While passing through Deadwood, SD you play a slot machine to pass a little time. Much to your surprise you win the Jackpot! The machine prints out a ticket. telling you to see the cashier for you winnings. The cashier informs you that your winnings are pretty large and that you must choose one of two options for receiving your winnings: Option 1:Receive $20,000 today. Option 2: Receive a payment of $4,000 each year for the next six years. Assume the current interest rate is 8%. Required (1) a) What is the present value of option 1 ? b) What is the present value of option 2? c) Which option will you choose? You have just accepted a new job in a new town. It seems that all the apartments close to your now job location require a two year contract and monthly rental payments. To compare options you decide to determine the present value of each contract you are interested in. Assuming the current APR is 12% answer the questions below. Required (2) d) What discount rate will you use in your present value calculations? e) What is the number of periods you will use in your calculation? After graduation you start working for a public accounting firm. You will begin your job on January 1 st. As part of the firm's compensation structure they offer a yearend bonus (paid December 31st) of $5,000 if you reach your work goals. The current market interest rate is 6%. Required (3) h) What is the present value of this bonus? B=Lyr=PV=PMT= Present Value $1 Lump Sum =FVN/(1+r)n FV= Future Value: n= number of periods: r= discount rate \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline Per & 1% & 2% & 3% & 4% & 5% & 6% & 7% & 8% & 9% & 10% & 11% & 12% & 13% & 14% & 15% & 16% & 17% & 18% & 19% & 20% \\ \hline 1 & 0.990 & 0.980 & 0.971 & 0.962 & 0.952 & 0.943 & 0.935 & 0.926 & 0.917 & 0.909 & 0.901 & 0.893 & 0.885 & 0.877 & 0.870 & 0.862 & 0.855 & 0.847 & 0.840 & 0.833 \\ \hline 2 & & & & 225 & 0.907 & 0.890 & 0.873 & 857 & 842 & 826 & & 797 & 0.783 & 0.769 & 0.756 & 0.743 & 0.731 & 0.718 & 0.706 & 0.694 \\ \hline 3 & 0 & 0.942 & 915 & .889 & 864 & 0.840 & 816 & 0.794 & 0.772 & 0.751 & 0.731 & 0.712 & 0.693 & 0.675 & 658 & .641 & 0.624 & 0.609 & 0.593 & 0.579 \\ \hline 4 & 761 & 0.924 & 0.888 & 0.855 & 0.823 & 0.792 & , & 0.735 & 0.708 & 0.683 & 0.659 & 0.636 & 613 & 0.592 & & 0.552 & 0.534 & 0.516 & 0.499 & 0.482 \\ \hline 