Question

What value of G makes the two series of cash flows described below (A and B) equivalent at an interest rate of 20% per year?

A: 14 annual deposits in the amount of $150

B: 7 annual deposits, starting in the amount of $150 in the first year and increasing by

$G each year.

Answer 1

This question is solved as follows. First calculate the PV of A, which is straightforward. Then calculate the PV of B without G first. Then we need to find the difference PV of A and PV of B, and this would be equal to the PV of a growing annuity G. It would be easy to solve for G. Pls see table below.

Step 1: PV of A = 692

		A / (1.2^Time)
Time	A	PV(A)
1	150	125
2	150	104
3	150	87
4	150	72
5	150	60
6	150	50
7	150	42
8	150	35
9	150	29
10	150	24
11	150	20
12	150	17
13	150	14
14	150	12
	Total	692

Step 2: PV of B, without G

		A / (1.2^Time)
Time	B	PV(B)
1	150	125
2	150	104
3	150	87
4	150	72
5	150	60
6	150	50
7	150	42
	Total	541

Step 3: PV of growing annuity G is 692 - 541 = 151

		1 / (1.2^Time)
Time	CF	PV Factor	CF * PV Factor (G omitted)
1	G	0.83	0.83
2	2G	0.69	1.39
3	3G	0.58	1.74
4	4G	0.48	1.93
5	5G	0.40	2.01
6	6G	0.33	2.01
7	7G	0.28	1.95
	Total		11.86

So 11.86G = 151, hence G = 12.73