In: Economics
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.
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 |