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Math Help - Compounded Continuously

  1. #1
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    Compounded Continuously

    How many years will it take for an initial investment of $10,000 to grow to $25,000? Assume a rate of interest of 6% compounded continuously.
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  2. #2
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    Quote Originally Posted by magentarita View Post
    How many years will it take for an initial investment of $10,000 to grow to $25,000? Assume a rate of interest of 6% compounded continuously.
    The continuous compound interest formula is:

    A = Pe^{rt}

    Where:
    • P = Principal amount (initial investment)
    • r = Annual interest rate (as a decimal)
    • t = Number of years
    • A = Amount after time t
    • e = Exponential function


    From the question, we can deduce that P=$10,000, r=0.06, t=?, A=$25,000 and hence inserting the values into the formula gives:

    25000= 10000e^{0.06t}

    Now, solve for t and you will have the amount of years for the investment to grow from $10000 to $25000 with continuous compound interest.
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    Air...

    Air, you are a great math professor!
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