Question

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.

Answer 1

Answer:

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