Julie has just retired. Her company’s retirement program has two options as to how retirement benefits can be received. Under the first option, Julie would receive a lump sum of $138,000 immediately as her full retirement benefit. Under the second option, she would receive $25,000 each year for 6 years plus a lump-sum payment of $57,000 at the end of the 6-year period.

Click here to view Exhibit 12B-1 and Exhibit 12B-2, to determine the appropriate discount factor(s) using tables.

Required:

1-a. Calculate the present value for the following assuming that the money can be invested at 12%.

1-b. If she can invest money at 12%, which option would you recommend that she accept?
Transcribed Image Text:EXHIBIT 12B-2 Present Value of an Annuity of $1 in Arrears; 1/r(1-(1/(1+r)^n)) Periods 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 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 0.826 | 0.820 0.813 0.806 0.800 1.886 1.859 2.775 | 2.723 3.630 | 3.546 | 3.465 | 3.387 3.312 | 3.240 3.170 3.102 | 3.037 2.974 2.914 | 2.855 2.798 2.743 2.690 2.639 | 2.589 | 2.540 | 2.494 2.448 2.404 2.362 4.452 4.329 4.212 | 4.100 | 3.993| 3.890 | 3.791 | 3.696 3.605 3.517 3.433 3.352 3.274 3.199 3.127 3.058 | 2.991 | 2.926| 2.864 2.803 2.745 2.689 5.242 5.076 4.917 6.002 5.786 5.582 | 5.389 | 5.206 | 5.033 | 4.868 | 4.712 | 4.564 | 4.423 4.288 4.160 4.039 | 3.922 | 3.812 | 3.706 | 3.605 3.508 | 3.416 | 3.327 | 3.242 | 3.161 6.733 6.463 6.210 5.971 | 5.747 5.535 | 5.335 5.146 4.968 4.799 4.639 4.487 4.344 4.207 4.078 3.954| 3.837 3.726 | 3.619 3.518 3.421 3.329 7.435 7.108 6.802 6.515 6.247| 5.995 5.759 5.537 5.328 5.132 4.946 4.772| 4.607 4.451 | 4.303 4.163 4.031 3.905 3.786 3.673| 3.566 3.463 8.111 8.760 8.306 | 7.887 9.385 8.863 | 8.384 9.986 9.394 8.853 8.358 | 7.904| 7.487 10.563 9.899 9.295 11.118 10.380 9.712 | 9.108 8.559 | 8.061 | 7.606| 7.191 6.811 | 6.462 6.142 5.847 5.575 5.324 5.092 4.876 4.675 4.489 4.315 4.153 4.001 | 3.859 11.652 10.838 10.106 9.447 8.851 | 8.313| 7.824 7.379 6.974| 6.604 6.265 5.954 5.668 5.405 5.162 | 4.938 4.730 4.536 4.357 4.189 | 4.033 3.887 12.166 11.274 10.477 9.763 9.122 | 8.544 8.022 7.549 7.120 | 6.729 6.373 6.047 5.749 5.475 5.222 4.990 4.775 4.576 4.391 | 4.219 | 4.059 3.910 12.659 11.690 10.828 10.059 9.372 | 8.756 8.201 7.702 7.250 | 6.840 6.467 13.134 12.085 11.158 10.336 9.604| 8.950 8.365 7.839 7.366 | 6.938 6.550 6.198 5.877 5.584 5.316 | 5.070 4.843 4.635 4.442 