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17 July, 12:41

you invest d dollars in a bank account that earns 5% compounded continuously. how long will it take your money to double?

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  1. 17 July, 14:55
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    It'll take take 13.8629 years to double the money.

    Step-by-step explanation:

    When an amount is compounded continuosly it's growth is determined by the following function:

    M = C*e^ (r*t)

    Where M is the final value, C is the initial value, r is the interest rate and t is the time elapsed. In this case we want a final value that is two times the initial one, therefore M = 2*C. We have:

    2*C = C*e^ (0.05*t)

    C*e^ (0.05*t) = 2*C

    e^ (0.05*t) = 2*C/C

    e^ (0.05*t) = 2

    ln[e^ (0.05*t) ] = ln (2)

    0.05*t = ln (2)

    t = ln (2) / 0.05 = 13.8629 years

    It'll take take 13.8629 years to double the money.
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