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

x=3

step-by-step explanation:

this is really simple i saw that there was only one term (5x) and thought if that was 15 what would i have to multiply everything else to get it there? well if 5x became 15 then x would have to be 3 so plug the 3 in the x for the other equations and you get 15 for the other ones. so there you go. : )