Consider the following present value (PV) tables: E: (Click the icon to view the present value factor table.) (Click the icon to view the present value annuity factor table.) Read the requirements Requirement 1. You have always dreamed of taking a safari i Africa. What lump sum do you have to invest today to have the $22,000 needed for the trip in 10 years if you can invest the money at (a) 8%, compounded annually, (b) 12%, compounded annually, and (c) 16%, compounded annually? (Round your final answers to the nearest cent.) Begin by selecting the formula you will need to answer this question for each of the three scenarios (a., b., and c.) Lump sum amount needed x Present value of $1 Present value 1a. Assume that you can invest the money at 8%, compounded annually. 1 Data Table Data Table Present Value of $1 Present Value of Ordinary Annuity of $1 Period 3% 4% 5% 6% 7% 8% 10% 12% 14% 16% 18% 20% Period 3% 4% 5% 6% 7% 8% 10% 12% 14% 16% 18% 20% 1 9709 9615 9524 9434 9346 .9259 .9091 8929 8772 8621 8475 .8333 1 9709 9615 9524 9434 9346 9259 .9091 .8929 8772 8621 .8475 8333 2 9426 9246 9070 8900 8734 .8573 .8264 7972 .7695 7432 .7182 .6944 2 1.9135 1.8861 1.8594 1.8334 1.8080 1.7833 1.7355 1.6901 1.6467 1.6052 1.5656 1.5278 3 9151 .8890 8638 .8396 8163 7938 .7513 7118 6750 6407 6086 5787 3 2.8286 2.7751 2.7232 2.6730 2.6243 4 2.5771 2.4869 2.4018 2.3216 2.2459 2. 1743 2.1065 3.3121 3.1699 3.0373 2.9137 2.7982 2.6901 2.5887 .8885 8548 8227 .7921 .7629 .7350 6830 6355 .5921 5523 5158 4823 4 3.7171 3.6299 3.5460 3.4651 3.3872 5 8626 8219 .7835 .7473 7130 .6806 6209 5674 5194 4761 4371 4019 5 4.5797 4.4518 4.3295 4.2124 4.1002 3.9927 3.7908 3.6048 3.4331 3.2743 3.1272 2.9906 6 .8375 7903 .7462 7050 6663 .6302 5645 5066 4556 4104 3704 3349 6 5.4172 5.2421 5.0757 4.9173 4.7665 4.6229 4.3553 4.1114 3.8887 3.6847 3.4976 3.3255 7 8131 .7599 .7107 .6651 .6227 5835 5132 4523 3996 3538 3139 2791 7 6.2303 6.0021 5.7864 5.5824 5.3893 5.2064 4.8684 4.5638 4.2883 4.0386 3.8115 3.6046 8 .7894 7307 6768 6274 5820 5403 4665 4039 3506 3050 2660 2326 8 7,0197 6.7327 6.4632 6.2098 5.9713 5.7466 5.3349 4.9676 4.6389 4.3436 4.0776 3.8372 9 .7664 .7026 .6446 5919 5439 5002 4241 3606 3075 2630 2255 1938 9 7.7861 7.4353 7.1078 6.8017 6.5152 6.2469 5.7590 5.3282 4.9464 4.6065 4.3030 4.0310 10 .7441 .6756 .6139 5584 5083 4632 3855 3220 2697 2267 . 1911 1615 10 8.5302 8.1109 7.7217 7.3601 7.0236 6.7101 6.1446 5.6502 5.2161 4.8332 4.4941 4.1925 15 .6419 5553 4810 4173 3624 3152 2394 1827 1401 1079 .0835 .0649 15 11.9379 11.1184 10.3797 9.7122 9.1079 8.5595 7.6061 6.8109 6.1422 5.5755 5.0916 4.6755 20 5537 4564 3769 3118 2584 2145 1486 1037 0728 .0514 .0365 0261 20 14.8775 13.5903 12.4622 11.4699 10.5940 9.8181 8.5136 7.4694 6.6231 5.9288 5.3527 4.8696 25 4776 3751 2953 2330 1842 1460 0923 0588 0378 0245 .0160 .0105 25 17.4131 15.6221 14.0939 12.7834 11.6536 10.6748 9.0770 7.8431 6.8729 6.0971 5.4669 4.9476 30 4120 3083 2314 1741 1314 0994 0573 0334 0196 0116 .0070 0042 30 19.6004 17.2920 15.3725 13.7648 12.4090 11.2578 9.4269 8.0552 7.0027 6.1772 5.5168 4.9789 1. You have always dreamed of taking a safari in Africa. What lump sum do you have to invest today to have the $22,000 needed for the trip in 10 years? Assume that you can invest the money at a. 8%, compounded annually. b. 12%, compounded annually. c. 16%, compounded annually. 2. You are considering partial retirement. To do so you need to use part of your savings to supplement your income for the next 8 years. Suppose you need an extra $40,000 per year. What lump sum do you have to invest now to supplement your income for 8 years? Assume that your required rate of return is a. 8%, compounded annually. b. 12%, compounded annually. c. 16%, compounded annually. 3. You just won a lump sum of $8,000,000 in a state lottery. You have decided to invest the winnings and withdraw an equal amount each year for 20 years. How much can you withdraw each year and have a zero balance left at the end of 20 years if you invest at a. 4%, compounded annually? b. 8%, compounded annually? 4. An NHL hockey player is offered the choice of two 4-year salary contracts, contract X for $3.46 million and contract Y for $3.38 million: Contract X Contract Y End of year 1 $ 340,000 $ 590,000 End of year 2 740,000 810,000 End of year 3 1,090,000 1,040,000 End of year 4 1,290,000 940,000 $ 3,460,000 $ 3,380,000 Total Which contract has the higher PV at 10% compounded annually? Show computations to support your
