The multistate Powerball Lottery, worth $182 million, was won by a single individual who had purchased...

The multistate Powerball Lottery, worth $182 million, was won by a single individual who had purchased five tickets at $1 each. The winner was given two choices: Receive 26 payments of $7 million each, with the first payment to occur now and the rest to be sent at the end of each of the next 25 years; OR receive a single lump-sum payment today that would be equivalent to the 26 payments of $7 million each. If the lottery uses an interest rate of 4%/yr/yr, find the amount of the lump sum payment.

Expert Solution

Today the lumpsum payment to be received is $116,354,560

The explanation is as follows:

YEAR	CASHFLOW	PVF @ 4%	PRESENT VALUE
0	7,000,000	1.000	7000000
1	7,000,000	0.962	6730769.2
2	7,000,000	0.925	6471893.5
3	7,000,000	0.889	6222974.5
4	7,000,000	0.855	5983629.3
5	7,000,000	0.822	5753489.7
6	7,000,000	0.790	5532201.7
7	7,000,000	0.760	5319424.7
8	7,000,000	0.731	5114831.4
9	7,000,000	0.703	4918107.1
10	7,000,000	0.676	4728949.2
11	7,000,000	0.650	4547066.5
12	7,000,000	0.625	4372179.3
13	7,000,000	0.601	4204018.6
14	7,000,000	0.577	4042325.6
15	7,000,000	0.555	3886851.5
16	7,000,000	0.534	3737357.2
17	7,000,000	0.513	3593612.7
18	7,000,000	0.494	3455396.8
19	7,000,000	0.475	3322497
20	7,000,000	0.456	3194708.6
21	7,000,000	0.439	3071835.2
22	7,000,000	0.422	2953687.7
23	7,000,000	0.406	2840084.3
24	7,000,000	0.390	2730850.3
25	7,000,000	0.375	2625817.6
Present value of Cash inflows			116354560

Rahul Sunny answered 2 years ago

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