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25 November, 22:19

In order to avoid estate taxes, your rich aunt Frederica will pay you $10,000 per year for 4 years, starting 1 year from now. What is the present value of your benefactor's planned

gifts? The interest rate is 7 percent. How much will you have 4 years from now if you

invest each gift at 7 percent?

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  1. 25 November, 23:12
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    a) present value $33,872.11

    b) future value $44, 399.43

    Explanation:

    The question is asking for two values

    1. The present value of Rich Aunt Frederica's planned $10,000 per yer for 4 years

    2. The future value of the plan if the gift of $10,000 is invested at 7% per annum in 4 years.

    First, to calculate the present value, the formula is to use the 7% rate to discount the annual value of $10,000 as follows:

    Formula for discounting = P / (1+r) ∧n

    P = Payment

    r = yearly rate

    n = number of years.

    Year 1 10,000 / (1.07) ∧1 $9,345.79

    Year 2 10,000 / (1.07) ∧2 $8,734.39

    Year 3 10,000 / (1.07) ∧3 $8162.98

    Year 4 10,000 / (1.07) ∧4 $7628.95

    Total $33,872.11

    Secondly, to calculate the future value, formula is to multiply the annual value by the 7% annual rate raised to the period.

    Formula for discounting = P x (1+r) ∧n

    P = Payment

    r = yearly rate

    n = number of years.

    Year 1 10,000 x (1.07) ∧1 $12,250.43

    Year 2 10,000 x (1.07) ∧2 $11,449

    Year 3 10,000 x (1.07) ∧3 $10,700

    Year 4 10,000 x (1.07) ∧4 $10,000

    Total $44, 399.43
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