Sarah has just finished her studies, and has started her career by accepting a position at an online learning company. Being a forward-thinking young woman, she is already looking ahead to her retirement, and wants to start putting money away now. She wants to retire 30 years from now, and wants a lump sum of R3 million at that point. To allow her to plan effectively, and to keep things simple, she wants to put away the same amount for the full period, at the end of each year. Using the tables, and showing your workings clearly, answer each of the following questions: 2.1 Assuming that she receives an average growth rate of 9% p.a. for the period, how much does Sarah need to put away at the end of each year? Start writing here: 2.2 If she were to invest a lump sum now instead, to reach R3 million in 30 years, which also grew at 9% p.a., compounded annually, how big would this lump sum need to be? Start writing here: 2.3 At retirement, if she were to then take that lump sum of R3 million and buy an annuity. that would pay out annually for 20 years, and have a guaranteed annual return of 12%, how much would she receive every year? Start writing here: 2.4 When looking ahead to retirement, one always needs to take into account the effects of inflation. Using the answer from question 2.3, and with an average annual inflation figure of 6% over the period, what would the value of the fifth one of these annuity payments received (received exactly 35 years from now) be worth today? 4 FVIF = (1 + )" 6 3% 4% % % % 1010 1.000 % % 10% 11% 12% 13% 1% 1% 1 20% 20% 30% 1.000 1.040 1.000 1.000 1.070 1.000 1.000 1.100 1.110 1.120 1,130 1,10 1,150 1.100 1200 1.250 1.300 3 1.000 1.0011.002 1.100 1.1241.145 1,106 1,188 1.210 1.232 1284 1277 1.200 1.329 134 140 1580 1.000 1.000 1.061 1.090 1.125 1,158 1.191 1,225 1.200 1.295 1.331 1,368 1408 1443 1.82 1.521 1.561 1720 1360 2.187 1041 1.082 1.128 1170 1.216 1.282 1,311 1.360 14121484 1518 1.874 1830 1830 1,70 107 2074 2H1 2.856 5 1051 1.104 1,159 1.217 1.276 1.338 1.400 1.469 1.530 1.611 1.685 1782 1.842 1823 2.on 2100 2180 3082 3.78 1062 1,126 1,194 1.286 1.340 1410 1.501 1.587 1.677 172 1.80 1.974 2012 2.100 2.319 2.436 2.900 39157 1.072 1.149 1,230 1.316 1.407 1.504 1,006 1,714 1.829 1.949 2.086 2.211 2383 2.500 2,000 2.000 3.588 1788 6:35 1.00 1,172 1287 1.300 1477 1504 1718 1851 1990 2.144 2,305 2.470 2,000 2.250 3.000 3.270 4300 5.960 2,157 1,094 1,196 1306 1.425 1.561 1600 1.838 1.9700 2172 2358 2568 2,773 2.004 3,252 3318 3,608 5.100 7,451 10,80 10 1,106 1219 1344 1.480 1.629 1,791 1.967 2.150 2.367 2.504 2,839 3.108 3.395 3,707 4046 447 6,192 0.313 13,70 1243 1.384 1.530 1710 1.808 2.105 2.332 2.580 2.853 3.152 3.49 3.636 4,226 4652 5,1177,480 11.64 17:32 11 1.116 1.127 1268 1426 1.601 1,796 2012 2.252 2.818 2.813 3,138 3.498 3,806 1,3384.816 5.350 5,808 6.916 14,58 23:30 1,138 