Question

Check my work Assume you won worldwide lottery that pays $1.25 million in year 0, $5 million in year 1, and $200,000 in years 5 through 100. Assuming that 100 years is as "long" as infinity, calculate the perpetual equivalent annual worth for years 1 through infinity at an interest rate of 10% per year. (Enter your answer in dollars and not in millions.) The perpetual equivalent annual worth for years 1 through infinity is $[

Answer 1

All amounts are in $

Value of Present Lottery payments

= Present Receipt + Present value of Receipt after 1 year + Present value of receipts received annually from year 5 to year 100

= 1.25 million + 5 million/(1+0.1) + [(200,000/0.1)-(200,000 x PVAF(4 years,10%)]

= 1.25 million + 4,545,455 + [2,000,000-633,973]

= 7,161,482

(As Given, 100 years are taken as annuity)

Present value of receipts receieved annually from year 5 to 100 is

= Perpetuity of 100 years - Present value of first 4 years (since the payment starts at 5th year)

We have to find perpetual equivalent annual worth for year 1 through infinity

Let that be "Y"

Y/0.1 = 7,161,482

Y = 716,148

Any minor difference is due to rounding off the intermediate calculations to dollars and not cents