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Math Help - Rearranging Annuitie formula to find R

  1. #1
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    Rearranging Annuitie formula to find R

    Hey everyone I need help really badly.
    I have a formula that looks like this
    A=PR^n + Q(R^n-1)/R-1

    But i need to rearrange it to make R the subject. Ive spent hours trying to work it out but i just can't do it. I need it for my maths assignment due tommorow so quick help would be very much appreciated.

    Thanks!
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  2. #2
    Senior Member tukeywilliams's Avatar
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    Is it  A = PR^n + \frac{Q(R^{n}-1)}{R-1} or  A = PR^n + \frac{Q(R^{n}-1)}{R}-1 ?
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  3. #3
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    yeah thats the exact same equation I have, but I'm having trouble rearranging it to find R.
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  4. #4
    Senior Member tukeywilliams's Avatar
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    which one is it?
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  5. #5
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    Oh sorry i didnt read it properly. Anyway its the first one.
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  6. #6
    Senior Member tukeywilliams's Avatar
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     R^{n} = \frac{A}{P} - \frac{Q}{P}


     R = \sqrt[n]{\frac{A}{P} - \frac{Q}{P}}

    This is how I did it:

    We know that  A = PR^n + \frac{Q(R^n-1)}{R-1} . Now  \frac{R^{n}-1}{R-1} = R^{n-1} + R^{n-2} + \ldots + 1 which is a geometric series. So its sum is  \frac{1}{1-R} .

    Then  A = PR^{n} + Q \left(\frac{1}{1-R} \right )

    So  A = \frac{PR^{n}(1-R) +Q}{1-R} or  A(1-R) = PR^{n}(1-R) + Q .

    Then  \frac{A}{P}(1-R) = R^{n}(1-R) + \frac{Q}{P} .

    Then  \frac{A}{P} - \frac{Q}{P} = R^{n} and so  R = \sqrt[n]{\frac{A-Q}{P}}
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  7. #7
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    Thankyou so much!
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  8. #8
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    This may be the beer talking but I donít think that

    is the solution to R in .

    With P=100, R=1.05, n=11, and Q=50,

    ≈ 881.37.

    But ≈ 1.21.
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