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Thread: In its first 10 years a mutual fund produced an average annual return of 21.38%

  1. #1
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    Exclamation In its first 10 years a mutual fund produced an average annual return of 21.38%

    Assume that money invested in this fund continues to earn 21.38%
    compounded annually. How long will it take money invested in this fund to double?

    It will take approximately 4 years for the money invested in this fund to double.

    How do I find the number of years here?


    I realize I put the answer here. I just need the formula, and the steps.
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  2. #2
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    Re: In its first 10 years a mutual fund produced an average annual return of 21.38%

    let $c$ be the initial amount invested

    $2c = c(1+0.2138)^n$

    $2 = 1.2138^n$

    $\ln(2) = n \ln(1.2138)$

    $n = \dfrac{\ln(2)}{\ln(1.2138)} \approx 3.5774 \approx 4$
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