Theo just won a prize that will pay him $12,000 a year for 12 years, starting at the end of Year 12. What is the current value of this prize if the discount rate is 9 percent, compounded annually?

Present Value = $30,550.64

Explanation:

Giving the following information:

Theo just won a prize that will pay him $12,000 a year for 12 years, starting at the end of Year 12.

Interest rate = 9%

To determine the value today of the prize, I will divide it into 2 different calculations. First, we will calculate the final value of the prize. Then, calculate the present value (24 years from now).

To calculate the final value, we need to use the following formula:

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

A = annual deposit = 12,000

i = 0,09

n=12

FV = {12,000*[ (1.09^12) - 1]} / 0.09 = 241,688.64

Now, we determine the present value:

PV = FV / (1+i) ^n

PV = 241,688.64 / (1.09^24) = $30,550.64