Question

Suppose that you receive $1,000 as a gift and decide to invest it in a fund that pays a particular interest rate compounded quarterly. The rate is 6.56%. Determine how long it will take for this investment to grow to $7,500 by showing the value of the investment after each compounding period.  Include columns showing the period number, the length of time that has passed.

Answer 1

Period	Beginning Value (B)	Periodic rate (r = 0.0656/4)	Interest earned (I = B x r)	Final Value (B +I)
1	1000	0.0164	16.40	1016.40
2	1016.40	0.0164	16.67	1033.07
3	1033.07	0.0164	16.94	1050.01
4	1050.01	0.0164	17.22	1067.23
5	1067.23	0.0164	17.50	1084.73
6	1084.73	0.0164	17.79	1102.52
7	1102.52	0.0164	18.08	1120.61
8	1120.61	0.0164	18.38	1138.98
9	1138.98	0.0164	18.68	1157.66
10	1157.66	0.0164	18.99	1176.65
11	1176.65	0.0164	19.30	1195.95
12	1195.95	0.0164	19.61	1215.56
13	1215.56	0.0164	19.94	1235.49
14	1235.49	0.0164	20.26	1255.76
15	1255.76	0.0164	20.59	1276.35
16	1276.35	0.0164	20.93	1297.28
17	1297.28	0.0164	21.28	1318.56
18	1318.56	0.0164	21.62	1340.18
19	1340.18	0.0164	21.98	1362.16
20	1362.16	0.0164	22.34	1384.50
21	1384.50	0.0164	22.71	1407.21
22	1407.21	0.0164	23.08	1430.28
23	1430.28	0.0164	23.46	1453.74
24	1453.74	0.0164	23.84	1477.58
25	1477.58	0.0164	24.23	1501.81
26	1501.81	0.0164	24.63	1526.44
27	1526.44	0.0164	25.03	1551.48
28	1551.48	0.0164	25.44	1576.92
29	1576.92	0.0164	25.86	1602.78
30	1602.78	0.0164	26.29	1629.07
31	1629.07	0.0164	26.72	1655.79
32	1655.79	0.0164	27.15	1682.94
33	1682.94	0.0164	27.60	1710.54
34	1710.54	0.0164	28.05	1738.59
35	1738.59	0.0164	28.51	1767.11
36	1767.11	0.0164	28.98	1796.09
37	1796.09	0.0164	29.46	1825.54
38	1825.54	0.0164	29.94	1855.48
39	1855.48	0.0164	30.43	1885.91
40	1885.91	0.0164	30.93	1916.84
41	1916.84	0.0164	31.44	1948.28
42	1948.28	0.0164	31.95	1980.23
43	1980.23	0.0164	32.48	2012.71
44	2012.71	0.0164	33.01	2045.71
45	2045.71	0.0164	33.55	2079.26
46	2079.26	0.0164	34.10	2113.36
47	2113.36	0.0164	34.66	2148.02
48	2148.02	0.0164	35.23	2183.25
49	2183.25	0.0164	35.81	2219.06
50	2219.06	0.0164	36.39	2255.45
51	2255.45	0.0164	36.99	2292.44
52	2292.44	0.0164	37.60	2330.03
53	2330.03	0.0164	38.21	2368.25
54	2368.25	0.0164	38.84	2407.09
55	2407.09	0.0164	39.48	2446.56
56	2446.56	0.0164	40.12	2486.68
57	2486.68	0.0164	40.78	2527.47
58	2527.47	0.0164	41.45	2568.92
59	2568.92	0.0164	42.13	2611.05
60	2611.05	0.0164	42.82	2653.87
61	2653.87	0.0164	43.52	2697.39
62	2697.39	0.0164	44.24	2741.63
63	2741.63	0.0164	44.96	2786.59
64	2786.59	0.0164	45.70	2832.29
65	2832.29	0.0164	46.45	2878.74
66	2878.74	0.0164	47.21	2925.95
67	2925.95	0.0164	47.99	2973.94
68	2973.94	0.0164	48.77	3022.71
69	3022.71	0.0164	49.57	3072.28
70	3072.28	0.0164	50.39	3122.67
71	3122.67	0.0164	51.21	3173.88
72	3173.88	0.0164	52.05	3225.93
73	3225.93	0.0164	52.91	3278.84
74	3278.84	0.0164	53.77	3332.61
75	3332.61	0.0164	54.65	3387.27
76	3387.27	0.0164	55.55	3442.82
77	3442.82	0.0164	56.46	3499.28
78	3499.28	0.0164	57.39	3556.67
79	3556.67	0.0164	58.33	3615.00
80	3615.00	0.0164	59.29	3674.28
81	3674.28	0.0164	60.26	3734.54
82	3734.54	0.0164	61.25	3795.79
83	3795.79	0.0164	62.25	3858.04
84	3858.04	0.0164	63.27	3921.31
85	3921.31	0.0164	64.31	3985.62
86	3985.62	0.0164	65.36	4050.98
87	4050.98	0.0164	66.44	4117.42
88	4117.42	0.0164	67.53	4184.95
89	4184.95	0.0164	68.63	4253.58
90	4253.58	0.0164	69.76	4323.34
91	4323.34	0.0164	70.90	4394.24
92	4394.24	0.0164	72.07	4466.31
93	4466.31	0.0164	73.25	4539.55
94	4539.55	0.0164	74.45	4614.00
95	4614.00	0.0164	75.67	4689.67
96	4689.67	0.0164	76.91	4766.58
97	4766.58	0.0164	78.17	4844.75
98	4844.75	0.0164	79.45	4924.21
99	4924.21	0.0164	80.76	5004.96
100	5004.96	0.0164	82.08	5087.05
101	5087.05	0.0164	83.43	5170.47
102	5170.47	0.0164	84.80	5255.27
103	5255.27	0.0164	86.19	5341.46
104	5341.46	0.0164	87.60	5429.06
105	5429.06	0.0164	89.04	5518.09
106	5518.09	0.0164	90.50	5608.59
107	5608.59	0.0164	91.98	5700.57
108	5700.57	0.0164	93.49	5794.06
109	5794.06	0.0164	95.02	5889.08
110	5889.08	0.0164	96.58	5985.66
111	5985.66	0.0164	98.16	6083.83
112	6083.83	0.0164	99.77	6183.60
113	6183.60	0.0164	101.41	6285.01
114	6285.01	0.0164	103.07	6388.09
115	6388.09	0.0164	104.76	6492.85
116	6492.85	0.0164	106.48	6599.33
117	6599.33	0.0164	108.23	6707.56
118	6707.56	0.0164	110.00	6817.57
119	6817.57	0.0164	111.81	6929.38
120	6929.38	0.0164	113.64	7043.02
121	7043.02	0.0164	115.51	7158.52
122	7158.52	0.0164	117.40	7275.92
123	7275.92	0.0164	119.33	7395.25
124	7395.25	0.0164	121.28	7516.53

124 quarters = 124/4 = 31 years

It will take 124 quarters or 31 years to grow the $ 1,000 to $ 7,500.