This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part and you will not be able to come back to the skloped part Tutorial Exercise Chol Home Repair needs to accumulate 521,000 in 6 years to purchase new equipment. What sinking fund payment would they need to make at the end of each three months, at 6% interest compounded quarterly? Use Table 12-1 Stap 1 A sinking fund is an account used for the purpose of saving for a future obligation. The amount of each payment needed to attain a needed future value is calculated using the following formula sinking fund payment future value of sinking fund future value table factor Chol Home Repair needs to accumulate $21,000, so this is the future value of the sinking fund. The future value table factor will be determined by the interest rate per period and the total 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 nominal rate interest rate per period periods per year The total number of compounding periods will be the number of years payments are made into the sinking fund multiplied by the number of compounding periods per year. There are 4 compounding periods per year and the full amount of the account will be needed in 6 years to purchase new equipment. Find the total number of compounding periods. total number of compounding periods number of years x number of compounding periods per year 7% Periods 1 2 3 1% 1% 2% 3% 1.00000 1.00000 1.00000 1.00000 1.00000 2.00500 2.01000 2.01500 2.02000 2.03000 3.01502 3.03010 3.04522 3.06040 3.09090 4,03010 4.06040 4.09090 4.12161 4.18363 5.05025 5.10101 5.15227 5.20404 5.30914 4% 5% 1.00000 1.00000 2.04000 2.05000 3.12160 3.15250 4.24646 4.31013 5,41632 5.52563 6% 1.00000 2.06000 3.18360 4.37462 5.63709 1.00000 2.07000 3.21490 4.43994 5.75074 8% 1.00000 2.08000 3.24640 4.50611 5.86660 Periods 1 2 3 4 5 4 5 6 6 7 8 7 6.07550 6.15202 6.22955 6.30812 6,46841 6.63298 6.80191 6.97532 7.10588 7.21354 7.32299 7.43428 7.66246 7.89829 8.14201 8.39384 8.14141 8.28567 8.43284 8.58297 8.89234 9.21423 9.54911 9.89747 9.18212 9.36853 9.55933 9.75463 10.15911 10,58280 11.02656 11.49132 10.22803 10.46221 10.70272 10.94972 11.46388 12.00611 12.57789 13.18079 7.15329 8.65402 10.25980 11.97799 13.81645 7.33593 8.92280 10.63663 12.48756 14.48656 8 9 10 9 10 11 12 13 11.27917 11.56683 11.86326 12.16872 12.80780 13.48635 14.20679 14.97164 15.78360 16.64549 12.33556 12.68250 13.04121 13.41209 14.19203 15.02581 15.91713 16.86994 17.88845 18.97713 13.39724 13.80933 14.23683 14.68033 15.61779 16.62684 17.71298 18.88214 20.14064 21.49530 14.46423 14.94742 15.45038 15.97394 17.08632 18.29191 19.59863 21.01507 22.55049 24.21492 15.53655 16.09690 16.68214 17.29342 18.59891 20.02359 21.57856 23.27597 25.12902 27.15211 11 12 13 14 15 14 15 16 16 17 18 19 20 16.61423 17.25786 17.93237 18.63929 20.15688 21.82453 23.65749 25.67253 27.88805 17.69730 18.43044 19.20136 20.01207 21.76159 23.69751 25.84037 28.21288 30.84022 18.78579 19.61475 20.48938 21.41231 23.41444 25.64541 28.13238 30.90565 33.99903 19.87972 20.81090 21.79672 22.84056 25.11687 27.67123 30.53900 33.75999 37.37896 20.97912 22.01900 23.12367 24.29737 26.87037 29.77808 33.06595 36.7855940.99549 30.32428 33.75023 37.45024 41.44626 45.76196 17 18 19 20 21 21 22 23 22.08401 23.23919 24.47052 25.78332 28.67649 31.96920 35.71925 39.9927344.86518 50.42292 23.19443 24.47159 25.83758 27.29898 30.53678 34.24797 38.50521 43.39229 