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18 March, 11:02

Charles invests $425 in a savings account that pays interest at an annual rate of 4 percent, compounded continuously. Approximately how much time will it take for his investment to double?

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  1. 18 March, 11:08
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    Answer: it will take 17.33 years to double.

    Step-by-step explanation:

    The formula for continuously compounded interest is

    A = P x e^ (r x t)

    Where

    A represents the future value of the investment after t years.

    P represents the present value or initial amount invested

    r represents the interest rate

    t represents the time in years for which the investment was made.

    e is the mathematical constant approximated as 2.7183.

    From the information given,

    P = 425

    A = 2 * 425 = 850

    r = 4% = 4/100 = 0.04

    Therefore,

    850 = 425 x 2.7183^ (0.04 x t)

    850/425 = 2.7183^ (0.04t)

    2 = 2.7183^ (0.04t)

    Taking ln of both sides, it becomes

    Ln 2 = 0.04t ln 2.7183

    0.693 = 0.04t

    t = 0.693/0.04

    t = 17.325
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