5 & 95! & 0.906 & & & .78 & 0.747 & 713 & 0.681 & 0.650 & 0.621 & 0.593 & & & 0.519 & 0.497 & 0.476 & 0.456 & 0.437 & 0.419 & 0.402 \\ \hline 6 & & 88 & 0 & & 0.746 & 0.705 & 0.666 & 0.630 & 0.596 & 0564 & 535 & 0.507 & 0.480 & 0.456 & 0.432 & 2.410 & 0.390 & 0.370 & 0.352 & 0.335 \\ \hline & 133 & 0.871 & 13 & 0.760 & 71 & 0.665 & 0.623 & 0. & & 0.513 & 482 & 0.452 & 25 & 0.400 & 376 & 0.354 & 0.333 & 0.314 & 0.296 & 0.279 \\ \hline 8 & 0.923 & 0.8 & 0 & 0.731 & 0.677 & 0.627 & 62 & 0.540 & 02 & 0.467 & .434 & & & 351 & 0327 & 305 & 0.285 & 0.266 & 49 & 0.233 \\ \hline 9 & 0.914 & 0.837 & 0.7 & 0.703 & 0.645 & 0.592 & 544 & 0.50 & 2.460 & 0.424 & 391 & 361 & 0.333 & 308 & 0.284 & 263 & 243 & 0.225 & 209 & 0.194 \\ \hline I & 905 & 0.8 & 0.7 & 676 & 0.6 & 0.55 & 0.508 & 0.4 & 0.422 & 0.386 & 0.352 & 322 & 295 & 270 & 0247 & 0.227 & 0.208 & 0.191 & 0.176 & 0.162 \\ \hline 1 & & 0.804 & 0.72 & 650 & 0.585 & 0.52 & 0.475 & 0.429 & 88 & 0 & 317 & 77 & 0.261 & 237 & 0215 & 0.195 & 0.178 & 0.162 & 0.148 & 0.135 \\ \hline & & 0.788 & 0.701 & 0.625 & 0.557 & 0.49 & 0.4 & 0 & 0.356 & 0319 & 0.286 & 7 & 0.231 & 208 & 0187 & .168 & 0.152 & 0.137 & 0.124 & 0.112 \\ \hline 13 & 0 & 0.77 & 0.681 & 6 & & 0.4 & 0.415 & 0.368 & 0.326 & 0290 & 0.258 & 229 & 04 & 182 & 0.163 & 145 & 130 & 0.116 & 0.104 & 0.093 \\ \hline 14 & 0 & 0 & 0 & 0.577 & 0.505 & 0.442 & 0.388 & 0.340 & 0.299 & & 0232 & 0205 & 0.181 & 160 & 0.141 & 0.125 & 0.111 & 0.099 & 0.088 & 0.078 \\ \hline & & 0.743 & 0.642 & 0.55 & 0.481 & 0.4 & 0 & 5 & 0.275 & 239 & 0.209 & 183 & 0.160 & 140 & 123 & 108 & 0.095 & 0.084 & 0.074 & 0.065 \\ \hline 16 & 0.853 & 0.728 & 0.623 & 0 & & 0394 & 0.339 & 0.292 & 0.252 & 218 & 0.188 & 3 & & .123 & 0.107 & 0.093 & 0.081 & 0.071 & 0.062 & 0.054 \\ \hline 1 & & 0.7 & 0 & 0.513 & 0.43 & 0.371 & 0.317 & 0.27 & 231 & 88 & 170 & 0.146 & 0.125 & .108 & 0.093 & 080 & 069 & 50 & 0.052 & 0.045 \\ \hline I & 36 & 0.700 & 0.587 & 0.494 & 0.4 & 50 & 0.2 & 0.250 & 0.212 & 0.180 & 0.153 & .130 & 111 & & 0.081 & 2.069 & 0.059 & 0.051 & 0.044 & 0.035 \\ \hline 19 & 0.828 & 0.686 & 0.5 & 0.475 & 0.3 & 0.331 & 0.277 & 0.232 & 0.194 & 0 & 38 & 16 & 8 & 083 & 0.070 & 0.060 & 0.051 & 0.043 & 0.037 & 0.031 \\ \hline & & 0 & 0.5 & 0.456 & 0.377 & 0.312 & 0.258 & 15 & 0 & 0.149 & 0.124 & 0.104 & 0.087 & 0073 & 0061 & 051 & & 37 & 0.031 & 0.026 \\ \hline 2 & 0.811 & 0.660 & 0.538 & 0.439 & 0.359 & 29 & 0 & 0.199 & 0.164 & 0.135 & 0.112 & .093 & 077 & .064 & 053 & 0044 & 0.037 & 0.031 & 0.026 & 0.022 \\ \hline 2 & 0.803 & 0.647 & 0 & 0.422 & 0.342 & 0.278 & 0.226 & 0.184 & 0.150 & 123 & 0.101 & .083 & 0.068 & 0.056 & 0.046 & 0.038 & 0.032 & 0.026 & 0.022 & 0.018 \\ \hline 2 & 0.795 & 0.634 & 0.507 & 0.406 & 0326 & 0.262 & 0.2 & 0.170 & 0.138 & 0.112 & 0.091 & 0.074 & 0.060 & 2049 & 2040 & 0.033 & 2027 & 0.022 & 0.018 & 0.015 \\ \hline 2 & 0.788 & 0.622 & 0.492 & .39 & 0.310 & 0.247 & 0.197 & 0.158 & 0.126 & 0.102 & 082 & 066 & 053 & 0.043 & 0.035 & 0.028 & 0.023 & 0.019 & 0.015 & 0.013 \\ \hline 2 & 80 & 0.610 & 0.478 & 0.375 & 0.295 & 0.233 & 0.184 & 0.146 & .116 & 0.092 & 0.074 & 0.059 & 0.047 & 0.038 & 030 & 24 & 020 & 0.016 & 0.013 & 0.010 \\ \hline 26 & 0.772 & 0.598 & 0.464 & 0361 & 0.281 & 0.220 & 0.172 & 0.135 & 0.106 & 0.084 & .066 & 0.053 & 042 & 0.033 & 0.026 & 0.021 & 0.017 & 0.014 & 0.011 & 0.009 \\ \hline 27 & 0.764 & 0.586 & 0.450 & 0.347 & 0.268 & 0.207 & 0.161 & 0.125 & 0.098 & 0.076 & .060 & 0.047 & 0.037 & 0.029 & 0.023 & 0.018 & 0.014 & 0.011 & 0.009 & 0.007 \\ \hline 28 & 0.757 & 0.574 & 0.437 & 0.333 & 0.255 & 0.196 & 0.150 & 0.116 & 0.090 & 0.069 & 0.054 & 0.042 & 0.033 & 0.026 & .020 & 0.016 & 0.012 & 0.010 & 0.008 & 0.006 \\ \hline 29 & 0.749 & 0.563 & 0.424 & 0.321 & 0.243 & 0.185 & 0.141 & 0.107 & 0.082 & 0.063 & 0.048 & 0.037 & 0.029 & 0.022 & 0.017 & 0.014 & 0.011 & 0.008 & 0.006 & 0.005 \\ \hline & 0.742 & 0552 & 0.412 & 0.308 & 0.231 & 0.174 & 0.131 & 0.099 & 0.075 & 0.057 & 0.044 & 0.033 & 0.026 & 0.020 & 2015 & 0.012 & 0.009 & 0.007 & 0.005 & 0.004 \\ \hline 3 & 0.735 & 0541 & 0.400 & 0.296 & 0.220 & 0.164 & 0.123 & 0.092 & 0.069 & 0.052 & 0.039 & 030 & 0.023 & 0.017 & 0.013 & 0.010 & 0.008 & 0.006 & 0.005 & 0.004 \\ \hline & 0.727 & 0.531 & 0388 & 0.285 & 0.210 & 155 & 0.115 & 0.085 & 0.063 & 0.047 & 0.035 & 0.027 & 0.020 & 0.015 & 0.011 & 0.009 & 0.007 & 0.005 & 0.004 & 0.003 \\ \hline \end{tabular} Present Value of an ordinary annuity of $1=1/r{Pmt[Pmt/(1+r)h]} Pmt = series of cash flows: n= number of periods: t= discount rate \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline Periods & 1% & 2% & 3% & 4% & 5% & 6% & 7% & 8% & 9% & 10% & 1% & 2% & 13% & 14% & 15% & 16% & 17% & 18% & 19% & 20% \\ \hline 1 & 