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11 July, 13:40

How much better is the return on a 6% yearly interest rate investment that is compounded 6 times per year as opposed to compounded yearly?

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  1. 11 July, 17:32
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    Answer: it is 1.004 times better

    Step-by-step explanation:

    Let $p represent the Initial amount invested into the account. Assumimg p = $1000

    Let t represent the number of years for which $p was invested. Assuming t = 3 years

    r = rate of investment = 6% = 6/100 = 0.06

    Let A represent the total amount in the account at the end of t years.

    The formula for compound interest is

    A = P (1+r/n) ^nt

    1) if the investment is compounded 6 times per year, then

    n = 6

    A = 1000 (1+0.06/6) ^6 * 3

    A = 1000 (1.01) ^18

    A = 1196.15

    2) if the investment is compounded yearly, then

    n = 1

    A = 1000 (1+0.06/1) ^1 * 3

    A = 1000 (1.06) ^3

    A = $1191.016

    Therefore,

    1196.15/1191.016 = 1.004

    The investment that is compounded 6 times per year is 1.004 times better that that compound yearly at the same rate and time
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