Question

Dusty Jones is 23 years old and has accumulated $4,000 in her self-directed defined contribution pension plan. Each year she contributes $2,000 to the plan, and her employer contributes an equal amount. Dusty thinks she will retire at age 67 and figures she will live to age 81. The plan allows for two types of investments. One offers a 3.5% risk-free real rate of return. The other offers an expected return of 10% and has a standard deviation of 23%. Dusty now has 5% of her money in the risk-free investment and 95% in the risky investment. She plans to continue saving at the same rate and keep the same proportions invested in each of the investments. Her salary will grow at the same rate as inflation. How much can Dusty be sure of having in the safe account at retirement?

A: 37,221

B: 16,423

C: 11,856

D: 21,156

E: 49,219

Answer 1

Answer is 21,156.

Working is as follows-

year	Opening	Addition	Interest	Closing
1	200.00	200.00	7.00	407.00
2	407.00	200.00	14.25	621.25
3	621.25	200.00	21.74	842.99
4	842.99	200.00	29.50	1,072.49
5	1,072.49	200.00	37.54	1,310.03
6	1,310.03	200.00	45.85	1,555.88
7	1,555.88	200.00	54.46	1,810.34
8	1,810.34	200.00	63.36	2,073.70
9	2,073.70	200.00	72.58	2,346.28
10	2,346.28	200.00	82.12	2,628.40
11	2,628.40	200.00	91.99	2,920.39
12	2,920.39	200.00	102.21	3,222.61
13	3,222.61	200.00	112.79	3,535.40
14	3,535.40	200.00	123.74	3,859.14
15	3,859.14	200.00	135.07	4,194.21
16	4,194.21	200.00	146.80	4,541.00
17	4,541.00	200.00	158.94	4,899.94
18	4,899.94	200.00	171.50	5,271.44
19	5,271.44	200.00	184.50	5,655.94
20	5,655.94	200.00	197.96	6,053.89
21	6,053.89	200.00	211.89	6,465.78
22	6,465.78	200.00	226.30	6,892.08
23	6,892.08	200.00	241.22	7,333.31
24	7,333.31	200.00	256.67	7,789.97
25	7,789.97	200.00	272.65	8,262.62
26	8,262.62	200.00	289.19	8,751.81
27	8,751.81	200.00	306.31	9,258.13
28	9,258.13	200.00	324.03	9,782.16
29	9,782.16	200.00	342.38	10,324.54
30	10,324.54	200.00	361.36	10,885.89
31	10,885.89	200.00	381.01	11,466.90
32	11,466.90	200.00	401.34	12,068.24
33	12,068.24	200.00	422.39	12,690.63
34	12,690.63	200.00	444.17	13,334.80
35	13,334.80	200.00	466.72	14,001.52
36	14,001.52	200.00	490.05	14,691.57
37	14,691.57	200.00	514.21	15,405.78
38	15,405.78	200.00	539.20	16,144.98
39	16,144.98	200.00	565.07	16,910.06
40	16,910.06	200.00	591.85	17,701.91
41	17,701.91	200.00	619.57	18,521.47
42	18,521.47	200.00	648.25	19,369.73
43	19,369.73	200.00	677.94	20,247.67
44	20,247.67	200.00	708.67	21,156.33

Note:

1. Assumed contribution is made at year end.