4.263 4.097| 3.942 13.590 12.462 11.470 10.594 9.818 | 9.129 8.514 | 7.963| 7.469| 7.025 6.623 | 6.259 | 5.929 | 5.628 | 5.353 | 5.101 4.870 4.657 4.460 | 4.279 | 4.110 | 3.954 14.029 12.821 11.764 10.836 10.017 9.292 8.649 8.075 7.562| 7.102 6.687 14.451 13.163 12.042 11.061 10.201 9.442 8.772 8.176 14.857 13.489 12.303 11.272 10.371 9.580 8.883 8.266 | 7.718| 7.230 6.792 6.399 6.044 5.723 5.432 5.167 4.925 4.703 4.499 4.311 | 4.137 3.976 15.247 13.799 12.550 11.469 10.529 9.707 15.622 14.094 12.783 11.654 10.675 9.823 9.077 8.422 7.843 7.330 6.873 6.464 6.097 5.766 5.467 5.195 4.948 4.721 | 4.514 4.323 4.147 3.985 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 | 4.728 4.520 | 4.328 | 4.151 | 3.988 16.330 14.643 13.211 | 11.987 10.935 10.027 9.237 | 8.548 16.663 14.898 13.406 12.137 11.051 10.116 9.307 8.602 |16.984 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 5.510 5.229 4.975 4.743 4.531 4.337 4.159 3.994 17.25 19.793 17.159 15.046 13.332 11.925 10.757 9.779 8.951 8.244 7.634 7.105 6.642 6.233 5.871 5.548 5.258 4.997 4.760 4.544 4.347 4.166 3.999 1 1.833 2.673 1.808 1.783 1.759| 1.736 | 1.713 | 1.690 1.668 2.624 2.577 2.531 | 2.487 2.444 2.402 2.361 2.322 2.283 2.246 | 2.210 2.174 2.140 2.106 2.074 2.042 2.011 | 1.981 | 1.952 1.626| 1.605 1.585 | 1.566 1.547 | 1.528 1.509 | 1.492 | 1.474 1.457 1.440 1.647 3 4 4.767 4.623 4.486 4.355 4.231 | 4.111| 3.998 | 3.889 3.784 3.685 | 3.589 3.498 | 3.410 3.326 3.245 3.167| 3.092 3.020 | 2.951 7 9 7.722 7.360 7.024 6.710 6.418 | 6.145 | 5.889 | 5.650 5.426 | 5.216 5.019 4.833 | 4.659 | 4.494 4.339 | 4.192 | 4.054 | 3.923 | 3.799 3.682 | 3.571 7.499 | 7.139 6.805 | 6.495 6.207 | 5.938 5.687 5.453 5.234 5.029 4.836 | 4.656 | 4.486 4.327 4.177 4.035 | 3.902 | 3.776 | 3.656 7.536| 7.161 | 6.814 6.492 6.194| 5.918 5.660 5.421 5.197 4.988 | 4.793 4.611 4.439 4.278 4.127 3.985 | 3.851 3.725 7.103 6.750 6.424 6.122 5.842 | 5.583 5.342 5.118 | 4.910 4.715 | 4.533 4.362 | 4.203 4.053 | 3.912 3.780 4.432 4.265 4.108 | 3.962 3.824 10 11 12 7.943 13 14 8.745 8.244 | 7.786 | 7.367 | 6.982 | 6.628 | 6.302 6.002 5.724 5.468 | 5.229 5.008 4.802 4.611 15 16 17 18 6.128 5.818 5.534 5.273 5.033 4.812 4.608 4.419 4.243 4.080 3.928 19 20 6.312 5.973 5.665| 5.384 5.127 4.891 | 4.675 4.476 4.292 4.121 | 3.963 7.645 7.170 6.743 | 6.359 | 6.011 5.696| 5.410 5.149 4.909 | 4.690 | 4.488 4.302 | 4.130 3.970 21 22 23 24 8.985 8.348 7.784| 7.283 6.835 | 6.434 6.073 | 5.746 5.451 