5.(20) Buy or lease a car? One option is to pay $3000 initially to lease it, plus $300 each month to use it for three years, and then replace it with another lease. The other option is to buy it for $20,000, pay $100 per month to operate it, and then sell it for $3000 after 7 years. No resale value is received for the lease. Assuming repeatability, which option has the least uniform annual cost EUAC or AW? Assume that the MARR = nominal rate of 9% compounded monthly. Hint: compare AW using monthly rate = MARR/12. Lease Buy Initial Cost $3,000 $20,000 Monthly Cost $300 $100 Resale Value $0 $3,000 Number of Years 3 years = 36 months = 84 months 7 years n 1 2 3 4 5 6 7 8 9 10 Single Payment Compound Present Amount Worth Factor Factor Find Find P Glven P Given F F/P PAF 1.080 9259 1.166 8573 1.260 .7938 1.360 7350 1.469 .6806 1.587 6302 1.714 15835 1.851 5403 1.999 5002 2.159 4632 2.332 .4289 2.518 .3971 2.720 3677 2.937 3405 3.172 3152 3.426 2919 3.700 2703 3.996 2502 2317 4.661 2145 5.034 .1987 5.437 1839 5.871 1703 1577 6.848 .1460 7.396 .1352 7.988 .1252 8.627 1159 9.317 .1073 10.063 0994 10.868 0920 11.737 0852 12.676 0789 13.690 .0730 14.785 0676 21.725 0460 31.920 0313 46.902 .0213 68.914 0145 101.257 00988 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 4.316 Compound Interest Factors Uniform Payment Series Capital Compound Recovery Amount Factor Factor Find A Find F Glven P Given A A/P FIA 1.0800 1.000 5608 2.OSO 3880 3.246 3019 4.506 2505 5.867 2163 7.336 .1921 8.923 . 1740 10.637 1601 12.488 1490 14.487 1401 16.645 1327 18 977 1265 21.495 1213 24.215 .1168 27.152 .1130 30.324 1096 33.750 1067 37.450 -1041 41.446 1019 45.762 0998 50.423 0980 55.457 0964 60.893 0950 66.765 1.0937 73.106 ,0925 79.954 0914 87.351 0905 95.339 0896 103.966 0888 113.283 .0881 123 346 0875 134.214 0869 145.951 0863 158.627 .0858 172317 0839 259.057 0826 386,506 087 573.771 0812 848.925 OSON 12532 Sinking Fund Factor Find A Given F A/F 1.0000 4808 3080 2219 .1705 1363 .1121 0940 .0801 .0690 0601 0527 0465 0413 0368 .0330 0296 0267 0241 0219 0198 0180 0164 .0150 20137 .0125 0114 0105 .00962 00883 .00811 .00745 00685 .00630 00580 00386 00259 .00174 00118 00080 Present Worth Factor Find P Given A P/A 0.926 1.783 2.577 3.312 3.993 4.623 5.206 5.747 6.247 6.710 7.139 7.536 7.904 8.244 8.559 8.851 9.122 9.372 9.604 9.818 10.017 10.201 10.371 10.529 10.675 10.810 10.935 11.051 11.158 11.258 11.350 11.435 IL 514 11.587 11.655 11.925 12.108 12.233 12.319 12.377 6.341 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 36 40 18 50 52 Single Payment Compound Present Amount Worth Factor Factor Find F Find P Glven P Given F FIP P/F 1.005 .9926 1.013 9852 1.023 9778 1.010 .9706 1.038 1.046 9562 1.054 9490 1.062 9420 1.070 9350 1.078 19280 1.086 9211 1.094 9142 1.102 9074 1.110 9007 1.119 8940 1.127 8873 1.135 8807 1.144 8742 1.153 8676 1.161 .8612 1170 8548 1.179 8484 1.188 8421 1.196 8358 1.205 8296 1.214 8234 1.224 8173 1.233 8112 1.242 8052 1.251 .7992 1.309 .7641 1.348 .7416 1.431 6986 1.453 6852 1.475 6780 1.566 .6387 1.687 5927 1.713 5839 1.818 5500 1.873 5338 Sinking Fund Factor Find A Given F A/F 1.0000 4981 3308 2472 1970 1636 1397 1218 1078 0967 0876 OSOO 0735 0680 0632 0591 0554 0521 0492 0465 0441 0420 0-100 0382 0365 Compound interest Factors Uniform Payment Series Capital Compound Recovery Amount Factor Factor Find A Find F Glven P Given A A/P FIA 1.0075 1.000 5056 2.008 3383 3.023 2547 4.045 2045 5.076 1711 6,114 1472 7.160 1293 8.213 1153 9.275 1042 10.344 .0951 11.422 0875 12 508 0810 13.602 0755 14.704 0707 15.814 0666 16.932 0629 18.059 0596 19.195 0567 20.339 0540 21.491 0516 22.653 0495 23.823 0475 25.001 0457 26.189 0440 27385 0425 28.591 0411 29.805 0397 31.029 0385 32.261 0373 33,503 0318 41.153 0290 46.447 0249 $7.521 0241 60,395 0233 63.312 0208 75.425 0184 91.621 0180 95.008 109.074 0161 116.428 Present Worth Factor Find P Given A P/A 0.993 1.978 2.956 3.926 4.889 5.846 6.795 7.737 8.672 9.600 10.521 11.435 12.342 13.243 14.137 15.024 15.905 16.779 17.647 18.505 19.363 20211 21.053 21 889 22.719 23.542 24.360 25.171 25.976 26.775 31.447 34.447 40.185 41.567 42.928 48.174 54.305 55.477 59.995 62.154 0350 0336 0322 0310 0298 0243 0215 0174 0166 0158 0133 0109 0105 00917 .00859 70 72 80 84 .0167
