Question

A major lottery advertises that it pays the winner $10 million. However this prize money is paid at the rate of $500,000 each year (with the first payment being immediate) for a total of 20 payments. What is the present value of this prize at 10% interest compounded annually? Report your answer in $millions, rounded to two decimal places. So, for example, if you compute the answer to be 5.7124 million dollars then you should submit an answer of 5.71.

Answer 1

The prize is worth 4.26 million dollars today.

Step-by-step explanation:

Giving the following information:

Cash flow= $500,000

Interest rate= 10% compounded annually

Number of years= 20

First, we will calculate the future value using the following formula:

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

A= annual cash flow

FV= {500,000*[(1.10^20) - 1]} / 0.10

FV= $28,637,499.75

Now, the present value:

PV= FV/(1+i)^n

PV= 28,637,499.75/1.10^20

PV= $4,256,781.86

The prize is worth 4.26 million dollars today.