20. Present Value Calculations (Annuities). For each of the following independent scenarios, use Table 8.8 in the appendix to calculate the present value of the cash flow described. Round to the nearest dollar 1. $20,000 will be received at the end of each year for 6 years. The rate is 12 percent. 2. $20,000 will be received at the end of each year for 6 years. The rate is 15 percent. 3. $20,000 will be received at the end of each year for 6 years. The rate is 7 percent. 4. $120,000 will be received at the end of each year for 4 years. The rate is 10 percent. Table 8.8 Present Value of $1 Received at the End of n Periods 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 18% 20% 25% 30% 1 0.9524 0.9434 0.9346 0.9259 0.9174 0.9091 0.9009 0.8929 0.8850 0.8772 0.8696 0.84746 0.8333 0.8000 0.7692 2 1.8594 1.8334 1.8080 1.7833 1.7591 1.7355 1.7125 1.6901 1.6681 1.6467 1.6257 1.56564 1.5278 1.4400 1.3609 3 2.7232 2.6730 2.6243 2.5771 2.5313 2.4869 2.4437 2.4018 2.3612 2.5313 2.4869 2.4437 2.4018 2.3612 2.3216 2.2832 2.17427 2.1065 1.9520 1.8161 4 3.5460 3.4651 3.3872 3.3121 3.2397 3.1699 3.1024 3.0373 2.9745 2.9137 2.2832 2.69006 2.5887 2.3616 2.1662 5 4.3295 4.2124 4.1002 3.9927 3.8897 3.7908 3.6959 3.6048 3.5172 3.7908 3.6959 3.6048 3.5172 3.4331 3.3522 3.12717 2.9906 3.4331 3.3522 3.12717 2.9906 2.6893 2.4356 6 5.0757 4.9173 4.7665 4.6229 4.4859 4.3553 4.2305 4.1114 3.9975 3.8887 3.8887 3.7845 3.4976 3.3255 2.9514 2.6427 7 5.7864 5.5824 5.3893 5.2064 5.0330 4.8684 4.7122 4.5638 4.4226 4.2883 4.1604 3.8115 3.6046 3.1611 2.8021 8 6.4632 6.2098 5.9713 5.7466 5.5348 5.3349 5.1461 4.9676 4.7988 4.9676 4.7988 4.6389 4.4873 4.0776 3.8372 3.3289 2.9247 9 7.1078 6.8017 6.5152 6.2469 5.9952 5.7590 5.5370 5.3282 5.1317 4.9464 4.7716 4.3030 40310 3.4631 3.0190 10 7.7217 7.3601 7.0236 6.7101 6.4177 6.1446 5.8892 5.6502 5.4262 5.2161 5.0188 4.4941 4.1925 3.5705 3.0915 11 8.3064 7.8869 7.4987 7.1390 6.8052 6.4951 6.2065 5.9377 5.6869 5.4527 5.2337 4.6560 4.3271 3.5705 3.1473 12 8.8633 8.3838 7.9427 7.5361 7.1607 6.8137 6.4924 6.1944 5.9176 5.6603 5.4206 4.7932 4.4392 3.7251 3.1903 13 9.3936 8.8527 8.3577 7.9038 7.4869 7.1034 6.7499 6.4235 6.1218 5.8424 5.5831 4.9095 4.5327 3.7801 3.2233 5.0081 4.6106 3.8241 3.2487 14 9.8986 9.2950 8.74558.2442 7.7862 7.3667 6.9819 7.3667 6.9819 6.6282 6.3025 6.0021 5.7245 Factor=[1-(1+r)*1/1 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 18% 20% 25% 30% 15 10.3797 9.7122 9.1079 8.5595 8.0607 7.6061 7.1909 6.8109 6.4624 6.1422 5.8474 5.0916 4.6755 3.8593 3.2682 9.4466 8.8514 8.3126 7.8237 7.3792 6.9740 6.6039 6.2651 5.9542 5.1624 4.7296 3.8874 3.2832 16 10.8378 10.1059 17 11.2741 10.4773 18 11.6896 10.8276 9.7632 9.1216 8.5436 8.0216 7.5488 7.1196 6.7291 6.3729 6.0472 5.2223 4.7746 3.9099 3.2832 9.3719 8.7556 8.2014 7.7016 7.2497 6.8399 6.4674 6.1280 5.2223 4.8122 3.9279 3.3037 10.0591 19 12.0853 11.1581 10.3356 9.6036 8.9501 8.3649 7.8393 7.3658 6.9380 6.5504 6.1982 5.3162 4.8435 3.9424 3.3105 20 12.4622 11.4699 10.5940 9.8181 9.1285 8.5136 7.9633 7.4694 7.0248 6.6231 6.2593 5.3527 4.8696 3.9539 3.3158 21 12.8212 11.7641 10.8355 10.0168 9.2922 8.6487 8.0751 7.5620 7.1016 6.6870 6.3125 5.3837 4.8913 3.9631 3.3198 22 13.1630 12.0416 11.0612 10.2007 9.4424 8.7715 8.1757 7.6446 7.1695 6.7429 6.3587 5.4099 4.9094 3.9705 3.3230 23 13.4886 12.3034 11.2722 10.3711 9.5802 8.8832 8.2664 7.7184 7.2297 6.7921 6.3988 5.4321 4.9245 3.9764 3.3254 9.7066 8.9847 8.3481 7.7843 7.2829 6.8351 6.4338 5.4509 4.9371 3.9811 3.3272 24 13.7986 12.5504 11.4693 10.5288 25 14.0939 12.7834 11.6536 11.6536 10.6748 9.8226 9.0770 8.4217 7.8431 7.3300 6.8729 6.4641 5.4669 4.9476 3.9849 3.3286 26 14.3752 13.0032 11.8258 10.8100 9.9290 9.1609 8.4881 7.8957 7.3717 6.9061 6.4906 5.4804 4.9563 3.9879 3.3297 27 14.6430 13.2105 11.9867 10.9352 10.0266 9.2372 8.5478 7.9426 7.4086 6.9352 6.5135 5.4919 4.9636 3.9903 3.3305 28 14.8981 13.4062 12.1371 11.0511 10.1161 9.3066 8.6016 79844 7.4412 6.9607 6.5335 5.5016 4.9697 3.9923 3.3312 29 15.1411 13.5907 12.2777 11.1584 10.1983 9.3696 8.6501 8.0218 7.4701 6.9830 6.5509 5.5098 4.9747 3.9938 3.3317 30 15.3725 13.7648 12.4090 11.2578 10.2737 9.4269 8.6938 8.0552 8.0552 7.4957 7.0027 6.5660 5.5168 4.9789 3.9950 3.3321 = 20. Present Value Calculations (Annuities) Present value = Amount received in future