Question

You just won the $55 million Ultimate Lotto jackpot. Your winnings will be paid as $2,200,000 per year for the next 25 years. If the appropriate interest rate is 5.5 percent, what is the value of your windfall?

$30,494,340.24

$31,133,737.70

$29,510,651.84

$28,933,737.70

$28,035,119.25

Answer 1

Correct Answer --- $29,510,651.84

Calculations and Explanation

Calculation of Present value of Windfall
Year	Yearly payments (A)	Discounting Factor at 5.5% (B)	Discounted Cash (A*B)a
1	$ 2,200,000.00	0.947867	$    2,085,308.06
2	$ 2,200,000.00	0.898452	$    1,976,595.31
3	$ 2,200,000.00	0.851614	$    1,873,550.06
4	$ 2,200,000.00	0.807217	$    1,775,876.84
5	$ 2,200,000.00	0.765134	$    1,683,295.58
6	$ 2,200,000.00	0.725246	$    1,595,540.83
7	$ 2,200,000.00	0.687437	$    1,512,360.98
8	$ 2,200,000.00	0.651599	$    1,433,517.52
9	$ 2,200,000.00	0.617629	$    1,358,784.37
10	$ 2,200,000.00	0.585431	$    1,287,947.27
11	$ 2,200,000.00	0.554911	$    1,220,803.10
12	$ 2,200,000.00	0.525982	$    1,157,159.34
13	$ 2,200,000.00	0.498561	$    1,096,833.50
14	$ 2,200,000.00	0.472569	$    1,039,652.60
15	$ 2,200,000.00	0.447933	$        985,452.71
16	$ 2,200,000.00	0.424581	$        934,078.39
17	$ 2,200,000.00	0.402447	$        885,382.36
18	$ 2,200,000.00	0.381466	$        839,224.99
19	$ 2,200,000.00	0.361579	$        795,473.92
20	$ 2,200,000.00	0.342729	$        754,003.72
21	$ 2,200,000.00	0.324862	$        714,695.47
22	$ 2,200,000.00	0.307926	$        677,436.46
23	$ 2,200,000.00	0.291873	$        642,119.87
24	$ 2,200,000.00	0.276657	$        608,644.43
25	$ 2,200,000.00	0.262234	$        576,914.15
Present value			$ 29,510,651.84

When cash is received in future then the value of future cash is ascertained by using appropriate discounting factor or interest rate. The Present value of 55000000 in 25 years received annually is 29510651.84. Present value of future cash flows will always be lower than undiscounted cash flow because value of money decreases over time.

Alternate Solution

Calculation of Present value of Windfall
Year	Yearly Payments (A)	Discounting Factor annuity (B)	Present value (A*B)
1-25.	$ 2,200,000.00	13.41393	$ 29,510,651.84