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Math Help - Continous compounding question

  1. #1
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    Continous compounding question

    Hello all, I am working out a question at the moment and im not too sure if it is write or wrong. Hope someone can help thanks!! the question goes like this: A loan of 100K is taken out and n.interest is 8 percent. Firstly i found that if the loan is to repaid within 12 years the answer i got was 1082. The problem i have at the moment is this: "If the monthly repayment are continuosly repaid over 12 years, what is the size of the monthly repayment?" I worked it out to be roughly 3000. Can anyone confirm this? Not too sure if this is right. Thanks!
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  2. #2
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    Re: Continous compounding question

    1082 (1082.45258...) is correct IF the rate is 8% annual compounding monthly.

    I don't follow the rest of your problem; quite unclear.
    Do you realise that 3000 * 144 = $432,000; are you willing to repay that if you borrow only $100,000?!
    Please repost CLEARLY.
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  3. #3
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    Re: Continous compounding question

    I will restate the question again, since there is a mistype.


    "If the monthly repayments are continously compounded over a 12yr period, calculate the size of the monthly repayment"


    Thanks
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  4. #4
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    Re: Continous compounding question

    Quote Originally Posted by Redeemer_Pie View Post
    I will restate the question again, since there is a mistype.
    "If the monthly repayments are continously compounded over a 12yr period, calculate the size of the monthly repayment"
    Thanks
    PVA = $100,000
    N = 12x12 = 144
    I = 8%/12 = 0.666666667%

    Continuous Compounding of Interest

    PVA = R x PVIFA(8%/12,144)

    PVIFA(8%/12,144) = [1 - e^(-in)] / [e^i - 1.0]
    PVIFA Continuous Compounding Calculator

    PVIFA(8%/12,144) = [1 - e^(-8%/12*144)] / [e^(8%/12) - 1.0]
    PVIFA(8%/12,144) = 92.2578563838

    R = PVA/PVIFA(8%/12,144)
    R = 100000/92.2578563838
    R = $1083.92

    Discrete Compounding of Interest

    PVA = R x PVIFA(8%/12,144)

    PVIFA(8%/12,144) = [1 - (1+i)^-n]/i
    PVIFA Discrete Compounding Calculator

    PVIFA(8%/12,144) = [1 - (1+0.6666666667%)^-144]/0.6666666667%
    PVIFA(8%/12,144) = [1 - (1.06666666667)^-144]/0.06666666667
    PVIFA(8%/12,144) = 92.3827995

    R = PVA/PVIFA(8%/12,144)
    R = 100000/92.3827995
    R = $1082.45
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  5. #5
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    Re: Continous compounding question

    Quote Originally Posted by Redeemer_Pie View Post
    I will restate the question again, since there is a mistype.
    "If the monthly repayments are continously compounded over a 12yr period, calculate the size of the monthly repayment"
    It's the INTEREST that continuously compounds, NOT the repayments.
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