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9 December, 04:21

You are considering an investment in a Third World bank account that pays a nominal annual rate of 18%, compounded monthly. If you invest $5,000 at the beginning of each month, how many months would it take for your account to grow to $250,000?

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  1. 9 December, 04:46
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    Answer: 262.752692months

    The account will take 21.8960577years = (262.75) months to grow to $250,000

    Explanation:

    Using Compound interest formula

    A = p + (1 + r/n) ^nt

    Note : (^) means raised to the power of

    A = amount = $250,000

    r = nominal rate = 18% = 18/100 = 0.18

    P = principal = $5,000

    n = number of compounded years

    =12 (it means 12 interest payment per year)

    t = time in years to grow

    250,000 = 5,000 (1+0.18/12) ^12 (t)

    250,000 = 5,000 (1 + 0.015) ^12t

    250,000 = 5,000 (1.015) ^12t

    Divide both sides by 5,000

    1.015^12t = 250,000/5,000

    1.015^12t = 50

    Take In of both sides

    In 1.015^12t = In 50

    Using exponential function rule to express the above equation

    12t In 1.015 = In 50

    12t = In 50 / In 1.015

    12t = 3.91202301 / 0.0148886125

    12t = 262.752692

    t = 262.752692 / 12

    t = 21.8960577 years

    t = 262.752692 months
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