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March 27, 2017

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How can I calculate how long an amount of money will last if I spend x dollars per month, at the same time as the pot of money is attracting interest at y percent? Is thare a formula?

Thanks

  • math - ,

    This is the same as the formula for borrowing money and repaying a monthly amount.
    Let
    P=principal
    n=number of months it will last
    y=interest rate, compounded monthly at y/12, (use 0.10 for 10% per annum)
    x=monthly spending
    then
    p(1+y/12)^n=x((1+y/12)^n-1)/(y/12)
    Unfortunately, to solve for n, you need to solve it by trial and error or Newton's method.
    There exist compound interest calculators, such as:
    http://www.thecalculatorsite.com/finance/calculators/compoundinterestcalculator.php#results

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