Question

1. The present value of a series of 50 payments starting at 100 at the end of the first year and increasing by 1 each year thereafter is equal to 2X. The annual effective rate of interest is 9%. Calculate X.

Answer 1

(a ) Year	(b) Payment $	( c) PV factor @9%(=1/(1+0.09)^a)	(d) Present Value (c*b) $
1	100	0.917	91.74
2	101	0.842	85.01
3	102	0.772	78.76
4	103	0.708	72.97
5	104	0.650	67.59
6	105	0.596	62.61
7	106	0.547	57.99
8	107	0.502	53.70
9	108	0.460	49.73
10	109	0.422	46.04
11	110	0.388	42.63
12	111	0.356	39.46
13	112	0.326	36.53
14	113	0.299	33.81
15	114	0.275	31.30
16	115	0.252	28.97
17	116	0.231	26.80
18	117	0.212	24.80
19	118	0.194	22.95
20	119	0.178	21.23
21	120	0.164	19.64
22	121	0.150	18.17
23	122	0.138	16.81
24	123	0.126	15.55
25	124	0.116	14.38
26	125	0.106	13.30
27	126	0.098	12.30
28	127	0.090	11.37
29	128	0.082	10.52
30	129	0.075	9.72
31	130	0.069	8.99
32	131	0.063	8.31
33	132	0.058	7.68
34	133	0.053	7.10
35	134	0.049	6.56
36	135	0.045	6.07
37	136	0.041	5.61
38	137	0.038	5.18
39	138	0.035	4.79
40	139	0.032	4.43
41	140	0.029	4.09
42	141	0.027	3.78
43	142	0.025	3.49
44	143	0.023	3.23
45	144	0.021	2.98
46	145	0.019	2.75
47	146	0.017	2.54
48	147	0.016	2.35
49	148	0.015	2.17
50	149	0.013	2.00
Total of PV $			1,210.49

Present Value = 2X

$ 1,210.49 = 2X

X = 1,210.49 / 2 = $605.25(Answer)