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28 March, 23:25

You invest $4000 in a bank account with 5% interest compounded annually. You are wondering how long it would take for your money to double.

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  1. 28 March, 23:41
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    A = P (1 + r) ^n; where A is the amount after time, n; P is the principal (the invested amount); r is the interest rate and n is the number of periods (i. e. no of years since the amount is compounded annually).

    8000 = 4000 (1 + 5/100) ^n

    8000/4000 = (1 + 0.05) ^n

    (1.05) ^n = 2

    n log 1.05 = log 2

    n = log 2 / log 1.05 = 14.2067

    Therefore, the amount will double in approximately 14 years.
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