1. Aiso deposits $170/month in a savings account paying 4%/year compounded conti
ID: 2753882 • Letter: 1
Question
1. Aiso deposits $170/month in a savings account paying 4%/year compounded continuously. Estimate the amount that will be in his account after 15 years. (Round your answer to the nearest whole number.)
2. The Armstrongs wish to establish a custodial account to finance their children's education. If they deposit $160 monthly for 10 years in a savings account paying 3%/year compounded continuously, how much will their savings account be worth at the end of this period? (Round your answer to the nearest whole number.)
Explanation / Answer
1. Balance in the fund at the end of 15 years = $41974.83
2. Balance in the fund at the endo of 10 years = $22414.52
Month Balance Investing Amount Total Investment Interest monthly Compounded Value 1 170 0.566666667 170.5666667 2 170.5667 170 340.5666667 1.135222222 341.7018889 3 341.7019 170 511.7018889 1.705672963 513.4075619 4 513.4076 170 683.4075619 2.278025206 685.6855871 5 685.6856 170 855.6855871 2.85228529 858.5378723 6 858.5379 170 1028.537872 3.428459574 1031.966332 7 1031.966 170 1201.966332 4.00655444 1205.972886 8 1205.973 170 1375.972886 4.586576288 1380.559463 9 1380.559 170 1550.559463 5.168531542 1555.727994 10 1555.728 170 1725.727994 5.752426647 1731.480421 11 1731.48 170 1901.480421 6.338268069 1907.818689 12 1907.819 170 2077.818689 6.926062296 2084.744751 13 2084.745 170 2254.744751 7.515815837 2262.260567 14 2262.261 170 2432.260567 8.107535223 2440.368102 15 2440.368 170 2610.368102 8.701227008 2619.069329 16 2619.069 170 2789.069329 9.296897764 2798.366227 17 2798.366 170 2968.366227 9.89455409 2978.260781 18 2978.261 170 3148.260781 10.4942026 3158.754984 19 3158.755 170 3328.754984 11.09584995 3339.850834 20 3339.851 170 3509.850834 11.69950278 3521.550336 21 3521.55 170 3691.550336 12.30516779 3703.855504 22 3703.856 170 3873.855504 12.91285168 3886.768356 23 3886.768 170 4056.768356 13.52256119 4070.290917 24 4070.291 170 4240.290917 14.13430306 4254.42522 25 4254.425 170 4424.42522 14.74808407 4439.173304 26 4439.173 170 4609.173304 15.36391101 4624.537215 27 4624.537 170 4794.537215 15.98179072 4810.519006 28 4810.519 170 4980.519006 16.60173002 4997.120736 29 4997.121 170 5167.120736 17.22373579 5184.344472 30 5184.344 170 5354.344472 17.84781491 5372.192287 31 5372.192 170 5542.192287 18.47397429 5560.666261 32 5560.666 170 5730.666261 19.10222087 5749.768482 33 5749.768 170 5919.768482 19.73256161 5939.501043 34 5939.501 170 6109.501043 20.36500348 6129.866047 35 6129.866 170 6299.866047 20.99955349 6320.8656 36 6320.866 170 6490.8656 21.63621867 6512.501819 37 6512.502 170 6682.501819 22.27500606 6704.776825 38 6704.777 170 6874.776825 22.91592275 6897.692748 39 6897.693 170 7067.692748 23.55897583 7091.251724 40 7091.252 170 7261.251724 24.20417241 7285.455896 41 7285.456 170 7455.455896 24.85151965 7480.307416 42 7480.307 170 7650.307416 25.50102472 7675.808441 43 7675.808 170 7845.808441 26.1526948 7871.961135 44 7871.961 170 8041.961135 26.80653712 8068.767672 45 8068.768 170 8238.767672 27.46255891 8266.230231 46 8266.23 170 8436.230231 28.12076744 8464.350999 47 8464.351 170 8634.350999 28.78117 8663.132169 48 8663.132 170 8833.132169 29.4437739 8862.575943 49 8862.576 170 9032.575943 30.10858648 9062.684529 50 9062.685 170 9232.684529 30.7756151 9263.460144 51 9263.46 