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10 April, 06:25

Sarah deposits $250 into an annuity due at the beginning of every 6-month period for 9 years. The account earns an annual 6% compounded semiannually. What is the future value of the annuity after 9 years? How much interest did she earn?

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  1. 10 April, 07:00
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    Answer: she earned $6007.5

    Step-by-step explanation:

    We would apply the formula for determining future value involving deposits at constant intervals. It is expressed as

    S = R[{ (1 + r) ^n - 1) }/r][1 + r]

    Where

    S represents the future value of the investment.

    R represents the regular payments made (could be weekly, monthly)

    r = represents interest rate/number of interval payments.

    n represents the total number of payments made.

    From the information given,

    R = $250

    r = 0.06/2 = 0.03

    n = 2 * 9 = 18

    Therefore,

    S = 250[{ (1 + 0.03) ^18 - 1) }/0.03][1 + 0.03]

    S = 250[{ (1.03) ^18 - 1) }/0.03][1.03]

    S = 250[{ (1.7 - 1) }/0.03][1.03]

    S = 250[{ (0.7) }/0.03][1.03]

    S = 250[23.3][1.03]

    S = 250 * 24.03

    S = $6007.5
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