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

Answer:

$21.277 million

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