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calculus

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What single deposit today in an account paying 7% interest compounded continuously would yield $18500 in 10yr?

  • calculus -

    r = interest percent/100
    dy/dt = r y
    y = a e^kt
    dy/dt = ak e^kt = r a e^kt
    r = k
    so
    y = a e^rt
    note when t = 0, y = a the original deposit
    18500 = a e^(.07*10)
    ln (18500/a) = .7
    ln 18500 - ln a = .7
    9.83 - .7 = ln a
    ln a = 9.1255
    a = 9186.83

    check y = 9187 e^(.7)
    y = 18500 check

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