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An alternative to using logarithms to determine the amount of time that it would take for...

An alternative to using logarithms to determine the amount of time that it would take for a lump-sum investment at a particular compound interest rate to grow to a certain value would be to use a spreadsheet to list the value of the investment after each compounding period for as many times as is necessary. 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. (6.91% compounded quarterly). Determine how long it will take for this investment to grow to $8,000 by showing the value of the investment after each compounding period. Include columns showing the period number, the length of time that has passed, and the amount in the account at the end of each period (you may want to include additional columns depending on your set-up). You may stop the process once you get to the first value for the amount in the account at the end of a period that is $8,000 or above.

Solutions

Expert Solution

Period Length of Time (in years) Amount
1 0.25 1017.275
2 0.5 1034.848426
3 0.75 1052.725432
4 1 1070.911264
5 1.25 1089.411256
6 1.5 1108.230836
7 1.75 1127.375523
8 2 1146.850935
9 2.25 1166.662785
10 2.5 1186.816885
11 2.75 1207.319147
12 3 1228.175585
13 3.25 1249.392318
14 3.5 1270.97557
15 3.75 1292.931673
16 4 1315.267068
17 4.25 1337.988307
18 4.5 1361.102055
19 4.75 1384.615093
20 5 1408.534318
21 5.25 1432.866749
22 5.5 1457.619522
23 5.75 1482.799899
24 6 1508.415267
25 6.25 1534.473141
26 6.5 1560.981165
27 6.75 1587.947114
28 7 1615.378901
29 7.25 1643.284571
30 7.5 1671.672312
31 7.75 1700.550451
32 8 1729.92746
33 8.25 1759.811957
34 8.5 1790.212709
35 8.75 1821.138633
36 9 1852.598803
37 9.25 1884.602447
38 9.5 1917.158955
39 9.75 1950.277876
40 10 1983.968926
41 10.25 2018.241989
42 10.5 2053.10712
43 10.75 2088.574545
44 11 2124.65467
45 11.25 2161.35808
46 11.5 2198.695541
47 11.75 2236.678006
48 12 2275.316619
49 12.25 2314.622713
50 12.5 2354.607821
51 12.75 2395.283671
52 13 2436.662196
53 13.25 2478.755535
54 13.5 2521.576037
55 13.75 2565.136263
56 14 2609.448992
57 14.25 2654.527224
58 14.5 2700.384181
59 14.75 2747.033318
60 15 2794.488319
61 15.25 2842.763104
62 15.5 2891.871837
63 15.75 2941.828923
64 16 2992.649018
65 16.25 3044.34703
66 16.5 3096.938124
67 16.75 3150.437731
68 17 3204.861542
69 17.25 3260.225525
70 17.5 3316.545921
71 17.75 3373.839252
72 18 3432.122325
73 18.25 3491.412238
74 18.5 3551.726385
75 18.75 3613.082458
76 19 3675.498458
77 19.25 3738.992694
78 19.5 3803.583792
79 19.75 3869.290702
80 20 3936.132699
81 20.25 4004.129392
82 20.5 4073.300727
83 20.75 4143.666997
84 21 4215.248844
85 21.25 4288.067268
86 21.5 4362.14363
87 21.75 4437.499661
88 22 4514.157468
89 22.25 4592.139538
90 22.5 4671.468749
91 22.75 4752.168371
92 23 4834.26208
93 23.25 4917.773957
94 23.5 5002.728503
95 23.75 5089.150637
96 24 5177.065715
97 24.25 5266.499525
98 24.5 5357.478304
99 24.75 5450.028742
100 25 5544.177988
101 25.25 5639.953663
102 25.5 5737.383863
103 25.75 5836.497169
104 26 5937.322657
105 26.25 6039.889906
106 26.5 6144.229005
107 26.75 6250.370561
108 27 6358.345712
109 27.25 6468.186134
110 27.5 6579.92405
111 27.75 6693.592238
112 28 6809.224044
113 28.25 6926.853389
114 28.5 7046.514781
115 28.75 7168.243324
116 29 7292.074727
117 29.25 7418.045318
118 29.5 7546.192051
119 29.75 7676.552519
120 30 7809.164964
121 30.25 7944.068288
122 30.5 8081.302068

jeff jeffy answered 7 months ago
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