Question

In: Economics

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.

Solutions

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

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