In: Finance
Jack and Diane are lottery winners. They hold the ticket to the Grand Prize in the “Set for Life” Prize that makes 20 consecutive annual payments of $50,000 starting immediately. There is one hitch: the eleventh payment (to be received at the end of year 10) is not $50,000 but only $20,000 (that is, this payment is $30,000 LESS than the other 20). Which of the following comes closest to the present value of the prize if interest rates are 5%?
a. |
$ 635,849 |
|
b. |
$ 686,430 |
|
c. |
$ 743,867 |
|
d. |
$ 591,154 |
|
e. |
$ 551,529 |
a. $ 635,849 |
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Statement showing Cash flows | ||||
Particulars | Time | PVF 5% | Amount | PV |
Cash Inflows | - | 1.0000 | 50,000.00 | 50,000.00 |
Cash Inflows | 1.00 | 0.9524 | 50,000.00 | 47,619.05 |
Cash Inflows | 2.00 | 0.9070 | 50,000.00 | 45,351.47 |
Cash Inflows | 3.00 | 0.8638 | 50,000.00 | 43,191.88 |
Cash Inflows | 4.00 | 0.8227 | 50,000.00 | 41,135.12 |
Cash Inflows | 5.00 | 0.7835 | 50,000.00 | 39,176.31 |
Cash Inflows | 6.00 | 0.7462 | 50,000.00 | 37,310.77 |
Cash Inflows | 7.00 | 0.7107 | 50,000.00 | 35,534.07 |
Cash Inflows | 8.00 | 0.6768 | 50,000.00 | 33,841.97 |
Cash Inflows | 9.00 | 0.6446 | 50,000.00 | 32,230.45 |
Cash Inflows | 10.00 | 0.6139 | 20,000.00 | 12,278.27 |
Cash Inflows | 11.00 | 0.5847 | 50,000.00 | 29,233.96 |
Cash Inflows | 12.00 | 0.5568 | 50,000.00 | 27,841.87 |
Cash Inflows | 13.00 | 0.5303 | 50,000.00 | 26,516.07 |
Cash Inflows | 14.00 | 0.5051 | 50,000.00 | 25,253.40 |
Cash Inflows | 15.00 | 0.4810 | 50,000.00 | 24,050.85 |
Cash Inflows | 16.00 | 0.4581 | 50,000.00 | 22,905.58 |
Cash Inflows | 17.00 | 0.4363 | 50,000.00 | 21,814.83 |
Cash Inflows | 18.00 | 0.4155 | 50,000.00 | 20,776.03 |
Cash Inflows | 19.00 | 0.3957 | 50,000.00 | 19,786.70 |
Present value of prize | 635,848.65 |