Question

Rita Gonzales won the $38 million lottery. She is to receive $1.1 million a year for the next 25 years plus an additional lump sum payment of $10.5 million after 25 years. The discount rate is 12 percent.

What is the current value of her winnings?

Answer 1

$9,178,921.52

To see the present worth of the winning, we would need to calculate present value of the 25 years of payment.

Present value is the value in the present of a sum of money, in contrast to some future value it will have when it has been invested at compound interest.

Present value = future value/(1+interest rate)*time

Present value of 1st year

= 1,100,000/(1 + 12%)^1

= $982,142.86

The present value of 2nd-year money

= 1,100,000/(1 + 12%)^2

= $876,913.27

The present value of 3rd-year money

= 1,100,000/(1 + 12%)^3

= $782,958.27

The present value of money received on 25th year

= 1,100,000/(1 + 12%)^25

= $64,705.64

We will also receive 10.5 million after 25 years or on 26th year

Its present value

= 10,500,000/(1 + 12%)^26

= $551,468.50

All the calculations are done in the following table form

Year	Winnings	PV
1	$1,100,000	$982,142.86
2	$1,100,000	$876,913.27
3	$1,100,000	$782,958.27
4	$1,100,000	$699,069.89
5	$1,100,000	$624,169.54
6	$1,100,000	$557,294.23
7	$1,100,000	$497,584.14
8	$1,100,000	$444,271.55
9	$1,100,000	$396,671.03
10	$1,100,000	$354,170.56
11	$1,100,000	$316,223.71
12	$1,100,000	$282,342.60
13	$1,100,000	$252,091.61
14	$1,100,000	$225,081.79
15	$1,100,000	$200,965.89
16	$1,100,000	$179,433.83
17	$1,100,000	$160,208.78
18	$1,100,000	$143,043.55
19	$1,100,000	$127,717.45
20	$1,100,000	$114,033.44
21	$1,100,000	$101,815.57
22	$1,100,000	$90,906.76
23	$1,100,000	$81,166.75
24	$1,100,000	$72,470.31
25	$1,100,000	$64,705.64
26	$10,500,000	$551,468.50
Total	$38,000,000.00	$9,178,921.52

The present value of the lottery is $9,178,921.52