1,204 1.460 1865 1.686 2,138 2,410 2,720 3,066 3.462 3,883 4.363 4,806 5,492 0,183 0,886 10,70 18,19 30:20 13 141,149 1,319 1513 1,732 1,080 2,281 2.570 2.937 3.342 3.797 4,310 4,8876,636 4,20170707.988 12,00 22,7 30,37 1,161 1,346 1.568 1.801 2.070 2,397 2,769 3.172 3.642 41774,786 5,474 6,254 7,138 0,137 0.200 10,41 2042 61,19 16 1,173 1,373 1.605 1,873 2,183 2,540 2,9623426 3,970 4,598 5.3116,130 7.087 ,1379,358 10.75 180 36.000454 171.184 1.400 1.663 1.948 2.292 2.000 3,109 3,700 4.328 5.0645,896 6.000 7.906 0.276 1970 12:47 22,10 4,416.50 18 1,196 1.428 1.702 2,028 2407 2.854 3.380 3.906 4,717 5.560 6544 7.000 2.024 10.50 12.38 M16 2862 38.51 112.5 1,754 2.107 2,827 3,008 2617 4.316 5142 6.118 7.283 8.813 10:20 12.08 .23 16.78 31.86 00.30 146.2 1.486 1,806 2,191 2.880 3,207 3,870 4,661 5,604 6,725 2,062 9.646 11.52 13,74 15,37 19,46 58,408,74900 1.45 Factors not included in this table may be calculated by means of the following equation forn Periods Table A Future Value Interest Factors for R1 compounded at k por cont 1,518 1.860 2.279 2,786 3,400 4,141 6.094 6,100 7,400 8.940 10.00 13.00 15.8 1682 2287 . 102471 1,245 1,546 1.916 2.370 2,925 3,604 4,430 5.437 6.669 6.140 3.334 12,10 1471 17.00 21,64 20,19 55,21 1383 2212 1.577 1,974 2,465 3,072 3,80 4,741 5,871 7258 0,964 11,00 13:56 16.63 20,30 24,00 30,38 66.28 100A 1975 1808 2,083 2583 3.2254.000 ,072 0341 7911 9.850 12,24 15,16 18,70 23,21 28,00 33,20 7230 210 542.0 1.841 2.094 2006 3.366 4,292 6.427 048 0.623 10,8 13,90 17.00 21,200,40 12,88 0,07 140 2047 2000 2.42 3.243 4,322 3,743 7.612 10,06 13:27 1745 22,00 20.96 30,12 50,98 06,21 55,00 237,400.8 2820 38 1417 2.000 2.814 3.0446 6.516 7.860 10.68 14,70 2041 28,10 38,57 62,60720720,10 1332 100,3 520,7 248 2720 2.208 3.262 4,801 7040 10,20 14,97 21,72 3141 4528 65.00 13.00 12,0 188,9 2879 378,7 1470 782330110 3,762 5.841 1.985 13,78 2100 31.92 4.33 72.00 100.5 164,0 34,6 303,7589 790.4 3057 2000 . 2,09243647,10 11,47 1842 29,40 40.907.38 117A 1848 2000 480,77002 106 1071 090070005 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 10 2 2 4 3.050 3.60 3.001 3.1222,160 3,184 3215 3.246 3278 3.310 1342 3374 3.40 | 2 2010 2.020 2,000 2,000 2,060 2,000 2,070 2,000 2,000 2,100 2110 2.120 2.100 2.40 2.100 2.10 2.300 m AM 341 3.600 960 am 6 s161015201 5.309 6.416 6,528 6.825.7515.8675.988 0,106 6,228 0.18 486041224,1844.246 4.310 4.3734104.508 4573 4841 47104,770 4,800 4.921 4.000.000 6.00 w ce 6,1626,308 6.188 0653 6.8026.973 7,150 7206 7.520 7710 7313 0.1136.32 6.480 6.070 0,70 AZT TAR 1.300.00 0.538 10.704 LITT 2,800 11.30 1274 6.2868.5836,802 02149.540 0.807 10,28 104 7 7214 7434 7662 7.000 0,142 6.3946.854 0.923 9:2000.487 078 10.00 10,408 10.730 11.087 11, 12910 13.0375 11.00 114 11.00 12:30 12,10 13:23 19.79 1424 18.0 10 23,00 10 0.369 0,786 10,16 0,56 11,00 11,0 11.98 12.40 13.02 13:58 14 16 18 18..18.0 17.58 20.00 18.0 32.00 1046 10.98 11,46 12.01 12,60 13,18 13.82 1440 15.10 18.94 1672 1796 1. 