You plan to retire at age 40 after a highly successful but short career. You would like to accumulate enough money by age 40 to withdraw $228,000 per year for 40 years. You plan to pay into your account 15 equal installments beginning when you are 25 and ending when you are 39. Your account bears interest of 12 percent per year. Use Appendix A for your reference. (Use appropriate factor(s) from the tables provided.) Required: 1. How much do you need to accumulate in your account by the time you retire? (Round your final answer to the nearest dollar amount.) 2. How much do you need to pay into your account in each of the 15 equal installments? (Round your final answer to 2 decimal places.) 1. Amount to be accumulated in your account 2. Annual installment Future Value and Present Value Tables Table I Future Value of $1.00(1 + " Period 4% 6% 8% 10% 12% 14% 20% 1 2 1.040 1.082 1.125 1.170 1.217 3 1.060 1.124 1.191 1.263 1.338 1.080 1.166 1.260 1.100 1.210 1.331 1.464 1.611 1.120 1.254 1.405 1.574 1.762 1.140 1.300 1.482 1.689 1.925 1.200 1.440 1.728 2.074 2.488 4 1.361 5 1.469 6 7 8 1.266 1.316 1.369 1.423 1.480 1.419 1.504 1.594 1.690 1.791 1.772 1.949 2.144 2.359 2.594 2.195 2.502 2.853 3.252 3.707 9 10 1.587 1.714 1.851 1.999 2.159 2.332 2.518 2.720 2.937 3.172 1.974 2.211 2.476 2.773 3.106 3.479 3.896 4.364 4.887 5.474 2.986 3.583 4.300 5.160 6.192 7.430 8.916 10.699 12.839 15.407 11 12 13 14 15 1.540 1.601 1.665 1.732 1.801 1.898 2.012 2.133 2.261 2.397 2.853 3.139 3.452 3.798 4.177 4.226 4.818 5.492 6.261 7.138 20 30 40 2.191 3.243 4.801 3.207 5.744 10.286 4.661 10.063 21.725 6.728 17.450 45.260 9.646 29.960 93.051 13.743 50.950 188.880 38.338 237.380 1,469.800 Period 4% 6% 8% 10% 12% 14% 20% 1 Table II Future Value of a Series of $1.00 Cash Flows (Ordinary Annuity) (1 + 1" - 1 r 2 3 1.000 2.040 3.122 4.247 5.416 1.000 2.060 3.184 4.375 5.637 1.000 2.080 3.246 4.506 5.867 1.000 2.120 3.374 4.779 6.353 1.000 2.140 3.440 4.921 6.610 1.000 2.220 3.640 5.368 7.442 4 5 6 7 8 6.633 7.898 9.214 10.583 12.006 6.975 8.394 9.898 11.491 13.181 7.336 8.923 10.637 12.488 14.487 1.000 2.100 3.310 4.641 6.105 7.716 9.487 11.436 13.580 15.938 18.531 21.385 24.523 27.976 31.773 8.115 10.089 12.300 14.776 17.549 9 10 9.930 12.916 16.499 20.799 25.969 32.150 39.580 48.497 59.196 72.035 11 12 13 14 15 13.486 15.026 16.627 18.292 20.024 14.972 16.870 18.882 21.015 23.276 16.646 18.977 21.495 24.215 27.152 45.762 113.283 259.057 8.536 10.730 13.233 16.085 19.337 23.045 27.271 32.089 37.581 43.842 91.025 356.790 1,342.000 20.655 24.133 28.029 32.393 37.280 20 30 29.778 56.085 96.026 36.778 79.058 154.762 57.276 164.496 442.597 75.052 241.330 767.090 186.690 1,181.900 7,343.900 40 Table III Present Value of $1.00 1 (1 + )" Period 40% 6% 8% 100% 12% 14% 16% 18% 20% 220% 24% 26% 28% 30% 32% 909 1 820 769 1826 672 592 2 3 962 1925 889 855 .822 926 857 .794 735 ,681 877 769 1.675 1.592 862 743 1641 552 476 833 694 579 1482 .806 650 .524 423 ,751 683 551 1451 1455 350 758 574 435 329 250 4 943 890 840 ,792 1747 705 665 627 592 558 794 -630 500 397 315 1250) 198 157 5 893 797 712 ,636 567 1507 452 404 361 322 6 7 621 564 1513 1,467 1424 386 ,790 760 731. 