Question

Ms. Smith plans to retire in 25 years (she will be 65). The IRS longevity table forecasts that Ms. Smith will live to be 85 years old. Ms. Smith is expected to have 20 years in retirement. Ms. Smith needs to be able to withdraw $60,000 annually (end of each year) from her retirement investment account before the balance is fully used. This plus her $35,000 annually in social security benefits will serve her needs (she believes). During her 20 years in retirement Ms. Smith expects the average annual compounded rate of return on her invested monies to be 5%. For the 25 years getting to retirement Ms. Smith expects her retirement investment account to earn an average annual compounded rate of return of 7%.

Please answer the following. Use the data as it is written above.

1. How much must the balance of the retirement investment account be when Ms. Smith retires so that she can withdraw $60,000 annually (20 withdrawals), at the end of each year, before the account balance is fully used?

2. How much must Ms. Smith invest each year for the 25 years leading up to the retirement date so that the account accumulates the needed amount by the time that retirement begins?

Answer 1

1.

We need to find out the present values of the 20 withdrawals that Ms Smith will make. The calculation is detailed as follows

Answer is 747,733

Age	Discount Period	Amount	PV Factor	PV
			1/(1+5%)^Discount Period	Amount X PV Factor
66	1	60,000	0.95238	57,143
67	2	60,000	0.90703	54,422
68	3	60,000	0.86384	51,830
69	4	60,000	0.8227	49,362
70	5	60,000	0.78353	47,012
71	6	60,000	0.74622	44,773
72	7	60,000	0.71068	42,641
73	8	60,000	0.67684	40,610
74	9	60,000	0.64461	38,677
75	10	60,000	0.61391	36,835
76	11	60,000	0.58468	35,081
77	12	60,000	0.55684	33,410
78	13	60,000	0.53032	31,819
79	14	60,000	0.50507	30,304
80	15	60,000	0.48102	28,861
81	16	60,000	0.45811	27,487
82	17	60,000	0.4363	26,178
83	18	60,000	0.41552	24,931
84	19	60,000	0.39573	23,744
85	20	60,000	0.37689	22,613
				747,733

2

Assuming amount is invested at beginning of each period

Amount is 11,048.64 (or 11,049) per year

Year	Beg balance	Addition	Interest	End Balance
1	0	$ 11,049	$ 773	$ 11,822
2	$ 11,822	$ 11,049	$ 1,601	$ 24,472
3	$ 24,472	$ 11,049	$ 2,486	$ 38,007
4	$ 38,007	$ 11,049	$ 3,434	$ 52,489
5	$ 52,489	$ 11,049	$ 4,448	$ 67,986
6	$ 67,986	$ 11,049	$ 5,532	$ 84,567
7	$ 84,567	$ 11,049	$ 6,693	$ 102,308
8	$ 102,308	$ 11,049	$ 7,935	$ 121,292
9	$ 121,292	$ 11,049	$ 9,264	$ 141,604
10	$ 141,604	$ 11,049	$ 10,686	$ 163,339
11	$ 163,339	$ 11,049	$ 12,207	$ 186,594
12	$ 186,594	$ 11,049	$ 13,835	$ 211,478
13	$ 211,478	$ 11,049	$ 15,577	$ 238,104
14	$ 238,104	$ 11,049	$ 17,441	$ 266,593
15	$ 266,593	$ 11,049	$ 19,435	$ 297,077
16	$ 297,077	$ 11,049	$ 21,569	$ 329,694
17	$ 329,694	$ 11,049	$ 23,852	$ 364,595
18	$ 364,595	$ 11,049	$ 26,295	$ 401,938
19	$ 401,938	$ 11,049	$ 28,909	$ 441,896
20	$ 441,896	$ 11,049	$ 31,706	$ 484,651
21	$ 484,651	$ 11,049	$ 34,699	$ 530,398
22	$ 530,398	$ 11,049	$ 37,901	$ 579,348
23	$ 579,348	$ 11,049	$ 41,328	$ 631,725
24	$ 631,725	$ 11,049	$ 44,994	$ 687,767
25	$ 687,767	$ 11,049	$ 48,917	$ 747,733