Question

An investor decides to purchase a five-year annuity with an annual nominal interest rate of 12%% convertible monthly for a price of X. Under the terms of the annuity, the investor is to receive 2 at the end of the first month. The payments increase by 2 each month thereafter. Calculate X.

Answer 1

Solution:

Period = 5 Years, 60 months

Interest rate = 12% p.a., 1% per month

X = Present value of monthly annuity amount discounted at 1% for 60 months

Computation of Present value of annuity
Period	Monthly Payment	PV Factor (1%)	Present Value
1	$2.00	0.99010	$1.98
2	$4.00	0.98030	$3.92
3	$6.00	0.97059	$5.82
4	$8.00	0.96098	$7.69
5	$10.00	0.95147	$9.51
6	$12.00	0.94205	$11.30
7	$14.00	0.93272	$13.06
8	$16.00	0.92348	$14.78
9	$18.00	0.91434	$16.46
10	$20.00	0.90529	$18.11
11	$22.00	0.89632	$19.72
12	$24.00	0.88745	$21.30
13	$26.00	0.87866	$22.85
14	$28.00	0.86996	$24.36
15	$30.00	0.86135	$25.84
16	$32.00	0.85282	$27.29
17	$34.00	0.84438	$28.71
18	$36.00	0.83602	$30.10
19	$38.00	0.82774	$31.45
20	$40.00	0.81954	$32.78
21	$42.00	0.81143	$34.08
22	$44.00	0.80340	$35.35
23	$46.00	0.79544	$36.59
24	$48.00	0.78757	$37.80
25	$50.00	0.77977	$38.99
26	$52.00	0.77205	$40.15
27	$54.00	0.76440	$41.28
28	$56.00	0.75684	$42.38
29	$58.00	0.74934	$43.46
30	$60.00	0.74192	$44.52
31	$62.00	0.73458	$45.54
32	$64.00	0.72730	$46.55
33	$66.00	0.72010	$47.53
34	$68.00	0.71297	$48.48
35	$70.00	0.70591	$49.41
36	$72.00	0.69892	$50.32
37	$74.00	0.69200	$51.21
38	$76.00	0.68515	$52.07
39	$78.00	0.67837	$52.91
40	$80.00	0.67165	$53.73
41	$82.00	0.66500	$54.53
42	$84.00	0.65842	$55.31
43	$86.00	0.65190	$56.06
44	$88.00	0.64545	$56.80
45	$90.00	0.63905	$57.51
46	$92.00	0.63273	$58.21
47	$94.00	0.62646	$58.89
48	$96.00	0.62026	$59.54
49	$98.00	0.61412	$60.18
50	$100.00	0.60804	$60.80
51	$102.00	0.60202	$61.41
52	$104.00	0.59606	$61.99
53	$106.00	0.59016	$62.56
54	$108.00	0.58431	$63.11
55	$110.00	0.57853	$63.64
56	$112.00	0.57280	$64.15
57	$114.00	0.56713	$64.65
58	$116.00	0.56151	$65.14
59	$118.00	0.55595	$65.60
60	$120.00	0.55045	$66.05
Total			$2,475.52

Therefore X = $2,475.52