Nicole has 5500 that she wants to invest in an IRA She expec

Nicole has $5,500 that she wants to invest in an IRA. She expects that this money will earn 6% and does not expect to withdraw the money from her IRA for another 32 years. Assuming that she will pay a 28% rate for combined state and federal income taxes, how much will she have after taxes if she invests in a traditional IRA? The answer is $25,555.41. How do I get it?

Solution

Year Opening balance Interest Total Amount Tax Income After Tax 1 5500 330 5830 1632.4 4197.6 2 5830 349.8 6179.8 1730.344 4449.456 3 6179.8 370.788 6550.588 1834.165 4716.423 4 6550.588 393.0353 6943.623 1944.215 4999.409 5 6943.623 416.6174 7360.241 2060.867 5299.373 6 7360.241 441.6144 7801.855 2184.519 5617.336 7 7801.855 468.1113 8269.966 2315.591 5954.376 8 8269.966 496.198 8766.164 2454.526 6311.638 9 8766.164 525.9699 9292.134 2601.798 6690.337 10 9292.134 557.5281 9849.662 2757.905 7091.757 11 9849.662 590.9797 10440.64 2923.38 7517.262 12 10440.64 626.4385 11067.08 3098.783 7968.298 13 11067.08 664.0248 11731.11 3284.71 8446.396 14 11731.11 703.8663 12434.97 3481.792 8953.18 15 12434.97 746.0983 13181.07 3690.7 9490.37 16 13181.07 790.8642 13971.93 3912.142 10059.79 17 13971.93 838.3161 14810.25 4146.87 10663.38 18 14810.25 888.615 15698.87 4395.682 11303.18 19 15698.87 941.9319 16640.8 4659.423 11981.37 20 16640.8 998.4478 17639.25 4938.989 12700.26 21 17639.25 1058.355 18697.6 5235.328 13462.27 22 18697.6 1121.856 19819.46 5549.448 14270.01 23 19819.46 1189.167 21008.62 5882.414 15126.21 24 21008.62 1260.517 22269.14 6235.359 16033.78 25 22269.14 1336.148 23605.29 6609.481 16995.81 26 23605.29 1416.317 25021.61 7006.05 18015.56 27 25021.61 1501.296 26522.9 7426.413 19096.49 28 26522.9 1591.374 28114.28 7871.998 20242.28 29 28114.28 1686.857 29801.13 8344.317 21456.82 30 29801.13 1788.068 31589.2 8844.976 22744.23 31 31589.2 1895.352 33484.55 9375.675 24108.88 32 33484.55 2009.073 35493.63 9938.215 25555.41