703 676 519 456 400 351 1308 270 ,630 .583 540 500 463 781 610 1477 373 .291 1.227 178 .139 .108 085 402 335 279 233 194 162 1410 354 305 263 227 370 303 249 .204 167 137 847 718 609. 516 1437 370 314 .266 .225 .191 .162 .137 116 ,099 1084 .037 1007 341 .275 1222 179 144 .116 8 269. .207 .159 123 ,094 073 189 143 108 9 125 -082 10 099 1062 11 1527 429 350 237 1079 047 ,650 625 287 257 195 168 112 ,092 ,056 043 1497 601 12 13 14 15 075 469 1442 417 397 368 340 1315 215 319 .200 263 239 149 ,057 022 208 .182 160 140 229 .205 183 1.135 112. 1093 1078 1,065 145 125 .108 577 555 1,456 1084 ,076 1.061 ,049 .040 062 10501 1039 031 ,066 ,052 1040 ,032 ,025 036 027 1021 016 033 025 020 -005 ,062 051 312 104 1,073 1051 1026 1019 014 010 ,004 20 30 40 ,007 ,001 012 1004 1003 .002 001 308 .208 174 097 1099 046 033 011 ,020 1005 003 ,001 1001 Table IV Present Value of Series of $1.00 Cash Flows 1 (1 + )) - dia) Period 4% 6% % 10% 12% 14% 16% 18% 20% 22% 24% 25% 26% 26% 30% 1 0.862 2 3 0.909 1.736 2.487 3.170 3.79] 4.355 4. BBS 5.335 1.605 2.246 2.798 3274 4 0.820 1.492 2.042 2.494 2.864 3.167 3.416 0.769 1.36] 1.816 2.16 2.436 0.781 1.392 1.68 2.241 2.532 2. 759 2.37 3.076 5 6 - 8 3.619 0.962 1996 2.775 3.830 4.452 5.242 6.002 6.733 7.435 8. 111 8.760 9.385 9.386 10.563 11118 13.590 17.292 19.793 9 0.943 1833 2.673 3.466 4.212 4.917 5.582 6.210 6.802 7.360 7.887 8.384 8.853 9.295 9712 11.470 13.766 15.046 0.806 1.57 1.81 2.404 2.745 3.020 3.242 3.421 3.566 3.82 0926 1783 2.577 3.312 3.993 4.623 5.206 5.747 6.247 6.710 7139 7.536 7.904 8.24 8.559 9.818 11.258 11.925 0.883 1.690 2.402 3.037 3.65 4.111 4.564 4.968 5.328 5.650 5.9388 6.194 6.424 6.628 6.811 7.48 8.05 8.244 5. 759 6.145 0.877 1.647 2.322 2.914 3.433 3.889 4.288 4.639 4.946 5.216 5.453 5.660 5.842 6.002 6.142 6.623 7.003 7.105 0.847 1566 2.174 2.690 3.127 3.498 3.812 4.078 4.303 4.494 4.656 4.793 4.910 5.008 5.092 5.353 5.517 5.548 0.833 1.528 2.106 2.589 2.991 3.326 3.605 3.837 4.031 4.192 4.327 4.439 4.533 4.611 4.675 4.870 4.979 4.997 3.786 3.923 0.800 1.440 1.52 2.362 2.689 2.51 3.161 3.329 3.463 3.571 3.66 3.725 3.780 3.824 3.859 3.54 3.995 3.999 0.74 1.424 1.23 2.320 2.635 2.885 3.083 3.241 3.366 3.465 3.54 3.06 3.66 3.685 3.726 3.808 3.842 3.846 3.184 3.269 3. 686 4.039 4.34 4.607 4.833 5.029 5.197 5.342 5.468 5.575 5.929 6.177 6.234 10 11 12 6.45 6.814 7.103 7.367 7.606 8.514 9427 9.79 13 14 4.035 4.127 4.203 4.265 4.315 4.460 4.534 4.544 3.776 3.851 3.12 3.962 4.001 4.110 4. 160 4. 