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12 November, 23:45

How long will it take for a $4000 investment to grow to $6000 at an annual rate of 15%, compounded monthly? Assume that no withdrawals are made. Do not round any intermediate computations, and round your answer to the nearest hundredth.

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  1. Yesterday, 01:04
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    It will take 2.72 years and 32.64 months.

    Explanation:

    Future value is the sum of principal amount and compounded interest amount invested on a specific rate for a specific period of time.

    Use following formula to calculate the time period.

    FV = PV x (1 + r) ^n

    FV = Future value = $6,000

    PV = Present Value = $4,000

    r = rate of interest = 15% yearly = 15% / 12 = 1.25%

    n = time period = ?

    $6,000 = $4,000 x (1 + 1.25%) ^n

    $6,000 = $4,000 x (1.0125) ^n

    $6,000 / $4,000 = (1.0125) ^n

    1.5 = (1.0125) ^n

    Log 1.5 = n log 1.0125

    n = Log 1.5 / log 1.0125

    n = 32.64 months

    n = 2.72 years
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