10. 20.21.0 20.0 228 11 11.57 12,17 12,811.40 14.21 14,97 15,78 16.88 1756 1859 12:56 2018 21.09 23.04 26.38 2.79 22,6 257 56, 12 1288 1341 14,19 15,00 15,02 16,87 17.00 18.98 20.14 21.38 2271 24,10 23,00 272) 20,00 3040 30.58 .21 14,3 13 13,81 14.88 15,62 15,63 17.71 18,68 2014 21.50 22.90 24.52 20,21 20,00 20.90 32,00 34,35 30,79 48,50 88,76 37.63 14 14.96 15.97 17.00 16,2019,60 21,00 22.58 2421 26.02 2797 3200 32,30 24,00 3700 20.50 0918 60.20 .801278 18,60 2002 21,58 23,28 28,13 2715 29.36 3177 341 3728 4042 43. 47.50 81.86 72,04 1903 16,10 197.3 15 1720 16 17:28 18,64 20,16 21,62 23,66 25,67 27.80 30,32 33,00 33,06 38.10 42,78 16,67 60.00 30,126040 87,44 101 218. 33,76 36.97 40.54 44.80 48.88 68.74 59,12 68.08 7167 105,9 1736 286.0 17 1843 20.01 2176 22.70 25,84 28.21 30,6 1819,61 2141 23,41 25.66 28, 13 3091 34,00 37,45 41.30 4660 50,40 6678 61.73 64.30 15.0 4.14 12,1 2180 3918 19 20,01 22,4 25,12 27,67 30,54 33,76 37,38 1148 46.02 51,1656.94 $344 70,79 7837 18:21 18:00 154.7 2738 434,0 20 22.02 24,30 26,87 29,70 33,07 36,70 4100 45,76 51,16 32,2764,20 12.00 10:30 11.00 102A 1154106, 3439 02 FVIFA - a + k- Factors not included in this table may be calculated by means of the following equation for n Porods Table B Future Value Interest Factors for a Rl annully compounded at k por cent 21 23,24 25,78 2868 31,97 38.72 30.90 448750A258,76 0400 72,2701,70 12,47 10401189 1948 225,0 42,72002 22 24 A7 27 30 3954 34,2838,81 43.30 4901 56.4662,877140 61,21 12:30 1058 1204 1374 1974 2710 1981 1087 23 25.72 28.84 3245 36.62 41.43 47,00 5344 60,00 09.53 795401,15 1046 1202 1943 1993 24 26,97 1836 3282 6738 1930 3042 34.43 30.08 44,50 50,82 58,18 66,76 76.70 18.50 102.2 1162 1963 1947 1842 2140 3825 BIO 1808 28,24 32,00 36.48 41,66 47,73 54,05 63.25 73,11 34,70 90,36 1544 1933 1558 1819 2120 2442 4720 1080 23:00 40.57 47,58 16.00 66.44 79.06 0446 1133 130.3 1645 190.0 2413 2002 306 307 3003 1182 221 8730 49.90 6946 73,66 90,32 111A 1302 1723 2157 27103416 431 546) 083800121121201673043 60.40 75.40 96.08 120,6 1948 19018 289.1 3379 4426 581, 8767,1 101 1942 170 23817342 66.4871.00 92,72 121,0 150.7 2127 205,73005 525.9 7189 383,6198018742891 1 0 644604.50 1120 132,7 200,3 2503 40658738 015.1 11641660 3400 0100 200 PVIF = + KM D 1% 2% 3% 5% % 7% .990 0.980 0,971 0.92 0.962 094 093 a % 10 l % 10% 10% 11% 11% 12% 12% 13% 13% 19 14% 15% 20 20 21 2 0.900 0.961 0.843 0.923 0.307 0.880 osroslav 1901 1900 0.000 0.877 0.870 0,002 0.130 0000 02 4 2,849 0.923 0.9070100087a 0.867 ose 0438 08124079 0.760 0,70 0,88 0754 One Molase 10710842 0.0160.6000064 0.40 0.818 0.700.772 0331 073140712amleslo 0.961 09242888 0,088 0.125 or 078 3 0,981 0.9050668 0.822 0.74 0.735 0.708 0.883 08800836 0.813.960572 0502 DARB 0.10 0.38 6 0347 0313 0681 