5.182 | 4.937 4.713| 4.507 | 4.318 | 4.143 | 3.981 25 26 7.943 7.409 6.935 | 6.514 | 6.136 5.798 5.492 5.215 | 4.964 | 4.734 | 4.524 4.332 | 4.154 | 3.990 7.984 | 7.441 27 28 6.961 6.534 6.152 5.810 5.502 5.223 | 4.970 4.739 4.528 4.335 4.157 3.992 29 30 13.765 12.409 11.258 10.274 9.427 8.694 | 8.055 7.496 7.003 6.566 6.177 5.829 79 4.746 4.534 4.339 4.160 | 3.995 40
Transcribed Image Text:EXHIBIT 12B-1 Present Value of $1; 1 (1+r)n 17% 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 0.925 | 0.907 0.890 0.873 0.857 0.842 0.826 | 0.812 0.797 |0.783 0.769 | 0.756 | 0.743 | 0.731 13% 16% 18% 21% 22% 24% 0.820 0.813 0.806 | 0.800 Periods 4% 5% 6% 7% 9% 10% 11% 12% 14% 15% 19% 20% 23% 25% 1 0.847 | 0.840 0.833 0.826 0.718 0.706 0.694 0.683 0.672 0.661 0.650 0.640 3 0.889 0.864 0.840 0.816 0.794 0.772 0.751 0.731 | 0.712 | 0.693 0.675 0.658 | 0.641 | 0.624 0.609 0.593 | 0.579 0.564 0.551 0.537 | 0.524 0.512 0.592 0.572 0.552 0.534 0.519 0.497 0.476 | 0.456 0.790 0.746 0.705 0.666 0.630 0.596 0.564 0.535 | 0.507 0.480 0.456 | 0.432 0.410 0.390 0.792 0.763 0.735 0.708 0.683 0.659 0.636 0.613 0.423 0.410 0.855 | 0.823 0.822 0.784 0.747 0.713 0.681 0.650 0.621 | 0.593 | 0.567 0.543 0.516 | 0.499| 0.482 0.437 0.419 0.402 0.386 0.370 0.355 0.341 0.328 0.370 0.352 0.335 0.319 0.303 0.289 0.275 0.262 4 0.467 0.451 | 0.437 5 6. 7 0.760 0.711 0.665 | 0.623 0.583 0.547 0.513 | 0.482 | 0.452 0.425 | 0.400 0.376 | 0.354 0.333 |0.314 | 0.296 | 0.279 |0.263 | 0.249 0.235 | 0.222 | 0.210 0.731 0.677 0.627 | 0.582 0.540 0.502 0.467 | 0.434 0.703 0.645 0.592 | 0.544 0.500 0.460 0.424 0.391 0.404 0.376 0.351 | 0.327 0.305 0.285 0.266 | 0.249 0.225 | 0.209 0.233 0.218 0.204 |0.191 0.179 0.168 0.194 0.180 0.167 |0.155 0.144 0.134 0.361 0.333 0.308 0.284 0.263 0.243 0.676 0.614 0.558 0.508 0.463 0.422 0.386 0.352 0.322 0.295 0.270 0.247 0.227 | 0.208 0.191 | 0.176 | 0.162 0.149 0.137 0.126 | 0.116 0.107 0.650 |0.585 | 0.527 | 0.475 0.429 |0.388 0.350 0.317 0.287 | 0.261 | 0.237 | 0.215 | 0.195 | 0.178 | 0.162 | 0.148 0.135 0.123 | 0.112 | 0.103 | 0.094 0.086 10 11 12 0.625 0.557 0.497 0.444| 0.397 0.356 0.319 0.286 | 0.257 0.231 0.208 0.187 0.168 | 0.152 0.137 0.124 0.112 | 0.102 0.092 0.083 0.076 0.069 13 0.601 0.530 0.469 0.415 0.368 0.326 0.290 0.258 | 0.229 0.204 0.182 0.163 0.145 0.130 0.116 | 0.104 0.093 0.084 0.075 0.068 0.061 0.055 0.577 0.505 0.442 0.388 0.340 0.299 0.263 0.232 0.205 0.181 0.160 0.141 0.125 15 0.555 