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1 June, 21:43

Sung Lee invests $5,000 at age 18. He hopes the investment will be worth $20,000 when he turns 25. If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Round to the nearest tenth of a percent.

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  1. 1 June, 22:03
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    19.8%

    Step-by-step explanation:

    We have the following formula for continuous compound interest:

    A = P * e ^ (i * t)

    Where:

    A is the final value

    P is the initial investment

    i is the interest rate in decimal

    t is time.

    The time can be calculated as follows:

    25 - 18 = 7

    That is, the time corresponds to 7 years. In addition, A is 20,000 for A and P would be 5,000, we replace:

    20000 = 5000 * e ^ (7 * i)

    20000/5000 = e ^ (7 * i)

    e ^ (7 * i) = 4

    ln e ^ (7 * i) = ln 4

    7 * i = ln 4

    i = (ln 4) / 7

    i = 0.198

    Which means that the rounded percentage will be 19.8% per year
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