In: Finance
A rich aunt has promised you $3,000 one year from today. In addition, each year after that, she has promised you a payment (on the anniversary of the last payment) that is 2% larger than the last payment. She will continue to show this generosity for 2020 years, giving a total of 2020 payments. If the interest rate is 4%, what is her promise worth today?
$ 48,274.95
Present Value of cash flow is calculated as follows: | ||||
Year | Last Cash flow | Current Cash flow | Discount factor | Present Value |
a | b | c=b*1.02 | d=1.04^-a | e=c*d |
1 | 3,000.00 | 0.961538 | 2,884.62 | |
2 | 3,000.00 | 3,060.00 | 0.924556 | 2,829.14 |
3 | 3,060.00 | 3,121.20 | 0.888996 | 2,774.74 |
4 | 3,121.20 | 3,183.62 | 0.854804 | 2,721.38 |
5 | 3,183.62 | 3,247.30 | 0.821927 | 2,669.04 |
6 | 3,247.30 | 3,312.24 | 0.790315 | 2,617.71 |
7 | 3,312.24 | 3,378.49 | 0.759918 | 2,567.37 |
8 | 3,378.49 | 3,446.06 | 0.73069 | 2,518.00 |
9 | 3,446.06 | 3,514.98 | 0.702587 | 2,469.58 |
10 | 3,514.98 | 3,585.28 | 0.675564 | 2,422.09 |
11 | 3,585.28 | 3,656.98 | 0.649581 | 2,375.51 |
12 | 3,656.98 | 3,730.12 | 0.624597 | 2,329.82 |
13 | 3,730.12 | 3,804.73 | 0.600574 | 2,285.02 |
14 | 3,804.73 | 3,880.82 | 0.577475 | 2,241.08 |
15 | 3,880.82 | 3,958.44 | 0.555265 | 2,197.98 |
16 | 3,958.44 | 4,037.61 | 0.533908 | 2,155.71 |
17 | 4,037.61 | 4,118.36 | 0.513373 | 2,114.25 |
18 | 4,118.36 | 4,200.72 | 0.493628 | 2,073.60 |
19 | 4,200.72 | 4,284.74 | 0.474642 | 2,033.72 |
20 | 4,284.74 | 4,370.43 | 0.456387 | 1,994.61 |
Total | 48,274.95 |