Question

Question 3 A basic lesson to be learned in life is to minimize annual maintenance fees (and sales commissions) on portfolios of securities (stocks and bonds). To illustrate this lesson, consider an actively managed stock market fund that charges 1% per year as its maintenance fee. A less actively managed fund charges 0.5% per year. For a one-time investment of $100,000, how much will this decrease in annual management fee (i.e., 0.5%) save during a 20-year period? Let i=8% per year and express your answer as a percentage of the original $100,000.

Answer 1

Problem is solved using excel

Amount received is amount before management fee at start of the year

Management fee = 1% or 0.5% of 100000

Amount invested = Amount received - Management fee

and Net asset value is Amount invested*1.08

100000 1000 99000 106920 2 3 106920 114319 1069.2 1143.19 105851 113176 114319 122230 122230 130688 139732 149401 1222.3 1306.88 1397.32 1494.01 121007 129381 138334 147907 130688 139732 149401 159740 к 8 9 10 159740 170794 182613 1597.4 1707.94 1826.13 158142169086 180786 170794 182613 195249 L M N O P Q R S T U 11 12 13 14 15 16 17 18 19 20 195249 208761 223207 238653 255167 272825 291705 311891 333473 356550 1952.49 2087.61 2232.07 2386.53 2551.67 2728.25 2917.05 3118.91 3334.73 3565.5 193297 206673 220975 236266 252616 270097 288788 308772 330139 352984 208761 223207 238653 255167 272825 291705 311891 333473 356550 381223 1 Timeline 2 Amount Received 3 Management Fee 4 Amount Invested 5 Net Asset Value 6 7 Timeline 8 Amount Received 9 Management Fee 10 Amount Invested 11 Net Asset Value 100000 500 99500 107460 5 107460 115477 124091 133348 537.3 577.383 620.455 666.741 106923 114899 123471 132682 115477 124091 133348 143296 143296 716.48 142580 153986 7 8 9 10 11 12 13 14 15 153986 165473 177818 191083 205338 220656 237117 254806 273814 769.93 827.366 889.088 955.414 1026.69 1103.28 1185.58 1274.03 1369.07 153216 164646 176928 190127 204311 219552 235931 253532 272445 165473 177818 191083 205338 220656 237117 254806 273814 294241 16 17 18 19 20 294241 316191 339779 365126 392365 1471.2 1580.95 1698.89 1825.63 1961.82 292769 314610 338080 363301 390403 316191 339779 365126 392365 421635 13 14 Management Fee-1% 15 Management Fee-0.5% 40639.2 21557.3 16 17 Fee Saved 18 As a % of 100000 19 19081.8 19.08%)

It can be seen that when fee is 1%, 100000 in 20 years = $381223

and when fee is 0.5%, 100000 in 20 years = $421635