Question

A rich aunt has promised you $6,000 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?

The present value of the​ aunt's promise is?

Answer 1

Given Payment next year = 6000

Thereafter the payment shall increase by 3%

Also interest rate is 9%

Hence present value of 20 payments made by aunt is given as = Summison of Present value of Cash flow in each year. The computation is given below is given in the following table

Year	Payment by Aunt	Discounting factor at 9% Interest rate	Present value of payment
	6000*(1+3%)^(N-1)	1/((1+9%)^N)
N	A	B	C=A*B
1	6000.00 (6000*(1+3%)^(1-1)	0.91743 [1/((1+9%)^1)]	5504.59
2	6180.00 (6000*(1+3%)^(2-1)	0.84168	5201.58
3	6365.40	0.77218	4915.26
4	6556.36	0.70843	4644.69
5	6753.05	0.64993	4389.02
6	6955.64	0.59627	4147.42
7	7164.31	0.54703	3919.12
8	7379.24	0.50187	3703.39
9	7600.62	0.46043	3499.54
10	7828.64	0.42241	3306.90
11	8063.50	0.38753	3124.87
12	8305.40	0.35553	2952.86
13	8554.57	0.32618	2790.32
14	8811.20	0.29925	2636.72
15	9075.54	0.27454	2491.58
16	9347.80	0.25187	2354.43
17	9628.24	0.23107	2224.83
18	9917.09	0.21199	2102.36
19	10214.60	0.19449	1986.63
20	10521.04	0.17843	1877.28
		Total	67773.40

Hence present worth of the promise made by aunt = 67773.40