Spivey just won the Powerball lottery! The $19 comma 000 comma 00019,000,000 jackpot will be paid in 1010 annual installments of $1 comma 900 comma 0001,900,000 each, with the first payment to be paid immediately. Spivey's opportunity cost of capital (interest rate) is 55 % per year. What is the present equivalent of Spivey's lottery winnings at the time of the first payment?

Present Value = $15,404,861.19

Explanation:

Giving the following information:

The $19,000,000 jackpot will be paid in 10 annual installments of $1,900,000 each, with the first payment to be paid immediately. Spivey's opportunity cost of capital (interest rate) is 5 % per year.

To calculate the present value, first, we need to calculate the final value:

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

A = annual pay = 1,900,000

i = 5%

n = 10

FV = {1,900,000*[ (1.05^10) - 1]}/0.05 + [ (1,900,000*1,05^10) - 1,900,000 = 23,897,995.82 + 1,194,899.80 = 25,092,895.62

Now, we can calculate the present value:

PV = FV / (1+i) ^n

PV = 25,092,895.62 / 1.05^10 = 15,404,861.19