Question

James has been employed by ABC Co.Ltd, drawing an annual salary of $120000, paid at the end of each year. He plans to work for five years before retiring. He buys a new home with mortgage repayments of $2800 per month for the next 20 years (payable at the end of each month), and donates $2000 per annum forever to his favourite charity. Assume an annual interest rate of 6% p.a, what annual amount, in present value terms, can James withdraw for the first five years of his retirement from the remainder of his savings?

Answer 1

Step 1: Computation of a Present value of Mortgage payments:

Given

Rate of interest = 6% p.a

Rate of Interest per month = 6% /12 = 0.5% per month.

Term = 20 years

No.of months = 20*12= 240 months

S.No	Cash flow	Disc @ 0.5%	Discounted Cash flows
1	$2,800	0.9950	$2,786.07
2	$2,800	0.9901	$2,772.21
3	$2,800	0.9851	$2,758.42
4	$2,800	0.9802	$2,744.69
5	$2,800	0.9754	$2,731.04
6	$2,800	0.9705	$2,717.45
7	$2,800	0.9657	$2,703.93
8	$2,800	0.9609	$2,690.48
9	$2,800	0.9561	$2,677.09
10	$2,800	0.9513	$2,663.77
11	$2,800	0.9466	$2,650.52
12	$2,800	0.9419	$2,637.33
13	$2,800	0.9372	$2,624.21
14	$2,800	0.9326	$2,611.16
15	$2,800	0.9279	$2,598.17
16	$2,800	0.9233	$2,585.24
17	$2,800	0.9187	$2,572.38
18	$2,800	0.9141	$2,559.58
19	$2,800	0.9096	$2,546.85
20	$2,800	0.9051	$2,534.18
21	$2,800	0.9006	$2,521.57
22	$2,800	0.8961	$2,509.02
23	$2,800	0.8916	$2,496.54
24	$2,800	0.8872	$2,484.12
25	$2,800	0.8828	$2,471.76
26	$2,800	0.8784	$2,459.46
27	$2,800	0.8740	$2,447.23
28	$2,800	0.8697	$2,435.05
29	$2,800	0.8653	$2,422.94
30	$2,800	0.8610	$2,410.88
31	$2,800	0.8567	$2,398.89
32	$2,800	0.8525	$2,386.95
33	$2,800	0.8482	$2,375.08
34	$2,800	0.8440	$2,363.26
35	$2,800	0.8398	$2,351.50
36	$2,800	0.8356	$2,339.81
37	$2,800	0.8315	$2,328.16
38	$2,800	0.8274	$2,316.58
39	$2,800	0.8232	$2,305.06
40	$2,800	0.8191	$2,293.59
41	$2,800	0.8151	$2,282.18
42	$2,800	0.8110	$2,270.82
43	$2,800	0.8070	$2,259.53
44	$2,800	0.8030	$2,248.28
45	$2,800	0.7990	$2,237.10
46	$2,800	0.7950	$2,225.97
47	$2,800	0.7910	$2,214.89
48	$2,800	0.7871	$2,203.88
49	$2,800	0.7832	$2,192.91
50	$2,800	0.7793	$2,182.00
51	$2,800	0.7754	$2,171.15
52	$2,800	0.7716	$2,160.34
53	$2,800	0.7677	$2,149.60
54	$2,800	0.7639	$2,138.90
55	$2,800	0.7601	$2,128.26
56	$2,800	0.7563	$2,117.67
57	$2,800	0.7525	$2,107.14
58	$2,800	0.7488	$2,096.65
59	$2,800	0.7451	$2,086.22
60	$2,800	0.7414	$2,075.84
61	$2,800	0.7377	$2,065.51
62	$2,800	0.7340	$2,055.24
63	$2,800	0.7304	$2,045.01
64	$2,800	0.7267	$2,034.84
65	$2,800	0.7231	$2,024.72
66	$2,800	0.7195	$2,014.64
67	$2,800	0.7159	$2,004.62
68	$2,800	0.7124	$1,994.65
69	$2,800	0.7088	$1,984.72
70	$2,800	0.7053	$1,974.85
71	$2,800	0.7018	$1,965.02
