Mr.Smith who deposits 100,000 in a bank on January 1 and then makes withdrawals

Question

Mr.Smith who deposits 100,000 in a bank on January 1 and then makes withdrawals monthly thereafter beginning February 1. The bank credits interest montly. All answers are numerical.

Hint: In each case think of the bank as paying Mr.Smith an annunity with a PV value of 100,000.

1: Smith withdrawals 1000 each month and continues until as long as possible with a smaller withdrawals one month after the final regular withdrawal of 1000. Find

a) the number of regular withdrawals and

b) the month and

c) the amount of the final smaller withdrawal, if the account earns interest at the rate i^(12) = 9%.

Explanation / Answer

Hi folk,

The no of Withdrawal is 188.

The no of month is 189

andd final small withdrawal is $573.76

For your ease refer excel table below

Months Amount Interest Withdrawal Closing Balance 1 100000 750 0 100750 2 100750 755.625 1000 100505.625 3 100505.625 753.7921875 1000 100259.4172 4 100259.4172 751.9456289 1000 100011.3628 5 100011.3628 750.0852211 1000 99761.44804 6 99761.44804 748.2108603 1000 99509.6589 7 99509.6589 746.3224417 1000 99255.98134 8 99255.98134 744.41986 1000 99000.4012 9 99000.4012 742.503009 1000 98742.90421 10 98742.90421 740.5717816 1000 98483.47599 11 98483.47599 738.6260699 1000 98222.10206 12 98222.10206 736.6657655 1000 97958.76783 13 97958.76783 734.6907587 1000 97693.45858 14 97693.45858 732.7009394 1000 97426.15952 15 97426.15952 730.6961964 1000 97156.85572 16 97156.85572 728.6764179 1000 96885.53214 17 96885.53214 726.641491 1000 96612.17363 18 96612.17363 724.5913022 1000 96336.76493 19 96336.76493 722.525737 1000 96059.29067 20 96059.29067 720.44468 1000 95779.73535 21 95779.73535 718.3480151 1000 95498.08336 22 95498.08336 716.2356252 1000 95214.31899 23 95214.31899 714.1073924 1000 94928.42638 24 94928.42638 711.9631979 1000 94640.38958 25 94640.38958 709.8029218 1000 94350.1925 26 94350.1925 707.6264438 1000 94057.81894 27 94057.81894 705.4336421 1000 93763.25259 28 93763.25259 703.2243944 1000 93466.47698 29 93466.47698 700.9985774 1000 93167.47556 30 93167.47556 698.7560667 1000 92866.23162 31 92866.23162 696.4967372 1000 92562.72836 32 92562.72836 694.2204627 1000 92256.94882 33 92256.94882 691.9271162 1000 91948.87594 34 91948.87594 689.6165696 1000 91638.49251 35 91638.49251 687.2886938 1000 91325.7812 36 91325.7812 684.943359 1000 91010.72456 37 91010.72456 682.5804342 1000 90693.305 38 90693.305 680.1997875 1000 90373.50479 39 90373.50479 677.8012859 1000 90051.30607 40 90051.30607 675.3847955 1000 89726.69087 41 89726.69087 672.9501815 1000 89399.64105 42 89399.64105 670.4973079 1000 89070.13836 43 89070.13836 668.0260377 1000 88738.16439 44 88738.16439 665.536233 1000 88403.70063 45 88403.70063 663.0277547 1000 88066.72838 46 88066.72838 660.5004629 1000 87727.22884 47 87727.22884 657.9542163 1000 87385.18306 48 87385.18306 655.388873 1000 87040.57193 49 87040.57193 652.8042895 1000 86693.37622 50 86693.37622 650.2003217 1000 86343.57654 51 86343.57654 647.5768241 1000 85991.15337 