0.680 0821 088008872540 .519 049 0478 QADB 0.000 0.000 7 0.853 0.942 0.888 2897 0.780 0,746 0708 0106 0630 0.500 0.54 0835 0.807 0480 0.40 0.62 0110 0.21 0.22 0.20 0.871 0,813 0,760 0,711 0888 0.823 2583 0.547 0.813 0482 0,452 0428 0.400 0.376 0364 0270 9210 2.150 0.923 0.86 0700 0,731 0,677 0.827 0.582 0.540 0,50 0,67 0434 0404 0.376 0,381 0.21 0.305 0290 01000, 123 0.914 0.837 0766 0.700 0,66 0.592 0.54 0.500 0.400 0.434 0.391 0.361 0.830 0.308 0.33 0.280 0,12 0,134 0,00 100,905 0.020 0,744 0,670 0.61 0.868 0.500 016 0.422 0.386 0.382 0.322 0.200 0.270 0.20 0.227 0,142 0,10 0,or 0.804 0,720,660 0,686 0.827 0478 0429 0.388 0.380 0.37 0.287 0,2010,237 0.20 0.100 0130 0.00 0.00 0,701 9626 0,56704970444 0.39703560,319 0.286 0.287 0231 0.806 0.167 0,168 0112 00000043 26010,890 0.400 0115 0,3600320 0.200 0.288 0.220 0.2040162 0.16 0.16 0.000 0.008 0.03. 0,861 0877 0,506 0,22 0,388 0,340 2290 0,263 0,232 0208 0,161 160 0,14 0,125 2.078 004 2003 0,642 0,886 0,481 0,417 0,362 0,315 0.276 0,230 0.200 0,18 0,160 0140 0,123 0,00 0,00 0000 0000 0,743 0.623 0.604 0,458 0,394 0.330 0,292 0.252 0.218 0.1800,1600,141 0.123 0,107 0.000 0.0040.000 2016 0,3710.317 0.270 0.231 0,198 0,170 0,146 0,125 0,108 0.000 0.000 0.045 0.025 0.012 0,436 212 0,1800,1800,1800,110,000 2,000,000,000 0.16 0.000 0.232 0,194 0,164 0,138 0,116 0.000 0.000 .00 0.00 0.00 0.014 0.007 2,390 0,331 0.27 0.377 0312 0.288 0.218 0,10 0,140 0,1240106 0,087 0,00 0,00 0,00 0,00 0,012 0,60 0.2040.242 0,1900,164 0,1350,112 0.003 0.077 0.00 0.00 0.04 0.07 0.000 0.004 0,342 0,278 0228 0,184 0,1800,123 0,101 0.000 0.000 0.000 0.048 0.038 0010 ,00 0,00 0.879 Factors not included in this table may be calculated by means of the following equation for n Periods Table C Prosent-Value Interest Factors for R1 Discounted atk per cent 0.329 0.262 0.211 0.170 0,10 0,112 0.001 0.074 0,000 0,00 0000 0000 0018 0.000 0.00 0,788 0.622 0402 0,380 0.310 0.247 0,197 0,158 0,18 0,10 5470 0.378 0.299 0230 0,16 0,002 0,00 0,0632000030 0,00 09132,000.00 6620412 0.300.231 0,174 0131 2010 0,078 0,087 004 0000 0000 0.000 2010 4146 0.116 0002 0074000000479,098 0000 0000 0010 0.00 0.001 2012 000 4000 500 0.368 0.283 0,1800,180 0.004 2068 0.040 0,036 0.02 0.010 2011 2.010 0.000 0.000 0.000 . 50 0.307 0.200 0,10 0,005 0.067 0.016 0,032 0,022 0015 001 0.000 0.000 0.000 0.000 0001 . 100.2010.17 0.11 0.07 0.01 0.001 0.021 0.01 0.000 0.000 0.00 0.00 0.00 0.00 0.000 -. 1372 0.220 0,141 0,00 0,004 0.014 0.021 0.013 0.00 0.00 0.00 0.00 0.00 0.00 0.00 11 D 2% 3% 4% 5% 6% 7% 0% 0% 10% 11% 12% 13% 14% 19 19 20 2 1 PVIFA - 1% 3 10.990 0.960 0,971 0.902 0982 0.943 0898 0.928 0.91 0.000 0.001 0.000000 sonra onlama 3,902 3,808 2.941 284 2,820 2,778 2,723 2.673 2.824 2.677 2.831 2,487 244 2 | 1970 1942 1,913 1,880 1.850 1.830 1.800 1.783 1780 1736 1713 1.000 1.000 1.60 120 1808 18000 2400 2.801 2.30 2200 220 2.100 