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28 July, 10:54

Rick invested money in a continuous compound account with an interest rate of 3%. How long will it take for Rick's account to double?

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  1. 28 July, 11:15
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    A = Pe^ (rt)

    Let A = 2P

    Let r = 0.03

    2P = Pe^ (0.03t)

    We need to find t.

    2P/P = e^ (0.03t)

    2 = e^ (0.03t)

    Take the natural log on both sides.

    ln (2) = ln (e^ (0.03t)

    ln (2) = 0.03t

    ln (2) / 0.03 = t

    23.1049060187 = t

    You did not indicate what we are talking about. I will assume weeks or months.

    So, t is about 23 weeks or 23 months.
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