52 85991.15337 644.9336503 1000 85636.08702 53 85636.08702 642.2706526 1000 85278.35767 54 85278.35767 639.5876825 1000 84917.94535 55 84917.94535 636.8845902 1000 84554.82994 56 84554.82994 634.1612246 1000 84188.99117 57 84188.99117 631.4174338 1000 83820.4086 58 83820.4086 628.6530645 1000 83449.06167 59 83449.06167 625.8679625 1000 83074.92963 60 83074.92963 623.0619722 1000 82697.9916 61 82697.9916 620.234937 1000 82318.22654 62 82318.22654 617.386699 1000 81935.61324 63 81935.61324 614.5170993 1000 81550.13034 64 81550.13034 611.6259775 1000 81161.75631 65 81161.75631 608.7131724 1000 80770.46949 66 80770.46949 605.7785212 1000 80376.24801 67 80376.24801 602.8218601 1000 79979.06987 68 79979.06987 599.843024 1000 79578.91289 69 79578.91289 596.8418467 1000 79175.75474 70 79175.75474 593.8181605 1000 78769.5729 71 78769.5729 590.7717967 1000 78360.3447 72 78360.3447 587.7025852 1000 77948.04728 73 77948.04728 584.6103546 1000 77532.65764 74 77532.65764 581.4949323 1000 77114.15257 75 77114.15257 578.3561443 1000 76692.50871 76 76692.50871 575.1938153 1000 76267.70253 77 76267.70253 572.007769 1000 75839.7103 78 75839.7103 568.7978272 1000 75408.50812 79 75408.50812 565.5638109 1000 74974.07194 80 74974.07194 562.3055395 1000 74536.37747 81 74536.37747 559.0228311 1000 74095.40031 82 74095.40031 555.7155023 1000 73651.11581 83 73651.11581 552.3833686 1000 73203.49918 84 73203.49918 549.0262438 1000 72752.52542 85 72752.52542 545.6439407 1000 72298.16936 86 72298.16936 542.2362702 1000 71840.40563 87 71840.40563 538.8030422 1000 71379.20867 88 71379.20867 535.3440651 1000 70914.55274 89 70914.55274 531.8591455 1000 70446.41188 90 70446.41188 528.3480891 1000 69974.75997 91 69974.75997 524.8106998 1000 69499.57067 92 69499.57067 521.24678 1000 69020.81745 93 69020.81745 517.6561309 1000 68538.47358 94 68538.47358 514.0385519 1000 68052.51214 95 68052.51214 510.393841 1000 67562.90598 96 67562.90598 506.7217948 1000 67069.62777 97 67069.62777 503.0222083 1000 66572.64998 98 66572.64998 499.2948748 1000 66071.94485 99 66071.94485 495.5395864 1000 65567.48444 100 65567.48444 491.7561333 1000 65059.24057 101 65059.24057 487.9443043 1000 64547.18488 102 64547.18488 484.1038866 1000 64031.28877 103 64031.28877 480.2346657 1000 63511.52343 104 63511.52343 476.3364257 1000 62987.85986 105 62987.85986 472.4089489 1000 62460.26881 106 62460.26881 468.452016 1000 61928.72082 107 61928.72082 464.4654062 1000 61393.18623 108 61393.18623 460.4488967 1000 60853.63512 109 60853.63512 456.4022634 1000 60310.03739 110 60310.03739 452.3252804 1000 59762.36267 111 59762.36267 448.21772 1000 59210.58039 112 59210.58039 444.0793529 1000 58654.65974 113 58654.65974 439.9099481 1000 58094.56969 114 58094.56969 435.7092727 1000 57530.27896 115 57530.27896 431.4770922 1000 56961.75605 116 56961.75605 427.2131704 1000 56388.96922 117 56388.96922 422.9172692 1000 55811.88649 118 55811.88649 418.5891487 1000 55230.47564 119 55230.47564 414.2285673 1000 54644.70421 120 54644.70421 409.8352816 1000 54054.53949 121 54054.53949 405.4090462 1000 53459.94854 122 