Question

1. With the company retirement plan, you set aside a 6% of your salary each year to a 401(k) plan, with your employer matching dollar to dollar. You make the first 401(k) contribution on your 29th birthday based on the current salary of $72,000. Assume the contributions are made annually. You expect your salary to increase 3% a year, and the expected return on the retirement account is 8% per annum. How much do you expect to have at your retirement at age 67 (last contribution on your 67th birthday)? Hint: first find the PV of the cash flows, and convert it to a FV

Answer 1

There are two approaches to this question:

Approach 1:

Calculate the present value of all the future cash flow and then calculate FV as per below table:

Year	Age	Cash Flow	PV of Cash Flow
0	29	8640.0	8640.0
1	30	8899.2	8240.0
2	31	9166.2	7858.5
3	32	9441.2	7494.7
4	33	9724.4	7147.7
5	34	10016.1	6816.8
6	35	10316.6	6501.2
7	36	10626.1	6200.2
8	37	10944.9	5913.2
9	38	11273.2	5639.4
10	39	11611.4	5378.3
11	40	11959.8	5129.3
12	41	12318.6	4891.9
13	42	12688.1	4665.4
14	43	13068.8	4449.4
15	44	13460.8	4243.4
16	45	13864.7	4047.0
17	46	14280.6	3859.6
18	47	14709.0	3680.9
19	48	15150.3	3510.5
20	49	15604.8	3348.0
21	50	16072.9	3193.0
22	51	16555.1	3045.2
23	52	17051.8	2904.2
24	53	17563.3	2769.7
25	54	18090.2	2641.5
26	55	18632.9	2519.2
27	56	19191.9	2402.6
28	57	19767.7	2291.3
29	58	20360.7	2185.3
30	59	20971.5	2084.1
31	60	21600.7	1987.6
32	61	22248.7	1895.6
33	62	22916.2	1807.8
34	63	23603.7	1724.1
35	64	24311.8	1644.3
36	65	25041.1	1568.2
37	66	25792.4	1495.6
38	67	26566.1	1426.3
Total			157241.2
FV at 67th year			2928661.2

Calculations: Cash flow values are calculated as

First value- 72000*6%*2 and then 3% increase every year

Present value is calculated taking discounting factor of 8%

Future value of all the cash flow is calculated as : Total PV*(1+8%)^38

Approach Two:

Age	Cash Flow	Cash flow invested for years	FV on 67th year
29	8640.0	38	160922.4
30	8899.2	37	153472.3
31	9166.2	36	146367.1
32	9441.2	35	139590.8
33	9724.4	34	133128.3
34	10016.1	33	126964.9
35	10316.6	32	121086.9
36	10626.1	31	115481.1
37	10944.9	30	110134.7
38	11273.2	29	105035.9
39	11611.4	28	100173.1
40	11959.8	27	95535.5
41	12318.6	26	91112.5
42	12688.1	25	86894.4
43	13068.8	24	82871.5
44	13460.8	23	79034.8
45	13864.7	22	75375.8
46	14280.6	21	71886.2
47	14709.0	20	68558.1
48	15150.3	19	65384.1
49	15604.8	18	62357.1
50	16072.9	17	59470.2
51	16555.1	16	56716.9
52	17051.8	15	54091.2
53	17563.3	14	51586.9
54	18090.2	13	49198.6
55	18632.9	12	46920.9
56	19191.9	11	44748.7
57	19767.7	10	42677.0
58	20360.7	9	40701.2
59	20971.5	8	38816.9
60	21600.7	7	37019.8
61	22248.7	6	35305.9
62	22916.2	5	33671.4
63	23603.7	4	32112.5
64	24311.8	3	30625.8
65	25041.1	2	29208.0
66	25792.4	1	27855.7
67	26566.1	0	26566.1
	Total		2928661.2