Tutorial Exercise Suppose that you invest $2,000 at 6% interest, compound quarterly, for 5 years use Table 11-1 to calculate the compound interest (in $) on your investment. Step 1 Before finding the compound interest, we must first find the final value of the investment after all the compounding periods. One way to find the value after all the compounding periods is to use a compound interest table. To use the compound interest table, we must know the interest rate per period and the number of compounding periods. The interest rate per period is calculated using the nominal, or annual, rate and the number of periods per year as follows. interest rate per period nominal rate periods per year The rate was given to be 6%. Interest is compounded quarterly, or 4 times per year. Find the interest rate per period. interest rate per period nominal rate periods per year The total number of compounding periods will be the number of years multiplied by the number of compounding periods per year. The investment accrues interest compounded quarterly, so there are 4 compounding periods per year. The investment is for 5 years. Find the total number of compounding periods. total number of compounding periods number of years x number of compounding periods per year - 5x TABLE 11-1 Compound Interest Table (Future Value of $1 at Compound Interest) Periods 1% 2% 1 2 100500 1.01003 1.02010 1.01000 1.01500 1.03023 1.02000 5% 1.05000 3 1.01508 1.03030 1.04568 4 1.02015 1,04060 3 102525 105101 1.06136 1.07728 6 103038 106152 109344 10155) 1.07214 1.10984 1.10408 1.12616 114869 104071 108286 112649 117166 9 1.04591 109369 134319 119509 10 1.05114 1.10462 116054 1.21899 3% 4% 6% 7% 1,03000 104000 106000 1.07000 1.08000 104040 1.06090 1.08160 1.10250 1.12360 114490 1.16640 1.06121 1.09273 1.12436 1.15763 1.19102 1.22504 1.25971 1.08243 1.12551 1.16986 1.21551 1.26248 131080 136049 1.15927 121665 127628 133823 140255 L19405 126532 134010 141852 1.50073 1.22987 131591 140710 150361 160578 126677 136857 147746 159385 171819 L85093 130477 142331 1.55133 1.68948 134392 148024 162889 1.79085 8% Periods 2 146933 1.58687 1.71382 183846 1.99900 196715 2.15892 10 11 105640 131567 1.17795 1.24337 138423 1.53945 12 106168 132683 1.19562 1,26824 142576 150103 13 1,06699 1.13809 1.21355 129361 146853 166507 14 107232 114947 1,23176 331948 151259 15 107768 1.16097 1.25023 134587 155797 16 108307 117258 17 1.08840 1.18430 18 1.09393 1,19615 19 1.09940 1.20811 20 L10490 122019 21 1.11042 123239 136706 22 1.11597 324472 138756 23 1.12155 125716 140838 24 1.12716 126973 142950 1.60544 151567 136029 2.27877 154598 191610 236992 1.57690 1.97359 203279 18900 2.10485 233164 1.79586 201220 2.25219 251817 12 138565 213293 2.40985 271962 13 173168 1.97993 226090 2.57853 293719 14 130094 207893 239656 275901 3:17217 15 1.26899 137279 160471 18729 2.18287 254035 295216 3.42594 16 1,28802 140024 165285 194790 2.29202 2.69277 315882 3.70002 17 130734 142825 E70043 201582 2.40662 285434 337993 199602 18 132695 145681 1,75351 210685 252695 302560 3.61653 431570 19 134686 1.48595 1.80611 2.19112 265330 3.20714 3.8696 4,66096 20 278596 339956 414056 292526 3.60154 171034 443040 5.03383 543654 22 21 246472 25 1.13280 128243 145095 164061 209378 256330 26654 3.07152 3.81975 322510 404893 3.38635 4.29187 4.74053 587146 23 5.07237 542743 634118 24 6.84848 25 Periods 9% 10% 11% 1.09000 130000 