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5 October, 14:31

How much money should be deposited in an account that earns 8% compounded semi-annually so that it will accumulate $9,000 in three years

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  1. 5 October, 15:20
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    US$ 7,112.83 should be deposited today in an account that earns 8 % compounded semi-annually so that it will accumulate US$ 9,000 in 3 years.

    Step-by-step explanation:

    1. Let's review the data given to us for solving the question:

    Future Value = US$ 9,000

    Annual interest rate = 8% compounded semi-annually = 4% each semester

    Duration of the investment = 3 years = 6 semesters

    2. Let's find the amount that should be deposited today, using the following formula:

    FV = PV * (1 + r) ⁿ

    Replacing with the real values, we have:

    9,000 = PV * (1 + 0.04) ⁶

    9,000 = PV * (1.04) ⁶

    9,000 = PV * 1.26531902

    PV = 9,000/1.26531902

    PV = US$ 7,112.83

    Note: Same answer to question 14017214, answered by me.
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