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Math Help - Find number of periods from annuity formula

  1. #1
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    Find number of periods from annuity formula

    I have attempted to separate the number of periods (n) from the following equation

    pv (1 + i)^n + pmt (1 + i * type) [{(1 + i)^n - 1}/i] + fv = 0

    Have I done this correctly?

    type has either a value of 0 for end of period payments and 1 for start of period payments

    n = log[ { pmt * ( 1 + i * type) - fv * i } / { pmt * ( 1 + i * type) + pv * i } ] / log( 1 + i * type)

    Thanks
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  2. #2
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    Re: Find number of periods from annuity formula

    I dont want to discourage questions, but wouldn't it be easier to test this yourself by substituting values, rather than ask us to repeat the algebra looking for errors?

    I have not checked your answer in any detail, but look at your denominator:
    n = log[ { pmt * ( 1 + i * type) - fv * i } / { pmt * ( 1 + i * type) + pv * i } ] / log( 1 + i * type)
    log( 1 + i * type)

    if type=0, then this is log(1). Log(1)=0 and so your expression is undefined (anything divided by 0 is undefined).


    My suggested approach to recover n would be to re-factorise your expression into the form:

    (1+i)^n(\text{stuff}_1) + \text{stuff}_2 =0

    (1+i)^n =\frac{-\text{stuff}_2}{\text{stuff}_1}

    n \ln (1+i)=\ln \left(\frac{-\text{stuff}_2}{\text{stuff}_1} \right)
    ...and finish. Depending on your level of study you may impress your teacher by noticing that ln(1+i) = \delta

    PS: I have NOT checked that the equation can be re-written in the form i mentioned, but at first glance it looks like it can.
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  3. #3
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    Re: Find number of periods from annuity formula

    Quote Originally Posted by SpringFan25 View Post
    I dont want to discourage questions, but wouldn't it be easier to test this yourself by substituting values, rather than ask us to repeat the algebra looking for errors?

    I have not checked your answer in any detail, but look at your denominator:


    log( 1 + i * type)

    if type=0, then this is log(1). Log(1)=0 and so your expression is undefined (anything divided by 0 is undefined)./
    I had a hunch there was something I did wrong
    Well time to go back to the paper and pencil and redo the math
    Will let you know if I come up with a correct solution
    Thanks
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  4. #4
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    Re: Find number of periods from annuity formula

    Finally got it working

    Thanks
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  5. #5
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    Re: Find number of periods from annuity formula

    My site provides complete access Edmonton Real Estate
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  6. #6
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    Re: Find number of periods from annuity formula

    Quote Originally Posted by bradhows View Post
    My site provides complete access Edmonton Real Estate
    Are spammers allowed on this forum
    Your site is a blog about real estate, what the heck that got to do with finding number of periods in an annuity
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