111000 2 1,18810 121000 123210 1.29503 1.33100 1.36763 4 141158 1.46410 1.51807 1.53862 161051 1.68506 12% 13% 1.12000 CL000 125440 127690 140491 144290 157352 163047 176234 184244 14% 15% 16% 17% 14000 E15000 L16000 129960 1.32250 134560 148154 152088 156090 196 1,7490 181064 192541 2.01136 2.10034 1.17000 18% 1.18000 Periods 1.36890 1.39240 2 160161 L64303 3 1.87389 1.93878 4 2.19245 228776 5 6 8 9 10 2.36736 1.67710 1.77156 187041 1.82804 1.94872 2.07616 199256 214359 2.30454 2.17189 2.35795 2.55804 2.59374 2.83942 1.97382 206195 221068 235261 247596 265544 2.77308 3.00404 3,10585 3.39457 2.39497 231306 243640 256516 2.69955 2.50227 2.66000 232622 3.00124 3.18547 285259 3.05902 3.27841 3.51145 3.75886 3.25195 351788 3.80296 4.10840 443545 3.70722 404556 441144 4.80683 5.23384 6 7 9 10 11 2.58043 2.85312 3.15176 12 13 14 15 16 17 18 4.71712 5.55992 20 19 5.14166 6.11591 5.60441 6.72750 3.97031 4.59497 5.31089 432763 5.05447 5.89509 6.54355 7.26334 8.06231 3.47855 383586 4.22623 465239 281266 3.13843 3.49845 339598 433452 481790 5.35025 5.93603 658007 7.28759 12 3.06580 3,45227 3.88328 4.36349 4.89801 549241 6.15279 6.88579 7.69868 8.59936 13 3.34173 3.79750 431044 4.88711 553475 6.26135 7.07571 7.98752 900745 10.14724 14 3,64248 437725 4.78459 5.47357 6.25427 7.33794 813706 9.26552 10.53872 11.97375 15 6.13039 7.06733 8.13725 935762 6.86604 7.98008 927646 10.76126 7.68997 9.02427 10.57517 12.37545 8.61276 10.19742 1205569 14.23177 9.64629 11.52309 1374349 16.36654 5.11726 5.62399 6.17593 21 8.94917 22 23 24 25 6.10881 740025 10.80385 13.02109 665860 8.14027 9.93357 12.10031 14.71383 7.25787 8.95430 11.02627 1355235 1663663 7.91106 9.84973 12.23916 15.17663 1878809 8.62308 1083471 13.58546 17.00006 2123054 10.74800 12.33030 14.12902 1246768 14.42646 16.67225 14.46251 16.87895 19.67325 18 16.77652 19.74838 2321444 19 19.46076 23.10560 27.39303 20 15.66758 18.82152 22.57448 27.03355 32.32378 21 1786104 21.64475 26.18640 3162925 38.14206 22 2036158 2489146 3037622 37.00623 45.00763 23 23.21221 28.62518 35.23642 43.29729 53.10901 24 26.46192 32.91895 40.87434 5065783 6266863 25 16 17 Tutorial Exercise Suppose that you invest $2,000 at 6% interest, compound quarterly, for 5 years use Table 11-1 to calculate the compound interest (in $) on your investment Step 1 Before finding the compound interest, we must first find the final value of the investment after all the compounding periods. One way to find the value after all the compounding periods is to use a compound interest table. To use the compound interest table, we must know the interest rate per period and the number of compounding periods. The interest rate per period is calculated using the nominal, or annual, rate and the number of periods per year as follows. interest rate per period nominal rate periods per year The rate was given to be 6%. Interest is compounded quarterly, or 4 times per year. Find the interest rate per period. interest rate per period nominal rate periods per year The total number of compounding periods will be the number of years multiplied by the number of compounding periods per year. The investment accrues interest compounded quarterly, so there are 4 compounding periods per year. The investment is for 5 years. Find the total number of compounding periods. total number of compounding periods number of years x number of compounding periods per year -5x