53459.94854 400.949614 1000 52860.89815 123 52860.89815 396.4567361 1000 52257.35489 124 52257.35489 391.9301617 1000 51649.28505 125 51649.28505 387.3696379 1000 51036.65469 126 51036.65469 382.7749102 1000 50419.4296 127 50419.4296 378.145722 1000 49797.57532 128 49797.57532 373.4818149 1000 49171.05713 129 49171.05713 368.7829285 1000 48539.84006 130 48539.84006 364.0488005 1000 47903.88886 131 47903.88886 359.2791665 1000 47263.16803 132 47263.16803 354.4737602 1000 46617.64179 133 46617.64179 349.6323134 1000 45967.2741 134 45967.2741 344.7545558 1000 45312.02866 135 45312.02866 339.8402149 1000 44651.86887 136 44651.86887 334.8890166 1000 43986.75789 137 43986.75789 329.9006842 1000 43316.65858 138 43316.65858 324.8749393 1000 42641.53351 139 42641.53351 319.8115014 1000 41961.34502 140 41961.34502 314.7100876 1000 41276.0551 141 41276.0551 309.5704133 1000 40585.62552 142 40585.62552 304.3921914 1000 39890.01771 143 39890.01771 299.1751328 1000 39189.19284 144 39189.19284 293.9189463 1000 38483.11179 145 38483.11179 288.6233384 1000 37771.73513 146 37771.73513 283.2880134 1000 37055.02314 147 37055.02314 277.9126735 1000 36332.93581 148 36332.93581 272.4970186 1000 35605.43283 149 35605.43283 267.0407462 1000 34872.47358 150 34872.47358 261.5435518 1000 34134.01713 151 34134.01713 256.0051285 1000 33390.02226 152 33390.02226 250.4251669 1000 32640.44742 153 32640.44742 244.8033557 1000 31885.25078 154 31885.25078 239.1393809 1000 31124.39016 155 31124.39016 233.4329262 1000 30357.82309 156 30357.82309 227.6836732 1000 29585.50676 157 29585.50676 221.8913007 1000 28807.39806 158 28807.39806 216.0554855 1000 28023.45355 159 28023.45355 210.1759016 1000 27233.62945 160 27233.62945 204.2522209 1000 26437.88167 161 26437.88167 198.2841125 1000 25636.16578 162 25636.16578 192.2712434 1000 24828.43702 163 24828.43702 186.2132777 1000 24014.6503 164 24014.6503 180.1098773 1000 23194.76018 165 23194.76018 173.9607013 1000 22368.72088 166 22368.72088 167.7654066 1000 21536.48629 167 21536.48629 161.5236472 1000 20698.00994 168 20698.00994 155.2350745 1000 19853.24501 169 19853.24501 148.8993376 1000 19002.14435 170 19002.14435 142.5160826 1000 18144.66043 171 18144.66043 136.0849532 1000 17280.74538 172 17280.74538 129.6055904 1000 16410.35097 173 16410.35097 123.0776323 1000 15533.42861 174 15533.42861 116.5007145 1000 14649.92932 175 14649.92932 109.8744699 1000 13759.80379 176 13759.80379 103.1985284 1000 12863.00232 177 12863.00232 96.47251739 1000 11959.47484 178 11959.47484 89.69606127 1000 11049.1709 179 11049.1709 82.86878173 1000 10132.03968 180 10132.03968 75.99029759 1000 9208.029976 181 9208.029976 69.06022482 1000 8277.090201 182 8277.090201 62.07817651 1000 7339.168378 183 7339.168378 55.04376283 1000 6394.212141 184 6394.212141 47.95659105 1000 5442.168732 185 5442.168732 40.81626549 1000 4482.984997 186 4482.984997 33.62238748 1000 3516.607385 187 3516.607385 26.37455539 1000 2542.98194 188 2542.98194 19.07236455 1000 1562.054305 189 1562.054305 11.71540728 1000 573.7697119

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