
    n =
    i = ( confused on )
    n = ?

    because of the 7% ccompounded quarterly and 9 % compounded quarterly both of them threw me off so i am stuck
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  2. #2
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    Step#1:
    7500(1 + .09/4)^16 = 10,707.16 : that's the initial FV
    Step#2:
    10707.16 / (1 + .07/4)^n = 9380.24
    Solve for n ; that'll be the number of quarters.

    Let us know if you need more help.
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  3. #3
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    solving for n

    the final step is to solve for the exponent as in sqare root it right?
    Last edited by diehardmath4; March 26th 2010 at 05:31 PM. Reason: missunderstod
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  4. #4
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    Quote Originally Posted by diehardmath4 View Post
    the final step is to solve for the exponent as in sqare root it right?
    I don't understand your question...

    I told you, just solve this for n:
    10707.16 / (1 + .07/4)^n = 9380.24

    Example:
    if a / x^n = b, then n = log(a/b) / log(x)
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  5. #5
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    Formula that i learned for solving for n

    n = LOG ( 10707.16/9380.24 ) / LOG ( 1 + 0.0225 )
    Last edited by diehardmath4; March 27th 2010 at 09:30 AM. Reason: typo
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  6. #6
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    Yes, that's the formula I gave you; but not .0225; .07/4 = .0175
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