0.481 0.417 0.362 0.315 0275 0.239 0.209 0.534 |0.458 0.394 0.339 0.292 |0.252 0.218 | 0.188 0.163 | 0.141 | 0.123 | 0.107 | 0.093 0.081 0.099 0.088 0.078 0.069 0.062 0.055 0.049 0.044 0.040 | 0.035 0.071 0.062 0.054 0.047 0.042 | 0.036 0.032 0.028 14 0.111 0.183 0.160 0.140 | 0.123 0.108 0.095 0.084 0.074 | 0.065 0.057 0.051 | 0.045 16 17 0.513 0.436 0.371 0.317 0.270 0231 0.198 0.170 0.146 0.125 0.108 0.093 0.080 0.069 0.060 0.052 0.045 0.039 0.034 0.030 | 0.026 0.023 0.095 | 0.081 0.494 0.416 0.350 0.296 0.250 0212 0.180 0.153 | 0.130 0.111 0.475 0.396 0.331 0.277 0.232 0.194 0.164 0.138 0.116 0.456 0.377 0.312 0.258 0.215 0.178 0.149 0.124 | 0.104 0.087 0.073 0.061 0.051 0.043 0.051 0.044 0.038 0.032 0.098 0.083 0.070 0.060 0.051 0.043 0.037 0.031 0.028 0.024 0.021 | 0.018 0.027 0.023 0.020 | 0.017 0.014 0.037 0.031 | 0.026 0.022 0.019 |0.016 0.014 0.012 18 0.069 0.059 19 20 21 0.439 0.359 0.294 0.242 0.199 |0.164 0.135 | 0.112| 0.093 0.077 0.064 0.053 | 0.044 0.037 0.031 0.026 0.022 0.018 | 0.015 | 0.013 | 0.011 0.009 0.422 0.342 0.278 0.226 0.184 0.150 0.123 0.101 | 0.083 0.406 0.326 0.262 | 0211| 0.170 0.138 0.112 0.091 | 0.074 0.060 0.049 0.040 0.033 0.068 0.056 0.046 0.038 0.032 0.026 0.022 0.018 0.015 | 0.013 0.027 0.011 0.009 0.007 0.022 | 0.018 0.015 | 0.012 0.010 | 0.009 0.007 0.006 22 23 24 0.390 0.310 0.247 | 0.197 0.158 | 0.126 0.102 0.082 0.066 | 0.053 0.043 0.035 | 0.028 0.023 | 0.019 0.015 | 0.013 0.010 | 0.008 | 0.007 | 0.006 0.005 25 0.375 | 0.295 | 0.233 | 0.184 0.146 | 0.116 0.092 0.074 0.059 | 0.047 0.038 0.030 | 0.024 | 0.020 | 0.016 | 0.013 0.361 0.281 0.347 0.268 0.207 | 0.161 | 0.125 | 0.098 0.076 | 0.060 0.047 | 0.037 0.029 0.023 | 0.018 0.014 | 0.011 | 0.009 0.010 0.009 0.007 0.006 0.005 0.004 0.004 | 0.003 0.003 0.002 0.006 0.005 0.004 26 0.220 |0.172 0.135 0.106 0.084 0.066 0.053 0.042 0.033 |0.026 0.021 0.017 | 0.014 | 0.011 | 0.009 0.007 27 0.007 0.006 0.005 28 0.333 0.255 0.196 0.150 0.116 0.090 0.069 0.054 | 0.042 0.033 0.026 | 0.020 0.016 0.012 | 0.010 0.008 0.006 0.005 | 0.004 0.003 0.002 0.002 29 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 0.004 0.003 0.002 0.002 0.002 30 0.308 0.231 0.174 0.131 0.099 0.075 0.057 0.044 0.033 0.026 0.020 0.015 | 0.012 0.009 0.007 0.005 | 0.004 0.003 0.003 0.002 | 0.002 0.001 40 0.208 0.142 0.097 0.067 0.046 | 0.032 0.022 0.015 0.011 | 0.008 | 0.005 0.004 0.003 0.002 0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.000

