Question

Assume that you just won $35 million in the Florida lottery, and hence the state will pay you 20 annual payments of $1.75 million each beginning immediately. If the similar risk to the lottery earnings (e.g., the rate on 20-year U.S. Treasury bonds) is 6 percent, what is the present value of your winnings

Answer 1

$21.277 million

Step-by-step explanation:

Data provided in the question:

Amount of lottery won = $35 million

Number of annual payments = 20

Amount of annual payment = $1.75 million

Interest rate = 6%

Now,

Present value of the payment = Payment × Present value factor

Also,

Present value factor = [1 + r]⁻ⁿ

Since the payment started immediately

Therefore,

Base year i.e n = 0

Thus,

we have

Year (n) Annual payment Present value

0 $1.75 million $1.75 million

1 $1.75 million $ 1.650943 million

2 $1.75 million $1.557494 million

3 $1.75 million $1.469334 million

4 $1.75 million $1.386164 million

5 $1.75 million $1.307702 million

6 $1.75 million $1.233681 million

7 $1.75 million $1.16385 million

8 $1.75 million $1.097972 million

9 $1.75 million $1.035822 million

10 $1.75 million $0.977191 million

11 $1.75 million $0.921878 million

12 $1.75 million $0.869696 million

13 $1.75 million $0.820468 million

14 $1.75 million $0.774027 million

15 $1.75 million $0.730214 million

16 $1.75 million $0.688881 million

17 $1.75 million $0.649888 million

18 $1.75 million $0.613102 million

19 $1.75 million $0.578398 million

Hence,

The present value of the winnings = ∑ Present value of payments

= $21.277 million