49.00574 55.45676 24.31040 25.71630 27.22514 28.84496 32.45288 36.61789 41.43048 46.99583 53.43614 60.89330 25.43196 26.97346 28.63352 30.42186 34.42647 39.08260 44 50200 50.81558 58.17667 66.76476 26.55912 28.24320 30.06302 32,03030 36.45926 41.64591 47.72710 54.86451 63.24904 73.10594 24 CAS 25 26 27 28 RAA 27.69191 29.52563 31.51397 33.67091 38.55304 44.31174 51.11345 59.15638 68.67647 79.95442 28.83037 30.82089 32.98668 35.34432 40.70963 47.08421 54.66913 63.70577 74.48382 87.35077 29.97452 32.12910 34.48148 37.05121 42.93092 49.96758 58.40258 68.52811 80.69769 95.33883 31.12439 33.45039 35.99870 38.79223 45.21885 52.96629 62.32271 73.63980 87.34653 103.96594 32.28002 34.78489 37.53868 40.56808 47.57542 56.08494 66.43885 79.0581994.46079 113.28321 26 27 28 29 30 29 30 31 32 33 34 35 36 33.44142 36.13274 39.10176 42.37944 50.00268 59.32834 70.76079 84.80168 102.07304 123.34587 34.60862 37 49407 40.6882944.22703 52.50276 62.70147 75.29883 90.88978 110.21815 134 21354 35.78167 38.86901 42.29861 46.11157 55,07784 66.20953 80.06377 97.34316 118.93343 145.95062 36.96058 40.25770 43.93309 48.03380 57.73018 69.85791 85.06696 104.18375 128.25876 158.62667 38.14538 41.66028 45.59209 49.99148 60.46208 73.65222 90.32031 111.43478 138.23688 172.31680 39.33610 43.07688 47.27597 51.99437 63.27594 77.59831 95.83632 119.12087 148.91346 187.10215 31 32 33 34 35 36 MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skjed part, and you will not be able to come back to the skipped part Tutorial Earth Chal Home Repair needs to accumulate $21,000 in 6 years to purchase new equipment. What sinking fund payment would they need to make at the end of each three months, we are interest compounded quarterly? Use Table 12-1 Step 1 A sinking tund is an account uned for the purpose of saving for a future obligation. The amount of each payment needed to attain a needed future value is calculated using the following formula inking fund payment future value of sinking ind mure value table factor Chol Home Repair needs to come $31,000, so this is the future value of the sinking hund. The future value table facter will be determined by the Interest rate per period and the total number of compounding periods The rest rate per period is calculated using the nominal, or annun, rate and the number of periods per year as follow terest rate per period The rate was given to be 0. Interest is compounded quarterly, or 4 times per year. Find the interest rate per period perds per year nominal rate periods per year interest rate per period nominate The total number of compounds pertes will be the number of year payments are made into the sinking funded by the number of compending proper year. There are compounding periods per year and the amount of the account will be needed over to purchase new equipment in the total number of compounding periods number of pounding per number of years number of compounding periods per year TABLE 12-1 Future Value Amount of an ordinary Annuity of Periods Periods 1 2 3 1.000,00 2.00500 3.01 502 4.03010 5.08025 1% 250 3% 1.00000 1.00000 1.00000 1.00000 2.01000 2.015002.020002.03000 3.03010 3.04522 3.06040 3.09090 4,06040 4.09090 4.12161 4.18363 5.10101 5.15227 5.20404 5.30914 496 5% 1.00000 1.00000 2.04000 2.05000 3.12160 3.15250 4.24646 4.31013 541632 5.52563 6% 1.00000 2.06000 3.18360 4.37462 5.63709 79 1.00000 2.07000 3.21490 4.43994 