Question
In: Finance
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 |
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