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Math Help - Years left on Loan

  1. #1
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    Years left on Loan

    I've tried to rearrange the equation below to give an equation in n, to show me the number of years left at a particular interest rate, monthly repayment and loan amount. I am getting lost around taking the n't root.

    The following formula is used to calculate the fixed monthly payment (P) required to fully amortize a loan of L dollars over a term of n months at a monthly interest rate of c. [If the quoted rate is 6%, for example, c is .06/12 or .005].

    P = L[c(1 + c)^n]/[(1 + c)^n - 1


    Any help appreciated, I'd like to see how you got there, about 15 years ago I was not bad at this sort of thing but have maybe lost it a little.

    thanks,
    Martin.
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  2. #2
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    Quote Originally Posted by martsbradley View Post
    I've tried to rearrange the equation below to give an equation in n, to show me the number of years left at a particular interest rate, monthly repayment and loan amount. I am getting lost around taking the n't root.

    The following formula is used to calculate the fixed monthly payment (P) required to fully amortize a loan of L dollars over a term of n months at a monthly interest rate of c. [If the quoted rate is 6%, for example, c is .06/12 or .005].

    P = L[c(1 + c)^n]/[(1 + c)^n - 1


    Any help appreciated, I'd like to see how you got there, about 15 years ago I was not bad at this sort of thing but have maybe lost it a little.

    thanks,
    Martin.
    Start by taking the logarithm of both sides.
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  3. #3
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    Thanks Mr fantastic,

    Done as you said, however and got the following which answers my question.

    n = log(A/(A-P*i))/log(1+i)

    Thanks,
    Martin.
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