1.10028 5 4.853 4713 4.580 4,452 4,29 4212 4.100 3717 3.630 3.546 3,465 3.387 3,312 3.240 3,170 3,100 3.087 2.074 2.04 2006 27W B 2560 2.82 2.100 1.900 3.000 3,701 3.600 3806 2.517 3,000 3,382 3.274 290 2.000 2.400 5,790 5.801 5417 5.242 6.00 1917 27874828 .486 4.36 4231 411 2.900 3.000 3.23.880 3.300 201 2040 6728 GAT2 6230 6.000 6.700 6.562 5.300 5200 5.000 4,800 4712 430 4430 4,000 4,00 4,000 58063 11 2.000 6.566 6.162 7700 7.438 7.10 788273257.000 .788 6.40 6210 58715,7475.588 5.30 5.146 4.968 4700 460 467 4.5458872590 2,005 6.000 6.318 6.247 5.905 5.750 5.537 5.3286,132 4,00 4,724.60 4001 3..010 10 2,471 6.983 8.530 ,111 7,722 7.300 7.024 6,710 6.418 6.18 6.880 5,860 5420 5.250 5,00 6,830 4,182 3571 3,062 11 10.37 0.787 0.283 6.760 0.308 7.887 7490 7.130 6,808 6,496 6.2015,908 6.687 5,460 5.20 5.20 4.327 3666 3,147 12 11,26 10.58 0.964 2,386 6.063 6.304 7,243 7.836 7,161 6,814 6.492 6,104 5.918 5,000 .421 6.107 4430 3,728 3,190 13 12,13 1136 10.60 ,906 0,39 0,000 0.368 7,804 7.487 7,100 6,70 61246126042 6.000 6.9424850 .7601.223 14 13,00 12,11 11,30 10,66 0.000 0.25 0.746 8.244 7.786 7,367 6,962 6.828 0.302 0.002 0.724 6.60 4.811 3.424 .240 15 13,8 12,86 1194 11,12 10,38 0,712 9,108 6,500 6,061 7,606 7.191 .811 6462 6.142 6,047 0,878 1879 3,000 3,286 1614,72 13.58 0447 0,861 8.313 7.8247,370 0.9746601 6.200 0,0046.000 4730 3.872,283 12,56 11,00 10,0 10,11 17 15,56 0,122 0.54 0,0227,80 7,120 6720 6.370 6,047 5.70 4.775 3,010 1.200 14,20 13,17 12,17 11,27 10,48 0,76 40 14,90 13,75 12,66 11,00 10,00 10,06 9,372 0,786 6,2017,707280 6.00 6467 ,120,40123,00 3,304 13,13 12,00 11,16 10,34 0,604 0,960 6,366 7,820 7368 4,838 6.500 6,700 6,071 4.943 1942 3311 15,68 14,32 14,00 13,00 12,40 1147 1990 2,610 0,129 ,5147.9637,4607,028 6.000 6.250 6.829 ANTO 3,064 0.010 18,42 14,08 12,82 1970 1969 10,020,28 ,640 307878627,108 0.007 0.312 .873.00 2,000 2.00 12.00 12.00 10,20 D4C 0,772 6.176 71840 7,170 0700.00 RON 4800 1.870 3.30 15,94 14,0 13,10 Factors not included in this table may be calculated by means of the following equation forn Porlods Table D Prosont-Value Inforest Factors for a R1 annuty discountod at k por cont 16,4 1,60 1340 12.30 11.27 10,37 0,580 6.003 0.26677187,230 6.700.00 RON 1009.470 . 6,04 15,25 13.00 12.86 11A710,58 0,707 3.865 6.548 730 7,280 6.00 6439607348 3.600 1,50 17,4115.60 14.00 12,70 11.88 10,67 0.023 BOTT BA22 .8437.330 6.8736,4046004941.000 2.389 19,60 17,2016,37 13,76 1241 11,28 10.27 0.0040.000 48 7.000 0.0000114870 2900 2.330 21,40 16.00 16,37 14,50 12,90 11,66 10,67 2,614 0.896 0.176 7.500 7.070 GA76.215 4902 2.000 1.300 201119,70 17,16 18.00 13.39 11.92 10,760.770 0,951 6.24 7634 7,1086.6626.230 1.000 1.000 2578 21:42 143 1870 18:40 12:21 10,08 2,03 2,042 03079757,183 0,00 0,00 100 100 9.8W 2462 20,72 17,77 18.40 13.61 12,00 10,000,000 3900662837,01 7,123 604 6942 4000 .30 31 A2 25.73