Question

Julie has just retired. Her company’s retirement program has two options as to how retirement benefits can be received. Under the first option, Julie would receive a lump sum of $138,000 immediately as her full retirement benefit. Under the second option, she would receive $25,000 each year for 6 years plus a lump-sum payment of $57,000 at the end of the 6-year period.

Click here to view Exhibit 12B-1 and Exhibit 12B-2, to determine the appropriate discount factor(s) using tables.

Required:

1-a. Calculate the present value for the following assuming that the money can be invested at 12%.

1-b. If she can invest money at 12%, which option would you recommend that she accept?

EXHIBIT 12B-2
Present Value of an Annuity of $1 in Arrears; 1/r(1-(1/(1+r)^n))
Periods
4%
5%
6%
7%
8%
9%
10%
11%
12%
13%
14%
15%
16%
17%
18%
19%
20%
21%
22%
23% 24%
25%
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 0.826 | 0.820 0.813 0.806 0.800
1.886 1.859
2.775 | 2.723
3.630 | 3.546 | 3.465 | 3.387 3.312 | 3.240 3.170 3.102 | 3.037 2.974 2.914 | 2.855 2.798 2.743 2.690 2.639 | 2.589 | 2.540 | 2.494 2.448 2.404 2.362
4.452 4.329 4.212 | 4.100 | 3.993| 3.890 | 3.791 | 3.696 3.605 3.517 3.433 3.352 3.274 3.199 3.127 3.058 | 2.991 | 2.926| 2.864 2.803 2.745 2.689
5.242 5.076 4.917
6.002 5.786 5.582 | 5.389 | 5.206 | 5.033 | 4.868 | 4.712 | 4.564 | 4.423 4.288 4.160 4.039 | 3.922 | 3.812 | 3.706 | 3.605 3.508 | 3.416 | 3.327 | 3.242 | 3.161
6.733 6.463 6.210 5.971 | 5.747 5.535 | 5.335 5.146 4.968 4.799 4.639 4.487 4.344 4.207 4.078 3.954| 3.837 3.726 | 3.619 3.518 3.421 3.329
7.435 7.108 6.802 6.515 6.247| 5.995 5.759 5.537 5.328 5.132 4.946 4.772| 4.607 4.451 | 4.303 4.163 4.031 3.905 3.786 3.673| 3.566 3.463
8.111
8.760 8.306 | 7.887
9.385 8.863 | 8.384
9.986 9.394 8.853 8.358 | 7.904| 7.487
10.563 9.899 9.295
11.118 10.380 9.712 | 9.108 8.559 | 8.061 | 7.606| 7.191 6.811 | 6.462 6.142 5.847 5.575 5.324 5.092 4.876 4.675 4.489 4.315 4.153 4.001 | 3.859
11.652 10.838 10.106 9.447 8.851 | 8.313| 7.824 7.379 6.974| 6.604 6.265 5.954 5.668 5.405 5.162 | 4.938 4.730 4.536 4.357 4.189 | 4.033 3.887
12.166 11.274 10.477 9.763 9.122 | 8.544 8.022 7.549 7.120 | 6.729 6.373 6.047 5.749 5.475 5.222 4.990 4.775 4.576 4.391 | 4.219 | 4.059 3.910
12.659 11.690 10.828 10.059 9.372 | 8.756 8.201 7.702 7.250 | 6.840 6.467
13.134 12.085 11.158 10.336 9.604| 8.950 8.365 7.839 7.366 | 6.938 6.550 6.198 5.877 5.584 5.316 | 5.070 4.843 4.635 4.442 4.263 4.097| 3.942
13.590 12.462 11.470 10.594 9.818 | 9.129 8.514 | 7.963| 7.469| 7.025 6.623 | 6.259 | 5.929 | 5.628 | 5.353 | 5.101 4.870 4.657 4.460 | 4.279 | 4.110 | 3.954
14.029 12.821 11.764 10.836 10.017 9.292 8.649 8.075 7.562| 7.102 6.687
14.451 13.163 12.042 11.061 10.201 9.442 8.772 8.176
14.857 13.489 12.303 11.272 10.371 9.580 8.883 8.266 | 7.718| 7.230 6.792 6.399 6.044 5.723 5.432 5.167 4.925 4.703 4.499 4.311 | 4.137 3.976