72	$2,800	0.6983	$1,955.25
73	$2,800	0.6948	$1,945.52
74	$2,800	0.6914	$1,935.84
75	$2,800	0.6879	$1,926.21
76	$2,800	0.6845	$1,916.63
77	$2,800	0.6811	$1,907.09
78	$2,800	0.6777	$1,897.60
79	$2,800	0.6743	$1,888.16
80	$2,800	0.6710	$1,878.77
81	$2,800	0.6677	$1,869.42
82	$2,800	0.6643	$1,860.12
83	$2,800	0.6610	$1,850.87
84	$2,800	0.6577	$1,841.66
85	$2,800	0.6545	$1,832.49
86	$2,800	0.6512	$1,823.38
87	$2,800	0.6480	$1,814.31
88	$2,800	0.6447	$1,805.28
89	$2,800	0.6415	$1,796.30
90	$2,800	0.6383	$1,787.36
91	$2,800	0.6352	$1,778.47
92	$2,800	0.6320	$1,769.62
93	$2,800	0.6289	$1,760.82
94	$2,800	0.6257	$1,752.06
95	$2,800	0.6226	$1,743.34
96	$2,800	0.6195	$1,734.67
97	$2,800	0.6164	$1,726.04
98	$2,800	0.6134	$1,717.45
99	$2,800	0.6103	$1,708.90
100	$2,800	0.6073	$1,700.40
101	$2,800	0.6043	$1,691.94
102	$2,800	0.6013	$1,683.53
103	$2,800	0.5983	$1,675.15
104	$2,800	0.5953	$1,666.82
105	$2,800	0.5923	$1,658.52
106	$2,800	0.5894	$1,650.27
107	$2,800	0.5865	$1,642.06
108	$2,800	0.5835	$1,633.89
109	$2,800	0.5806	$1,625.76
110	$2,800	0.5777	$1,617.67
111	$2,800	0.5749	$1,609.63
112	$2,800	0.5720	$1,601.62
113	$2,800	0.5692	$1,593.65
114	$2,800	0.5663	$1,585.72
115	$2,800	0.5635	$1,577.83
116	$2,800	0.5607	$1,569.98
117	$2,800	0.5579	$1,562.17
118	$2,800	0.5551	$1,554.40
119	$2,800	0.5524	$1,546.67
120	$2,800	0.5496	$1,538.97
121	$2,800	0.5469	$1,531.32
122	$2,800	0.5442	$1,523.70
123	$2,800	0.5415	$1,516.12
124	$2,800	0.5388	$1,508.57
125	$2,800	0.5361	$1,501.07
126	$2,800	0.5334	$1,493.60
127	$2,800	0.5308	$1,486.17
128	$2,800	0.5281	$1,478.78
129	$2,800	0.5255	$1,471.42
130	$2,800	0.5229	$1,464.10
131	$2,800	0.5203	$1,456.81
132	$2,800	0.5177	$1,449.57
133	$2,800	0.5151	$1,442.35
134	$2,800	0.5126	$1,435.18
135	$2,800	0.5100	$1,428.04
136	$2,800	0.5075	$1,420.93
137	$2,800	0.5050	$1,413.86
138	$2,800	0.5024	$1,406.83
139	$2,800	0.4999	$1,399.83
140	$2,800	0.4975	$1,392.87
141	$2,800	0.4950	$1,385.94
142	$2,800	0.4925	$1,379.04
143	$2,800	0.4901	$1,372.18
144	$2,800	0.4876	$1,365.35
145	$2,800	0.4852	$1,358.56
146	$2,800	0.4828	$1,351.80
147	$2,800	0.4804	$1,345.08
148	$2,800	0.4780	$1,338.38
149	$2,800	0.4756	$1,331.73
150	$2,800	0.4733	$1,325.10
151	$2,800	0.4709	$1,318.51
152	$2,800	0.4686	$1,311.95
153	$2,800	0.4662	$1,305.42
154	$2,800	0.4639	$1,298.93
155	$2,800	0.4616	$1,292.46
156	$2,800	0.4593	$1,286.03
157	$2,800	0.4570	$1,279.64
158	$2,800	0.4547	$1,273.27
159	$2,800	0.4525	$1,266.93
160	$2,800	0.4502	$1,260.63
161	$2,800	0.4480	$1,254.36
162	$2,800	0.4458	$1,248.12
163	$2,800	0.4435	$1,241.91
164	$2,800	0.4413	$1,235.73
165	$2,800	0.4391	$1,229.58
166	$2,800	0.4370	$1,223.47
167	$2,800	0.4348	$1,217.38
168	$2,800	0.4326	$1,211.32
169	$2,800	0.4305	$1,205.30