5.75074 8% 1.00000 2.08000 3.24640 4.50611 5.86660 1 2 3 4 4 5 5 6 7 6 7 8 6.07550 6.15202 6.22955 6.30812 6.46841 6.63298 6.80191 6.97532 7.15329 7.33593 7.10588 721354 7.32299 7.43428 7.66246 7.89829 8.14201 8.39384 8.65402 8.92280 8.14141 8.28567 8.43284 8.58297 8.89234 9.21423 9.54911 9.89747 10.25980 10.63663 9.18212 9.36853 9.55933 9.75463 10.15911 10.58280 11.02656 11.49132 11.97799 12.48756 10.22803 10.46221 10.70272 1094972 11.46388 12.00611 12.57789 13.18079 13.81645 14.48656 8 9 9 TO 10 11 12 13 14 15 11.27917 11.56683 11.86326 12.16872 12.80780 13.48635 14.2067 14.97164 15.78360 16.64549 1233556 12.68250 13.04121 13.41209 14.19203 15.02581 1591713 16.86994 17.88845 18.97713 13.39724 13.80933 14.23683 14.68033 15.61779 16.62684 17.71298 18.88214 20.14064 21.49530 14.46423 14.94742 15.45038 1597394 17.08632 18.29191 19.59863 21.01507 22.55049 24.21492 15.53655 16.09690 16,68214 17.29342 18.59891 20.02359 21.57856 23.27597 25.12902 27.15211 11 12 13 14 15 16 16 17 18 17 16,61423 17.25786 1793237 18.63929 20.15688 21.82453 23.65749 25.67253 27.88805 30.32428 17.69730 18.43044 19.20136 20.01207 21.76159 23.69751 25.84037 28.21288 30.84022 33.75023 18.78579 19.61475 20.48938 21.41231 23.41444 25.64541 28.13238 30 90565 33.99903 37.45024 19.87972 20.81090 21.79672 22.84056 25.11687 27.67123 30.53900 33.75999 37.37896 41.44626 20.97912 22.01900 23.12367 24 29737 26.87037 29.77808 33,06595 36.78559 40.99549 45.76196 19 18 19 20 20 2.1 22 21 22 22 24 25 22.08401 23.23919 24.47052 25.78332 28.67649 31.96920 35.71925 39.9927344.86518 50.42292 23.19443 24.47159 25.83758 27.29898 30.53678 34 24797 38.50521 43.39229 49.00574 55.45676 2431040 25.71630 27.22514 28.84496 32.45288 36,61789 41.43048 46.99583 53.43614 60.89330 25.43196 26.97346 28.633523042186 34.42647 39.08260 44.50200 50.81558 58.17667 66.76476 26.55912 28.24320 30.0630232.03030 36.45926 41.64591 47.72710 54.86451 63.24904 73.10594 23 24 25 26 27 28 29 30 27.69191 2952563 31.51397 33.67091 38.55304 44.31174 51.1134559.15638 68.67647 79.95442 28.83037 30.82089 3298668 35.34432 40.70963 47.08421 54 66913 63.70577 7448382 87.35077 29.97452 32.12910 34.48148 37.05121 42.93092 49.96758 58.40258 68.52811 80.69769 9533883 31.12439 33.45039 35.99870 38.79223 45.21885 52.96629 62 32271 73.63980 87.34653 103.96594 32.28002 34.78489 37.5386840.56808 47.57542 56.08494 66.4388579,0581994.46079 113.28321 26 27 28 29 20 31 32 33 34 35 36 33.44142 36.13274 39.10176 42 379.14 50,00268 59.32834 70.76079 84,80168 102.07304 123.34587 34,60862 37.49407 40.68829 44.22703 52.50276 62.7014775.29883 90.88978 110.21815 134.21354 35.78167 38.86901 42 29861 46.11157 55.07784 66,20953 30.06377 97.34316 118.93343 145.95062 36.96058 4025770 43.93309 48.03380 57.73018 69.85791 85.06696 104.18375 128 25876 158,62667 38.14538 41.66028 45 59209 49.99448 6046208 73.6522290.32031 111.43478 138.23688 17231680 39,33610 43.07688 47.27597 51.99437 63.27594 77.59831 95,83632 119.12087 148.91346 187.10215 31 32 13 35 36 (1 + )" - 1 The values in Table 12.1 were generated by the formula and rounded to five decimal places, where i is the interest rate per period and is the total number of periods. TABLE 12-1 Future Value (Amount) of an Ordinary Annuity of 51 (Continued) Periods 1 2 99 10% 1.00000 1.00000 2.09000 2.10000 3.27810 3.31000 4.57313 4.64100 5.98471 6.10510 119 1.00000 2.11000 3.34210 4.70973 6.22780 12% 13% 14% 