Question

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 3% larger than the last payment. She will continue to show this generosity for 20 years, giving a total of 20 payments. If the interest rate is 9%​, what is her promise worth​ today?

Answer 1

$ 33,886.70

Present Value of cash flow is calculated as follows:
Year	Last Cash flow	Current Cash flow	Discount factor	Present Value
a	b	c=b*1.03	d=1.09^-a	e=c*d
1		3,000.00	0.917431	2,752.29
2	3,000.00	3,090.00	0.84168	2,600.79
3	3,090.00	3,182.70	0.772183	2,457.63
4	3,182.70	3,278.18	0.708425	2,322.35
5	3,278.18	3,376.53	0.649931	2,194.51
6	3,376.53	3,477.82	0.596267	2,073.71
7	3,477.82	3,582.16	0.547034	1,959.56
8	3,582.16	3,689.62	0.501866	1,851.70
9	3,689.62	3,800.31	0.460428	1,749.77
10	3,800.31	3,914.32	0.422411	1,653.45
11	3,914.32	4,031.75	0.387533	1,562.44
12	4,031.75	4,152.70	0.355535	1,476.43
13	4,152.70	4,277.28	0.326179	1,395.16
14	4,277.28	4,405.60	0.299246	1,318.36
15	4,405.60	4,537.77	0.274538	1,245.79
16	4,537.77	4,673.90	0.25187	1,177.21
17	4,673.90	4,814.12	0.231073	1,112.41
18	4,814.12	4,958.54	0.211994	1,051.18
19	4,958.54	5,107.30	0.19449	993.32
20	5,107.30	5,260.52	0.178431	938.64
	Total			33,886.70