Twins Invest. Kathryn Ake, of Omaha, Nebraska, plans to invest $3000 in mutual f

Question

Twins Invest. Kathryn Ake, of Omaha, Nebraska, plans to invest $3000 in mutual fund for the next 25 years to accumulate savings for retirement. Her twin sister, Kristin, plans to invest the same amount for the same length of time in the same mutual fund. Instead of investing with after-tax money, Kristin will invest through an employer-sponsored retirement plan. If both mutual fund accounts provide an 8 percent rate of return, how much more will Kristin have in her retirement account after 40 years? How much will Kristin have if she also invests the amount saved in income taxes? Assume both women pay income taxes at a 25% rate.

Explanation / Answer

After tax Investment Before tax Investment Beginning Amont Interest Investment Ending amount Year Beginning Amont Interest Investment Ending amount 0 0 3000 3000 1 0 0 4285.71 4285.714286 3000.00 240 3000 6240.00 2 4285.71 342.8571 4285.71 8914.29 6240.00 499.2 3000 9739.20 3 8914.29 713.1429 4285.71 13913.14 9739.20 779.136 3000 13518.34 4 13913.14 1113.051 4285.71 19311.91 13518.34 1081.46688 3000 17599.80 5 19311.91 1544.953 4285.71 25142.58 17599.80 1407.98423 3000 22007.79 6 25142.58 2011.406 4285.71 31439.70 22007.79 1760.62297 3000 26768.41 7 31439.70 2515.176 4285.71 38240.59 26768.41 2141.47281 3000 31909.88 8 38240.59 3059.247 4285.71 45585.55 31909.88 2552.79063 3000 37462.67 9 45585.55 3646.844 4285.71 53518.11 37462.67 2997.01388 3000 43459.69 10 53518.11 4281.448 4285.71 62085.27 43459.69 3476.77499 3000 49936.46 11 62085.27 4966.821 4285.71 71337.80 49936.46 3994.91699 3000 56931.38 12 71337.80 5707.024 4285.71 81330.54 56931.38 4554.51035 3000 64485.89 13 81330.54 6506.443 4285.71 92122.70 64485.89 5158.87118 3000 72644.76 14 92122.70 7369.816 4285.71 103778.23 72644.76 5811.58087 3000 81456.34 15 103778.23 8302.258 4285.71 116366.20 81456.34 6516.50734 3000 90972.85 16 116366.20 9309.296 4285.71 129961.21 90972.85 7277.82793 3000 101250.68 17 129961.21 10396.9 4285.71 144643.82 101250.68 8100.05416 3000 112350.73 18 144643.82 11571.51 4285.71 160501.04 112350.73 8988.0585 3000 124338.79 19 160501.04 12840.08 4285.71 177626.84 124338.79 9947.10318 3000 137285.89 20 177626.84 14210.15 4285.71 196122.70 137285.89 10982.8714 3000 151268.76 21 196122.70 15689.82 4285.71 216098.23 151268.76 12101.5011 3000 166370.27 22 216098.23 17287.86 4285.71 237671.81 166370.27 13309.6212 3000 182679.89 23 237671.81 19013.74 4285.71 260971.27 182679.89 14614.3909 3000 200294.28 24 260971.27 20877.7 4285.71 286134.68 200294.28 16023.5422 3000 219317.82 25 286134.68 22890.77 4285.71 313311.17 219317.82 17545.4256 0.00 236863.25 26 313311.17 25064.89 0.00 338376.06 236863.25 18949.0596 0.00 255812.31 27 338376.06 27070.09 0.00 365446.15 255812.31 20464.9844 0.00 276277.29 28 365446.15 29235.69 0.00 394681.84 276277.29 22102.1832 0.00 298379.47 29 394681.84 31574.55 0.00 426256.39 298379.47 23870.3578 0.00 322249.83 30 426256.39 34100.51 0.00 460356.90 322249.83 25779.9864 0.00 348029.82 31 460356.90 36828.55 0.00 497185.45 348029.82 27842.3854 0.00 375872.20 32 497185.45 39774.84 0.00 536960.29 375872.20 30069.7762 0.00 405941.98 33 536960.29 42956.82 0.00 579917.11 405941.98 32475.3583 0.00 438417.34 34 579917.11 46393.37 0.00 626310.48 438417.34 35073.3869 0.00 473490.72 35 626310.48 50104.84 0.00 676415.32 473490.72 37879.2579 0.00 511369.98 36 676415.32 54113.23 0.00 730528.55 511369.98 40909.5985 0.00 552279.58 37 730528.55 58442.28 0.00 788970.83 552279.58 44182.3664 0.00 596461.95 38 788970.83 63117.67 0.00 852088.49 596461.95 47716.9557 0.00 644178.90 39 852088.49 68167.08 0.00 920255.57 644178.90 51534.3122 0.00 695713.21 40 920255.57 73620.45 0.00 993876.02 620713.214 75000 Total 886733.2 107142.857 after Tax Before Tax Incremental Interest Earnings 620713.21 886733.16 266019.95 Total Deposit 75000.00 107142.86 32142.86 Amount After 40 years 695713.21 993876.02 298162.81 Tax @ 30% on Interest 186213.96 266019.95 79805.98 Tax @ 30% on Deposits 0.00 32142.86 32142.86 Net Tax Payment 186213.96 298162.81 111948.84 Net Amount 509499.25 695713.21 186213.96 So, Kirsten will have $695713.21 after 40 years.

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