170	$2,800	0.4283	$1,199.30
171	$2,800	0.4262	$1,193.33
172	$2,800	0.4241	$1,187.40
173	$2,800	0.4220	$1,181.49
174	$2,800	0.4199	$1,175.61
175	$2,800	0.4178	$1,169.76
176	$2,800	0.4157	$1,163.94
177	$2,800	0.4136	$1,158.15
178	$2,800	0.4116	$1,152.39
179	$2,800	0.4095	$1,146.66
180	$2,800	0.4075	$1,140.95
181	$2,800	0.4055	$1,135.27
182	$2,800	0.4034	$1,129.63
183	$2,800	0.4014	$1,124.01
184	$2,800	0.3994	$1,118.41
185	$2,800	0.3974	$1,112.85
186	$2,800	0.3955	$1,107.31
187	$2,800	0.3935	$1,101.80
188	$2,800	0.3915	$1,096.32
189	$2,800	0.3896	$1,090.87
190	$2,800	0.3877	$1,085.44
191	$2,800	0.3857	$1,080.04
192	$2,800	0.3838	$1,074.67
193	$2,800	0.3819	$1,069.32
194	$2,800	0.3800	$1,064.00
195	$2,800	0.3781	$1,058.71
196	$2,800	0.3762	$1,053.44
197	$2,800	0.3744	$1,048.20
198	$2,800	0.3725	$1,042.98
199	$2,800	0.3706	$1,037.80
200	$2,800	0.3688	$1,032.63
201	$2,800	0.3670	$1,027.49
202	$2,800	0.3651	$1,022.38
203	$2,800	0.3633	$1,017.30
204	$2,800	0.3615	$1,012.24
205	$2,800	0.3597	$1,007.20
206	$2,800	0.3579	$1,002.19
207	$2,800	0.3561	$997.20
208	$2,800	0.3544	$992.24
209	$2,800	0.3526	$987.30
210	$2,800	0.3509	$982.39
211	$2,800	0.3491	$977.51
212	$2,800	0.3474	$972.64
213	$2,800	0.3456	$967.80
214	$2,800	0.3439	$962.99
215	$2,800	0.3422	$958.20
216	$2,800	0.3405	$953.43
217	$2,800	0.3388	$948.69
218	$2,800	0.3371	$943.97
219	$2,800	0.3355	$939.27
220	$2,800	0.3338	$934.60
221	$2,800	0.3321	$929.95
222	$2,800	0.3305	$925.32
223	$2,800	0.3288	$920.72
224	$2,800	0.3272	$916.14
225	$2,800	0.3256	$911.58
226	$2,800	0.3239	$907.04
227	$2,800	0.3223	$902.53
228	$2,800	0.3207	$898.04
229	$2,800	0.3191	$893.57
230	$2,800	0.3175	$889.13
231	$2,800	0.3160	$884.70
232	$2,800	0.3144	$880.30
233	$2,800	0.3128	$875.92
234	$2,800	0.3113	$871.56
235	$2,800	0.3097	$867.23
236	$2,800	0.3082	$862.91
237	$2,800	0.3067	$858.62
238	$2,800	0.3051	$854.35
239	$2,800	0.3036	$850.10
240	$2,800	0.3021	$845.87
		Total	$390,826.16

Present vaue of Donation = Annual Donation Amount / Rate of interest

$ 2000/0.06

$33333.33

So the Total Present value of Payments = $ 390826.16+$ 33,333.33 = $ 424159.49

Step 2: Calculation of Annual withdrwals amount:

We know that present value of the Annual withdrwals should be equal to the present value of the futute payments.

Let the Annual withdrawings be X

Year	Cash flows	Disc @ 6%	Discoounting Factor
1	X	1/( 1.06)^1	0.9434
2	X	1/( 1.06)^2	0.8900
3	X	1/( 1.06)^3	0.8396
4	X	1/( 1.06)^4	0.7921
5	X	1/( 1.06)^5	0.7473
			4.2124

X*PVAF ( 6%,5) = $ 424159.49

X * 4.2124 = $ 424159.49

X = $ 424159.49/4.2124

X = $ 100693.070

So James Should withdraw $ 10069.3.070 per year from the remainder of his savings.

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