166 2.643 2.802 2.925 3.019 3.092 3.147 3.190 3.223 3.249 3.268 3.316 3.332 3.333 3.335 3.397 3.427 3.459 3.483 3.546 3.569 3.571 15 20 30 0 You plan to retire at age 40 after a highly successful but short career. You would like to accumulate enough money by age 40 to withdraw $228,000 per year for 40 years. You plan to pay into your account 15 equal installments beginning when you are 25 and ending when you are 39. Your account bears interest of 12 percent per year. Use Appendix A for your reference. (Use appropriate factor(s) from the tables provided.) Required: 1. How much do you need to accumulate in your account by the time you retire? (Round your final answer to the nearest dollar amount.) 2. How much do you need to pay into your account in each of the 15 equal installments? (Round your final answer to 2 decimal places.) 1. Amount to be accumulated in your account 2. Annual installment Future Value and Present Value Tables Table I Future Value of $1.00(1 + " Period 4% 6% 8% 10% 12% 14% 20% 1 2 1.040 1.082 1.125 1.170 1.217 3 1.060 1.124 1.191 1.263 1.338 1.080 1.166 1.260 1.100 1.210 1.331 1.464 1.611 1.120 1.254 1.405 1.574 1.762 1.140 1.300 1.482 1.689 1.925 1.200 1.440 1.728 2.074 2.488 4 1.361 5 1.469 6 7 8 1.266 1.316 1.369 1.423 1.480 1.419 1.504 1.594 1.690 1.791 1.772 1.949 2.144 2.359 2.594 2.195 2.502 2.853 3.252 3.707 9 10 1.587 1.714 1.851 1.999 2.159 2.332 2.518 2.720 2.937 3.172 1.974 2.211 2.476 2.773 3.106 3.479 3.896 4.364 4.887 5.474 2.986 3.583 4.300 5.160 6.192 7.430 8.916 10.699 12.839 15.407 11 12 13 14 15 1.540 1.601 1.665 1.732 1.801 1.898 2.012 2.133 2.261 2.397 2.853 3.139 3.452 3.798 4.177 4.226 4.818 5.492 6.261 7.138 20 30 40 2.191 3.243 4.801 3.207 5.744 10.286 4.661 10.063 21.725 6.728 17.450 45.260 9.646 29.960 93.051 13.743 50.950 188.880 38.338 237.380 1,469.800 Period 4% 6% 8% 10% 12% 14% 20% 1 Table II Future Value of a Series of $1.00 Cash Flows (Ordinary Annuity) (1 + 1" - 1 r 2 3 1.000 2.040 3.122 4.247 5.416 1.000 2.060 3.184 4.375 5.637 1.000 2.080 3.246 4.506 5.867 1.000 2.120 3.374 4.779 6.353 1.000 2.140 3.440 4.921 6.610 1.000 2.220 3.640 5.368 7.442 4 5 6 7 8 6.633 7.898 9.214 10.583 12.006 6.975 8.394 9.898 11.491 13.181 7.336 8.923 10.637 12.488 14.487 1.000 2.100 3.310 4.641 6.105 7.716 9.487 11.436 13.580 15.938 18.531 21.385 24.523 27.976 31.773 8.115 10.089 12.300 14.776 17.549 9 10 9.930 12.916 16.499 20.799 25.969 32.150 39.580 48.497 59.196 72.035 11 12 13 14 15 13.486 15.026 16.627 18.292 20.024 14.972 16.870 18.882 21.015 23.276 16.646 18.977 21.495 24.215 27.152 45.762 113.283 259.057 8.536 10.730 13.233 16.085 19.337 23.045 27.271 32.089 37.581 43.842 91.025 356.790 1,342.000 20.655 24.133 28.029 32.393 37.280 20 30 29.778 56.085 96.026 36.778 79.058 154.762 57.276 164.496 442.597 75.052 241.330 767.090 186.690 1,181.900 7,343.900 40 Table III Present Value of $1.00 1 (1 + )" Period 40% 6% 8% 100% 12% 14% 16% 18% 20% 220% 24% 26% 28% 30% 32% 909 1 820 769 1826 672 592 2 3 962 1925 889 855 .822 926 857 .794 735 ,681 877 769 1.675 1.592 862 743 1641 552 476 833 694 579 1482 .806 650 .524 423 ,751 683 551 1451 1455 350 758 574 435 329 250 4 943 890 840 ,792 1747 705 665 627 592 558 794 -630 500 397 315 1250) 198 157 5 893 797 712 ,636 567 1507 452 404 361 322 6 7 621 564 1513 1,467 1424 386 ,790 760 731. 