Question

A lottery winner wins the One Million Dollar Prize. After winning, she finds out that the payments are actually made annually over the next 15 years in installments of $50,000 each for each of the first 10 years, and $100,000 each for each of the next 5 years. What is the value of the prize today, if ROI is 9%

Answer 1

Total PV= $790,228.23

Step-by-step explanation:

Giving the following information:

Annual payment= $50,000

Number of periods= 10 years

Annual payment= $100,000

Number of periods= 5 years

Discount rate= 9% = 0.09

First, we need to calculate the future value of each annual payment:

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

A= annual paymeny

First 10 years:

FV= {50,000*[(1.09^10) - 1]} / 0.09

FV= $759,646.49

Next 5 years:

FV= {100,000*[(1.09^5) - 1]} / 0.09

FV= $1,709,582.17

Now, the present value of the prize:

PV= FV/(1+i)^n

First 10 years:

PV= 759,646.49/(1.09^10)

PV= $320,882.89

Next 5 years:

PV= 1,709,582.17/(1.09^15)

PV= 469,345.34

Total PV= $790,228.23