(Click the icon to view the present value annuity Consider the following present value (PV) tables: (Click the icon to view the present value factor table.) factor table.) Read the fequirements Requirement 1. You have always dreamed of taking a safari in Africa. What lump sum do you have to invest today to have the $18,000 needed for the trip in 4 years if you can invest the money at (a) 4%, compounded annually, (b) 10%, 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 4%, compounded annually. $ 15386 1. You have always dreamed of taking a safari in Africa. What lump sum do you have to invest today to have the $18,000 needed for the trip in 4 years? Assume that you can invest the money at a. 4%, compounded annually. b. 10%, 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 $15,000 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. 4%, compounded annually. b. 10%, 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 10 years. How much can you withdraw each year and have a zero balance left at the end of 10 years if you invest at a. 6%, compounded annually? b. 12%, compounded annually? 4. An NHL hockey player is offered the choice of two 4-year salary contracts, contract X for $2.4 million and contract Y for $2.32 million: Contract X Contract Y $ End of year 1 End of year 2 300,000 $ 400,000 550,000 420,000 650.000 End of vear 2 zon on Print Done Requirements - C. 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 $15,000 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. 4%, compounded annually. b. 10%, compounded annually. 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 10 years. How much can you withdraw each year and have a zero balance left at the end of 10 years if you invest at a. 6%, compounded annually? b. 12%, compounded annually? 4. An NHL hockey player is offered the choice of two 4-year salary contracts, contract X for $2.4 million and contract Y for $2.32 million: Contract X Contract Y 300,000 $ 550,000 th End of year 1 End of year 2 End of year 3 End of year 4 400,000 700,000 1,000,000 420,000 650,000 700,000 $ 2,400,000 $ 2,320,000 Total Which contract has the higher PV at 14% compounded annually? Show computations to support your answer. i Data Table - X Present Value of $1 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 .9426 .9246 .9070 .8900 8734 .8573 2. 3 .8264.7972 .7695 .7432 .7182 .6944 .9151 .8890 .8638 .8396 .8163 .7938 .7513 .7118 .6750 6407 .6086 5787 4 .8885 .8548 .7921 .7629 .7350 .6830 6355 5921 .5523 .5158 .4823 .8227 .7835 5 .8626 .8219 .7473 .7130 .6806 .6209 .5674 .5194 4761 4371 4019 6 .8375 .7903 .7462 .7050 .6663 .6302 5645 5066 .4556 4104 .3704 3349 7 .8131 .7599 .7107 .6651 .6227 .5835 5132 .4523 .3996 3538 .3139 2791 8 .7894 .7307 .6768 .6274 .5820 .5403 .4665 .4039 .3506 .3050 .2660 .2326 9 .7664 .7026 .6446 .5919 5439 .5002 .4241 .3606 3075 2630 .2255 .1938 10 .7441 .6756 .6139 .1911 .1615 15 .6419 .5553 .4810 .5584 5083 4632 .3855 3220 2697 2267 .4173 .3624 .3152 2394 .1827 .1401 .1079 .3118 2584 2145.1486 . 1037 .0728 .0514 .0835 0649 20 .5537 .4564 .3769 .0365 .0261 25 .4776 .3751 .2953 .2330 .1842 1460 .0923 .0588 0378 .0245 ..0160 0105 30 4120 .3083 .2314 .1741 .1314 .0994 .0573 0334 0196 .0116 .0070 .0042 Data Table - Present Value of Ordinary Annuity of $1 Period 3% 4% 5% 6% 7% 8% 10% 12% 14% 16% 18% 20% 1 .9709 .9615 9524 .9434 .9346 2 1.9135 1.8861 3 2.8286 2.7751 1.8594 1.8334 1.8080 2.7232. 2.6730 2.6243 3.5460 3.4651 3.3872 .9259 .9091 .8929 .8772 .8621 .8475 .8333 1.7833 1.7355 1.6901 1.6467 1.6052 1.5656 1.5278 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 3.9927 3.7908 3.6048 3.4331 3.2743 3.1272 2.9906 4.6229 4.3553 4.1114 3.8887 3.6847 3.4976 3.3255 4 3.7171 3.6299 5 4.5797 4.4518 4.3295 4.2124 4.1002 6 5.4172 5.2421 5.0757 4.9173 4.7665 7 6.2303 6.0021 5.7864 5.5824 5.3893 8 7.0197 6.7327 6.4632 6.2098 5.9713 5.2064 4.8684 4.5638 4.2883 4.0386 3.8115 3.6046 5.7466 5.3349 4.9676 4.6389 4.3436 4.0776 3.8372 6.2469 5.7590 5.3282 4.9464 4.6065 4.3030 4.0310 6.7101 6.1446 5.6502 5.2161 4.8332 4.4941 4.1925 9 7.7861 7.4353 7.1078 6.8017 6.5152 10 8.5302 8.1109 7.7217 7.3601 7.0236 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 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 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 19.6004 17.2920 15.3725 13.7648 12.4090 11.2578 9.4269 8.0552 7.0027 6.1772 5.5168 4.9789