How long will it take 500 dollars to double if it is invested at 7% interest compounded semi-annually

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How long will it take 500 dollars to double if it is invested at 7% interest compounded semi-annually

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Diễm Kiều 4 years 2021-07-30T16:13:42+00:00 1 Answers 17 views 0

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  1. Gerda
    0
    2021-07-30T16:15:31+00:00
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    Answer:

    11 half years

    Step-by-step explanation:

    The formula for compound interest is

    A = P(1+r/n)^(nt), with r representing the interest rate, n being the number of times interest is applied over the time period, and t being the amount of time periods.

    If we make the time period a half year (so interest is compounded once per time period), n=2. Then, our interest rate is 7%, or 0.07 (to convert from percent to decimal, simply divide by 100). Our starting amount is 500, and we want it to double, making it 1000. Our formula is thus

    1000 = 500 (1+0.07)^(t)

    divide both sides by 500

    2 = (1+0.07)^(t)

    2 = (1.07)^(t)

    Using logarithms, we can say that

    log_{1.07} 2 = t

    and using a calculator, we get

    10.24 = t

    Since interest is only compounded once per time period, though, we have to round up to make sure it doubles, so t = 11

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