703 676 519 456 400 351 1308 270 ,630 .583 540 500 463 781 610 1477 373 .291 1.227 178 .139 .108 085 402 335 279 233 194 162 1410 354 305 263 227 370 303 249 .204 167 137 847 718 609. 516 1437 370 314 .266 .225 .191 .162 .137 116 ,099 1084 .037 1007 341 .275 1222 179 144 .116 8 269. .207 .159 123 ,094 073 189 143 108 9 125 -082 10 099 1062 11 1527 429 350 237 1079 047 ,650 625 287 257 195 168 112 ,092 ,056 043 1497 601 12 13 14 15 075 469 1442 417 397 368 340 1315 215 319 .200 263 239 149 ,057 022 208 .182 160 140 229 .205 183 1.135 112. 1093 1078 1,065 145 125 .108 577 555 1,456 1084 ,076 1.061 ,049 .040 062 10501 1039 031 ,066 ,052 1040 ,032 ,025 036 027 1021 016 033 025 020 -005 ,062 051 312 104 1,073 1051 1026 1019 014 010 ,004 20 30 40 ,007 ,001 012 1004 1003 .002 001 308 .208 174 097 1099 046 033 011 ,020 1005 003 ,001 1001 Table IV Present Value of Series of $1.00 Cash Flows 1 (1 + )) - dia) Period 4% 6% % 10% 12% 14% 16% 18% 20% 22% 24% 25% 26% 26% 30% 1 0.862 2 3 0.909 1.736 2.487 3.170 3.79] 4.355 4. BBS 5.335 1.605 2.246 2.798 3274 4 0.820 1.492 2.042 2.494 2.864 3.167 3.416 0.769 1.36] 1.816 2.16 2.436 0.781 1.392 1.68 2.241 2.532 2. 759 2.37 3.076 5 6 - 8 3.619 0.962 1996 2.775 3.830 4.452 5.242 6.002 6.733 7.435 8. 111 8.760 9.385 9.386 10.563 11118 13.590 17.292 19.793 9 0.943 1833 2.673 3.466 4.212 4.917 5.582 6.210 6.802 7.360 7.887 8.384 8.853 9.295 9712 11.470 13.766 15.046 0.806 1.57 1.81 2.404 2.745 3.020 3.242 3.421 3.566 3.82 0926 1783 2.577 3.312 3.993 4.623 5.206 5.747 6.247 6.710 7139 7.536 7.904 8.24 8.559 9.818 11.258 11.925 0.883 1.690 2.402 3.037 3.65 4.111 4.564 4.968 5.328 5.650 5.9388 6.194 6.424 6.628 6.811 7.48 8.05 8.244 5. 759 6.145 0.877 1.647 2.322 2.914 3.433 3.889 4.288 4.639 4.946 5.216 5.453 5.660 5.842 6.002 6.142 6.623 7.003 7.105 0.847 1566 2.174 2.690 3.127 3.498 3.812 4.078 4.303 4.494 4.656 4.793 4.910 5.008 5.092 5.353 5.517 5.548 0.833 1.528 2.106 2.589 2.991 3.326 3.605 3.837 4.031 4.192 4.327 4.439 4.533 4.611 4.675 4.870 4.979 4.997 3.786 3.923 0.800 1.440 1.52 2.362 2.689 2.51 3.161 3.329 3.463 3.571 3.66 3.725 3.780 3.824 3.859 3.54 3.995 3.999 0.74 1.424 1.23 2.320 2.635 2.885 3.083 3.241 3.366 3.465 3.54 3.06 3.66 3.685 3.726 3.808 3.842 3.846 3.184 3.269 3. 686 4.039 4.34 4.607 4.833 5.029 5.197 5.342 5.468 5.575 5.929 6.177 6.234 10 11 12 6.45 6.814 7.103 7.367 7.606 8.514 9427 9.79 13 14 4.035 4.127 4.203 4.265 4.315 4.460 4.534 4.544 3.776 3.851 3.12 3.962 4.001 4.110 4. 160 4. 166 2.643 2.802 2.925 3.019 3.092 3.147 3.190 3.223 3.249 3.268 3.316 3.332 3.333 3.335 3.397 3.427 3.459 3.483 3.546 3.569 3.571 15 20 30 0