170 9433.460144 31.44486715 9464.905011 52 9464.905 170 9634.905011 32.11635004 9667.021361 53 9667.021 170 9837.021361 32.7900712 9869.811433 54 9869.811 170 10039.81143 33.46603811 10073.27747 55 10073.28 170 10243.27747 34.14425824 10277.42173 56 10277.42 170 10447.42173 34.8247391 10482.24647 57 10482.25 170 10652.24647 35.50748823 10687.75396 58 10687.75 170 10857.75396 36.19251319 10893.94647 59 10893.95 170 11063.94647 36.87982156 11100.82629 60 11100.83 170 11270.82629 37.56942097 11308.39571 61 11308.4 170 11478.39571 38.26131904 11516.65703 62 11516.66 170 11686.65703 38.95552344 11725.61255 63 11725.61 170 11895.61255 39.65204185 11935.2646 64 11935.26 170 12105.2646 40.35088199 12145.61548 65 12145.62 170 12315.61548 41.05205159 12356.66753 66 12356.67 170 12526.66753 41.75555843 12568.42309 67 12568.42 170 12738.42309 42.46141029 12780.8845 68 12780.88 170 12950.8845 43.169615 12994.05411 69 12994.05 170 13164.05411 43.88018038 13207.93429 70 13207.93 170 13377.93429 44.59311431 13422.52741 71 13422.53 170 13592.52741 45.30842469 13637.83583 72 13637.84 170 13807.83583 46.02611944 13853.86195 73 13853.86 170 14023.86195 46.74620651 14070.60816 74 14070.61 170 14240.60816 47.46869386 14288.07685 75 14288.08 170 14458.07685 48.19358951 14506.27044 76 14506.27 170 14676.27044 48.92090147 14725.19134 77 14725.19 170 14895.19134 49.65063781 14944.84198 78 14944.84 170 15114.84198 50.38280661 15165.22479 79 15165.22 170 15335.22479 51.11741596 15386.3422 80 15386.34 170 15556.3422 51.85447401 15608.19668 81 15608.2 170 15778.19668 52.59398893 15830.79067 82 15830.79 170 16000.79067 53.33596889 16054.12664 83 16054.13 170 16224.12664 54.08042212 16278.20706 84 16278.21 170 16448.20706 54.82735686 16503.03442 85 16503.03 170 16673.03442 55.57678138 16728.6112 86 16728.61 170 16898.6112 56.32870399 16954.9399 87 16954.94 170 17124.9399 57.083133 17182.02303 88 17182.02 170 17352.02303 57.84007678 17409.86311 89 17409.86 170 17579.86311 58.5995437 17638.46265 90 17638.46 170 17808.46265 59.36154218 17867.8242 91 17867.82 170 18037.8242 60.12608065 18097.95028 92 18097.95 170 18267.95028 60.89316759 18328.84344 93 18328.84 170 18498.84344 61.66281148 18560.50626 94 18560.51 170 18730.50626 62.43502085 18792.94128 95 18792.94 170 18962.94128 63.20980426 19026.15108 96 19026.15 170 19196.15108 63.98717027 19260.13825 97 19260.14 170 19430.13825 64.7671275 19494.90538 98 19494.91 170 19664.90538 65.5496846 19730.45506 99 19730.46 170 19900.45506 66.33485021 19966.78991 100 19966.79 170 20136.78991 67.12263304 20203.91255 101 20203.91 170 20373.91255 67.91304182 20441.82559 102 20441.83 170 20611.82559 68.70608529 20680.53167 103 20680.53 170 20850.53167 69.50177225 20920.03345 104 20920.03 170 21090.03345 70.30011149 21160.33356 105 21160.33 170 21330.33356 71.10111186 21401.43467 106 21401.43 170 21571.43467 71.90478223 21643.33945 107 21643.34 170 21813.33945 72.7111315 21886.05058 108 21886.05 170 22056.05058 73.52016861 22129.57075 109 22129.57 170 22299.57075 74.33190251 22373.90265 110 22373.9 170 22543.90265 75.14634218 22619.049 111 22619.05 170 22789.049 75.96349665 22865.01249 112 22865.01 170 23035.01249 76.78337498 23111.79587 113 23111.8 170 23281.79587 77.60598623 23359.40185 114 23359.4 170 23529.40185 78.43133951 23607.83319 115 23607.83 170 23777.83319 79.25944398 23857.09264 116 23857.09 170 24027.09264 80.09030879 24107.18295 117 