0.990 & 0.980 & 0.971 & 0.962 & 0.952 & 0.943 & 935 & 0.926 & 0.917 & 0.909 & 901 & 899 & & 0.877 & 0.870 & 0.862 & 0.855 & 0.847 & 0.840 & 0.833 \\ \hline 2 & 1970 & 1.942 & 1.913 & 1.886 & 1.859 & & 808 & 1.783 & 759 & 1.736 & 713 & 1.690 & 1.668 & 1.647 & 1.626 & .605 & 585 & 866 & .547 & 528 \\ \hline 3 & 2.941 & 2.884 & 28.29 & 2775 & 2.723 & 2.673 & 2.624 & 2.577 & 2531 & 2.487 & 444 & 2.402 & & 2.322 & 2.283 & 246 & 210 & 2.174 & 2.140 & 2.106 \\ \hline 4 & 902 & 3.808 & 3.717 & 3.630 & 3.546 & 3.465 & 387 & 12 & 240 & 170 & 02 & 037 & & 914 & 2.855 & .798 & 2.743 & 2.690 & 2.639 & 2589 \\ \hline 5 & 853 & 713 & 4.580 & 452 & 4.329 & 4.212 & .100 & 3.993 & .890 & 3.791 & 3.696 & 3.605 & 3.517 & 3.433 & 3.352 & 274 & 199 & 127 & 3.058 & 2.991 \\ \hline 6 & 795 & 5.601 & .5 .417 & 5.242 & 5.076 & 4.917 & 4.767 & 4.623 & 4.486 & 4355 & 231 & 4.111 & 3.998 & 3.889 & & & & & 3.410 & 3.326 \\ \hline & 28 & 6.472 & 6.230 & 6.002 & 5.786 & 22 & 389 & 206 & 5.0 & & & 564 & & 4.288 & 60 & 4.039 & & 3.812 & 3.706 & 3.605 \\ \hline 8 & 652 & 7.325 & 7.020 & 6.733 & 6.463 & 210 & 971 & .747 & 535 & 135 & 46 & 968 & & 539 & 87 & 344 & & .078 & 854 & 2837 \\ \hline 9 & 866 & 8.162 & 786 & 7.435 & 7.108 & 02 & & 247 & 995 & 759 & 5.537 & 328 & 32 & 46 & & 4.607 & 51 & 03 & 4.163 & .031 \\ \hline 10 & & 8 & & 8.111 & 7. & 50 & 124 & 10 & 6.418 & 6.145 & 89 & 650 & 5.426 & 216 & 19 & 833 & 59 & 94 & 4 & 4.192 \\ \hline 1 & 1 & 9.787 & 53 & 8.760 & 8.306 & 7.887 & 499 & 139 & 05 & 95 & 97 & 938 & & 53 & & 029 & 36 & 4.656 & 486 & 4327 \\ \hline 1 & & & 9.954 & 35 & 8.863 & 84 & 7.943 & 536 & 7.161 & 14 & 6.492 & 6.194 & 5.918 & 5.660 & 5.421 & 5.197 & 88 & 4.793 & 4.611 & 4.439 \\ \hline 13 & & 48 & 10.635 & 986 & 93 & 53 & 8.358 & 904 & 487 & 103 & & 424 & & 42 & & 42 & & 10 & & 533 \\ \hline 1 & & 106 & 11.296 & 10.563 & 9 & & & & & & & 628 & & 002 & 5.7 & 5.468 & 29 & 5.008 & 4.802 & 4.611 \\ \hline & & & & .118 & 10 & 112 & 9.108 & 8.559 & 8.061 & 9.606 & 7.191 & .811 & 6.462 & 142 & 5.8 & 775 & 24 & 5.092 & 76 & 4.675 \\ \hline 16 & 18 & 13.578 & 12.561 & 11.652 & 10.838 & 10.106 & 9.447 & 851 & s & 24 & & & & & & & & & & 4.730 \\ \hline & & 14 & & & & & 9.763 & 9.122 & 8.544 & 8.022 & 7.549 & 7.120 & 6.729 & 6.373 & 6. & 5.749 & 5.475 & 5222 & 4990 & 4.775 \\ \hline 1 & & 92 & 54 & 12659 & 11.690 & 10.828 & 10.059 & 9.372 & 8.756 & 8.201 & 102 & 250 & 40 & 67 & & & & & & 12 \\ \hline 1 & 226 & 15.678 & 14.324 & 13.134 & & & & & & 65 & 39 & 7.366 & 6 & 6.550 & 6 & 77 & 5. & 5,316 & 5.070 & 4.843 \\ \hline & & & & 13.590 & 12.462 & 11.470 & 10.594 & 9.818 & 9.129 & 8514 & 7.963 & 7.469 & 7.025 & 623 & 6.2 & 29 & 5.628 & 53 & 5.101 & 4.870 \\ \hline 2 & & 17.011 & 15.415 & 14.029 & 12.821 & 11.764 & 10.836 & 10.017 & 9 & & 075 & 7562 & 7. & 87 & 6. & 5. & 5.6 & 84 & 5.1 & 4.891 \\ \hline & 660 & 17.658 & & & 13.163 & 12.042 & 61 & 10.201 & 9.442 & 8.772 & 8.176 & 7.645 & 7.170 & 6.743 & 6.359 & 6.011 & 5.696 & 5.410 & 5.149 & 4909 \\ \hline 23 & & 18.292 & 16.444 & 14.857 & 13.489 & 12.303 & 11.272 & 10.371 & 9.580 & 883 & 8 & 718 & 30 & 792 & 6. & 44 & & 5.432 & 5.167 & 4.925 \\ \hline 24 & 243 & 18.914 & 16.936 & 15247 & & 50 & 469 & 10.529 & 9.707 & 8.985 & 8.348 & 7.784 & 7.283 & 6.835 & 6.434 & 6.073 & 5.746 & 5.451 & 5.182 & 4.937 \\ \hline & .023 & 19.523 & 17.413 & 15.622 & 14.094 & 12.783 & 11.654 & 10.675 & 9.823 & 9.077 & 8.422 & 7843 & 7.330 & 873 & 6.464 & 6.097 & 5,766 & 67 & 5.195 & 4948 \\ \hline 26 & 795 & 520.121 & 17.877 & 15.983 & 14.375 & 13.003 & 11.826 & 10.810 & 9.929 & 9.161 & 8.488 & 7.896 & 7.372 & 6.906 & 6.491 & 6.118 & 5.783 & 5.480 & 5.206 & 4.956 \\ \hline & 560 & 707 & 18.327 & 16.330 & 14.643 & 13.211 & 11.987 & 10.935 & 10.027 & 9.237 & 8.548 & 7.943 & 7,409 & 6.935 & 6.514 & 6.136 & 5,798 & 5.492 & 5.215 & 4.964 \\ \hline 2 & & 321.281 & 18.764 & 16.663 & 14.898 & 13.406 & 12.137 & 11.051 & 10.116 & 9307 & 8.602 & 7984 & 7.441 & 6.961 & 6.534 & 6.152 & 5.810 & 5.502 & 5223 & 4970 \\ \hline & & 5. 21.844 & 19.188 & 16984 & 15,141 & 13.591 & 12.278 & 11.158 & 10.198 & 9.370 & 8.650 & 8.022 & 7.470 & 6.983 & 6.551 & 6.166 & 5.820 & 5510 & 5,229 & 4.975 \\ \hline 3 & 25,808 & 8. 22.396 & 19.600 & 17.292 & 15,372 & 13.765 & 12.409 & 11.258 & 10.274 & 9.427 & 8.694 & 8.055 & 7.496 & 7.003 & 6.566 & 6.177 & 5.829 & 5.517 & 5235 & 4979 \\ \hline & & 222.938 & 20.000 & 17.588 & 15.593 & 13.929 & 12532 & 11.350 & 10.343 & 9.479 & 8.733 & 8.055 & 7.518 & 7.020 & & & & 5.523 & 5.239 & 4982 \\ \hline 32 & 27.270 & 0:23,468 & 20.389 & 17.874 & 15.803 & 14.084 & 12.647 & 11.435 & 10.406 & 9.526 & 8.769 & 8.112 & 7.538 & 7.035 & 6.591 & 6.196 & 5.844 & 5.528 & 5.243 & 4.985 \\ \hline \end{tabular}