Question

Assume you plan to retire in 35 years. If you invest $180.00 per month in the broad U.S. equity market and earn annual returns of 9.5% over that period, how much money will you have accumulated on the day you plan to retire?

Note: Enter your answer rounded to the nearest dollar. For example, if your calculated accumulated amount is $225,784.63 enter it as: 225,785 or 225785.

Answer 1

Each year a FIXED amount of $ 2160 (180*12 months) is invested.

r= interest rate = 9.5% p.a (annual return)

years = 35

The principle increases each year by an amount of $2160 plus the previous year's principle and interest and each year's interest is compounded on the increasing principle.

Hence the total amount of money on the day you plan to retire will be $ 571642.

Year	Principle (Total+ 2160)	r= 9.5%	Interest (P* r)	Total (P+interest)
1	2160	0.095	205.20	2365.20
2	4525.20	0.095	429.89	4955.09
3	7115.09	0.095	675.93	7791.03
4	9951.03	0.095	945.35	10896.38
5	13056.38	0.095	1240.36	14296.73
6	16456.73	0.095	1563.39	18020.12
7	20180.12	0.095	1917.11	22097.23
8	24257.23	0.095	2304.44	26561.67
9	28721.67	0.095	2728.56	31450.23
10	33610.23	0.095	3192.97	36803.20
11	38963.20	0.095	3701.50	42664.70
12	44824.70	0.095	4258.35	49083.05
13	51243.05	0.095	4868.09	56111.14
14	58271.14	0.095	5535.76	63806.90
15	65966.90	0.095	6266.86	72233.75
16	74393.75	0.095	7067.41	81461.16
17	83621.16	0.095	7944.01	91565.17
18	93725.17	0.095	8903.89	102629.06
19	104789.06	0.095	9954.96	114744.02
20	116904.02	0.095	11105.88	128009.90
21	130169.90	0.095	12366.14	142536.05
22	144696.05	0.095	13746.12	158442.17
23	160602.17	0.095	15257.21	175859.38
24	178019.38	0.095	16911.84	194931.22
25	197091.22	0.095	18723.67	215814.88
26	217974.88	0.095	20707.61	238682.50
27	240842.50	0.095	22880.04	263722.53
28	265882.53	0.095	25258.84	291141.37
29	293301.37	0.095	27863.63	321165.00
30	323325.00	0.095	30715.88	354040.88
31	356200.88	0.095	33839.08	390039.96
32	392199.96	0.095	37259.00	429458.96
33	431618.96	0.095	41003.80	472622.76
34	474782.76	0.095	45104.36	519887.12
35	522047.12	0.095	49594.48	571641.60