24107.18 170 24277.18295 80.92394315 24358.10689 118 24358.11 170 24528.10689 81.7603563 24609.86725 119 24609.87 170 24779.86725 82.59955749 24862.4668 120 24862.47 170 25032.4668 83.44155601 25115.90836 121 25115.91 170 25285.90836 84.2863612 25370.19472 122 25370.19 170 25540.19472 85.1339824 25625.3287 123 25625.33 170 25795.3287 85.98442901 25881.31313 124 25881.31 170 26051.31313 86.83771044 26138.15084 125 26138.15 170 26308.15084 87.69383614 26395.84468 126 26395.84 170 26565.84468 88.5528156 26654.39749 127 26654.4 170 26824.39749 89.41465831 26913.81215 128 26913.81 170 27083.81215 90.27937384 27174.09153 129 27174.09 170 27344.09153 91.14697175 27435.2385 130 27435.24 170 27605.2385 92.01746166 27697.25596 131 27697.26 170 27867.25596 92.8908532 27960.14681 132 27960.15 170 28130.14681 93.76715604 28223.91397 133 28223.91 170 28393.91397 94.6463799 28488.56035 134 28488.56 170 28658.56035 95.5285345 28754.08888 135 28754.09 170 28924.08888 96.41362961 29020.50251 136 29020.5 170 29190.50251 97.30167504 29287.80419 137 29287.8 170 29457.80419 98.19268063 29555.99687 138 29556 170 29725.99687 99.08665623 29825.08352 139 29825.08 170 29995.08352 99.98361175 30095.06714 140 30095.07 170 30265.06714 100.8835571 30365.95069 141 30365.95 170 30535.95069 101.7865023 30637.7372 142 30637.74 170 30807.7372 102.6924573 30910.42965 143 30910.43 170 31080.42965 103.6014322 31184.03109 144 31184.03 170 31354.03109 104.513437 31458.54452 145 31458.54 170 31628.54452 105.4284817 31733.973 146 31733.97 170 31903.973 106.3465767 32010.31958 147 32010.32 170 32180.31958 107.2677319 32287.58731 148 32287.59 170 32457.58731 108.1919577 32565.77927 149 32565.78 170 32735.77927 109.1192642 32844.89853 150 32844.9 170 33014.89853 110.0496618 33124.9482 151 33124.95 170 33294.9482 110.9831607 33405.93136 152 33405.93 170 33575.93136 111.9197712 33687.85113 153 33687.85 170 33857.85113 112.8595038 33970.71063 154 33970.71 170 34140.71063 113.8023688 34254.513 155 34254.51 170 34424.513 114.7483767 34539.26138 156 34539.26 170 34709.26138 115.6975379 34824.95892 157 34824.96 170 34994.95892 116.6498631 35111.60878 158 35111.61 170 35281.60878 117.6053626 35399.21414 159 35399.21 170 35569.21414 118.5640471 35687.77819 160 35687.78 170 35857.77819 119.5259273 35977.30412 161 35977.3 170 36147.30412 120.4910137 36267.79513 162 36267.8 170 36437.79513 121.4593171 36559.25445 163 36559.25 170 36729.25445 122.4308482 36851.68529 164 36851.69 170 37021.68529 123.4056176 37145.09091 165 37145.09 170 37315.09091 124.3836364 37439.47455 166 37439.47 170 37609.47455 125.3649152 37734.83946 167 37734.84 170 37904.83946 126.3494649 38031.18893 168 38031.19 170 38201.18893 127.3372964 38328.52623 169 38328.53 170 38498.52623 128.3284208 38626.85465 170 38626.85 170 38796.85465 129.3228488 38926.17749 171 38926.18 170 39096.17749 130.3205916 39226.49809 172 39226.5 170 39396.49809 131.3216603 39527.81975 173 39527.82 170 39697.81975 132.3260658 39830.14581 174 39830.15 170 40000.14581 133.3338194 40133.47963 175 40133.48 170 40303.47963 134.3449321 40437.82456 176 40437.82 170 40607.82456 135.3594152 40743.18398 177 40743.18 170 40913.18398 136.3772799 41049.56126 178 41049.56 170 41219.56126 137.3985375 41356.9598 179 41356.96 170 41526.9598 138.4231993 41665.383 180 41665.38 170 41835.383 139.4512767 41974.83427Related Questions
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