1.00000 1.00000 100000 2.12000 2.13000 2.14000 3.37440 3.40690 3.43960 4.77933 4.84980 4.92114 6.35285 6.48027 6.61010 3 15% 1.00000 2.15000 3.47250 499338 6.74238 16% 1.00000 2.16000 3.50560 5.06650 6.87714 175 1.00000 2.17000 3.53890 5.14051 7.01440 185 Periods 1.000001 2.18000 2 3.57240 3 5.215434 7.15421 5 4 5 6 7 X 752333 7.71561 791286 8.11519 8.32271 8.53552 8.75374 897748 9.20013 9.48717 9.78327 10.08901 10,40466 10.73049 11.06680 11.41387 11.02847 11.43589 11.85943 12.29969 12.75726 13.23276 13.72682 14.24009 13.02104 13.57948 14.16397 14.77566 15.41571 16,08535 16.78584 17.51851 15.19293 15.93742 16.72201 17.54874 18.41975 19.33730 20.30372 21.32147 9.20685 9.441976 11.77201 12.14552 7 14.77325 15.32700 8 18.28471 19.085859 22 39311 235213110 9 10 11 12 13 14 15 17.56029 18.53117 19.56143 20.65458 21.81432 23.04452 24 34928 25.73290 20.14072 21.38428 22.71319 24.13313 25.65018 27.27075 29.00167 30.85017 22.95338 24.52271 26.21164 28.02911 29.98470 32.08865 34.35192 36.78620 26.01919 27.97498 30.09492 32 39260 34.88271 37.58107 40.50471 43,67199 29.36092 31.77248 34.40536 37.27971 40.4174643.842414758041 51.65951 27.19994 28.75514 11 32.82393 3493107 12 39.40399 42.21866 13 47.10267 50.81802 14 5611013 60.96527 15 u 16 17 18 19 20 33.00340 35.94973 39.18995 42.75328 46.67173 50.98035 55.71747 60.92503 66.64885 72.9390116 36.97370 40.54470 44 50084 48.88367 53.73906 59.1176065.07509 71.67303 78.97915 87,06804 17 41.30134 45.59917 50.39594 55.74971 61.72514 68.39407 75.83636 84.14072 93.40561 103.74028 18 46.01846 S1.15909 56.93949 63.43968 70.74941 78.96923 88.21181 98.60323 110.28456 123.41353 19 51.16012 57.27500 64.2028372.05244 80.94683_91.02493 102.44358 115 37975 130.03294 146.62797 20 21 22 23 56.76453 64.00250 72.26514 81.69874 92.46992 104.76842 118.8101213484051 153.13854 174,02100 21 62.87334 71.40275 81.21431 92.50258 105.49101 120.43600 137.63164 15741499 180.17209 206.34479 22 69.53194 79.54302 91.14788 104.60289 120.20484 138.29704 159.27638 183.60138 211.80134 244.48685 23 7678981 88.49733 102.17415 118.15524 136,83147 158.65862 184.16784 213.97761 248.80757 289.49448 24 84.70090 98.34706 114.41331 133.33387 155.61956 181.87083 212.79302 249 21402292.1048634260349 25 24 25 26 27 28 29 30 93.32398 109.18177 127.99877 150.33393 176.85010 208.33274 245.71197 290,08827 342.76268 405.27211 26 102.72313 121.09994 143.07864 169.37401 200.84061 238.49933 283.56877 337.50239 402.03234 479.22109 27 112.96822 134 20994 159.81729. 190.69889 227.94989 272.88923 327.10408 392 50277 471.37783 566 48089 28 124.13536 148.63093 178.39719 214.58275 258.58338 312.09373 377.16969 456,30322 552 51207 66944745 29 136 30754 164.49402 199.02088 241.33268 293.19922 356.78685 434.74515 530.3117364743912 790.944799 30 31 32 33 34 35 36 149.57522 181.94342 221.91317 271.29261 332 31511 407.73701 500 95692 616.1616175850377 93431863 31 164.03699 201.13777 247.32362 304.84772 376.51608 465.82019 577.10046 715 74746 8844941 1103.4959832 179.80032 222 25154 27552922 34242945 426 46317 532.03501 66466552 831.26706 104048581 1303.12526 33 196.98234 245.47670 306.83744 384.52098 482.90338 607.51991 765.36535 965.26979 121836839 153568781 34 215.71075 271.02437 341.58955 431.66350 546.68082 693.57270 881.17016 1120,71295 1426.49102 1816.65161 35 236.12472 299.12681 380.16441 484 46312 618.74933 791.67288 101434568 1301.02703 1669 99450 21446489036