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March 30, 2017

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How long, to the nearest tenth of a year, will it take $12,500 to grow to $20,000 at 6.5% annual interest compounded quartely? (Use the formula for compound interest with n compoundings per year to solve for t.)

  • Algebra - ,

    With k compounding a year, the compound interest formula becomes:

    FV = PV*Rkn
    where
    FV=future value
    PV=present value
    r=annual rate of interest, in fraction.
    For example, 0.12 stands for 12%.
    k=number of compounding a year, 4 for compounding every three months.
    n=number of years
    R=compounding rate, = 1+r/k

    For example,
    at 8% annual interest compounded 4 times a year, $10000 will accumulate to $20000 in n years.
    20000=10000*(1+0.08/4)4n
    divide by 10000,
    1.024n = 2.0
    take log on both sides
    4n log(1.02) = log(2.0)
    n = (1/4)log(2)/log(1.02)
    =8.75 years

  • Algebra - ,

    Still not sure what the answer is.

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