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?

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