Congratulations, you just won a "million dollar" jackpot! With the first payment to be received immediately, you will receive $100,000 each year for the next nine years. What is the present value of your jackpot if you assume an interest rate of 4%? What if you assume an interest rate of 6%? Did you actually win one million dollars? Explain.

You did not recieve 1 million.

Explanation:

Giving the following information:

With the first payment to be received immediately, you will receive $100,000 each year for the next nine years.

1) Interest rate = 4%

First, we need to calculate the final value and then the present value using the following formula.

FV = {A*[ (1+i) ^n-1]}/i + {[A * (1+i) ^n]-A}

Because it is at the beginning of each period, we need to add an extra period of interest ([A * (1+i) ^n]-A)

FV = {100,000*[ (1.04^10) - 1]}/0.04 + {[100,000 * (1.04^10) ]-100,000}

FV = 1,200,610.71 + 48,024.43 = 1,248,635.14

Now, we can calculate the present value:

PV = FV / (1+i) ^n = 1,248,635.14 / 1.04^10 = $843,533.16

B) i = 0.06

FV = {100,000*[ (1.06^10) - 1]}/0.06 + {[100,000 * (1.06^10) ]-100,000}

FV = 1,397,164.26

PV = 1,397,164.26 / 1.06^10 = $780,169.23