15.247 13.799 12.550 11.469 10.529 9.707
15.622 14.094 12.783 11.654 10.675 9.823 9.077 8.422 7.843 7.330 6.873 6.464 6.097 5.766 5.467 5.195 4.948 4.721 | 4.514 4.323 4.147 3.985
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 | 4.728 4.520 | 4.328 | 4.151 | 3.988
16.330 14.643 13.211 | 11.987 10.935 10.027 9.237 | 8.548
16.663 14.898 13.406 12.137 11.051 10.116 9.307 8.602
|16.984 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 5.510 5.229 4.975 4.743 4.531 4.337 4.159 3.994
17.25
19.793 17.159 15.046 13.332 11.925 10.757 9.779 8.951 8.244 7.634 7.105 6.642 6.233 5.871 5.548 5.258 4.997 4.760 4.544 4.347 4.166 3.999
1
1.833
2.673
1.808 1.783 1.759| 1.736 | 1.713 | 1.690 1.668
2.624 2.577 2.531 | 2.487 2.444 2.402 2.361 2.322 2.283 2.246 | 2.210 2.174 2.140 2.106 2.074 2.042 2.011 | 1.981 | 1.952
1.626| 1.605 1.585 | 1.566 1.547 | 1.528 1.509 | 1.492 | 1.474 1.457 1.440
1.647
3
4
4.767
4.623
4.486 4.355 4.231 | 4.111| 3.998 | 3.889 3.784 3.685 | 3.589 3.498 | 3.410 3.326 3.245 3.167| 3.092 3.020 | 2.951
7
9
7.722 7.360
7.024 6.710 6.418 | 6.145 | 5.889 | 5.650 5.426 | 5.216 5.019 4.833 | 4.659 | 4.494 4.339 | 4.192 | 4.054 | 3.923 | 3.799 3.682 | 3.571
7.499 | 7.139 6.805 | 6.495 6.207 | 5.938 5.687 5.453 5.234 5.029 4.836 | 4.656 | 4.486 4.327 4.177 4.035 | 3.902 | 3.776 | 3.656
7.536| 7.161 | 6.814 6.492 6.194| 5.918 5.660 5.421 5.197 4.988 | 4.793 4.611 4.439 4.278 4.127 3.985 | 3.851 3.725
7.103 6.750 6.424 6.122 5.842 | 5.583 5.342 5.118 | 4.910 4.715 | 4.533 4.362 | 4.203 4.053 | 3.912 3.780
4.432 4.265 4.108 | 3.962 3.824
10
11
12
7.943
13
14
8.745
8.244 | 7.786 | 7.367 | 6.982 | 6.628 | 6.302 6.002 5.724 5.468 | 5.229 5.008 4.802 4.611
15
16
17
18
6.128 5.818 5.534 5.273 5.033 4.812 4.608 4.419 4.243 4.080 3.928
19
20
6.312 5.973 5.665| 5.384 5.127 4.891 | 4.675 4.476 4.292 4.121 | 3.963
7.645 7.170 6.743 | 6.359 | 6.011 5.696| 5.410 5.149 4.909 | 4.690 | 4.488 4.302 | 4.130 3.970
21
22
23
24
8.985 8.348 7.784| 7.283 6.835 | 6.434 6.073 | 5.746 5.451 5.182 | 4.937 4.713| 4.507 | 4.318 | 4.143 | 3.981
25
26
7.943 7.409 6.935 | 6.514 | 6.136 5.798 5.492 5.215 | 4.964 | 4.734 | 4.524 4.332 | 4.154 | 3.990
7.984 | 7.441
27
28
6.961 6.534 6.152 5.810 5.502 5.223 | 4.970 4.739 4.528 4.335 4.157 3.992
29
30
13.765 12.409 11.258 10.274 9.427 8.694 | 8.055 7.496
7.003 6.566 6.177 5.829
79 4.746
4.534 4.339 4.160 | 3.995
40

EXHIBIT 12B-1
Present Value of $1; 1 (1+r)n
17%
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
0.925 | 0.907 0.890 0.873 0.857 0.842 0.826 | 0.812 0.797 |0.783 0.769 | 0.756 | 0.743 | 0.731
13%
16%
18%
21%
22%
24%
0.820 0.813 0.806 | 0.800
Periods
4%
5%
6%
7%
9%
10%
11%
12%
14%
15%
19%
20%
23%
25%
1
0.847 | 0.840 0.833 0.826
0.718 0.706 0.694 0.683 0.672 0.661 0.650 0.640
3
0.889 0.864 0.840 0.816 0.794 0.772 0.751 0.731 | 0.712 | 0.693 0.675 0.658 | 0.641 | 0.624 0.609 0.593 | 0.579 0.564 0.551 0.537 | 0.524 0.512
0.592 0.572 0.552 0.534
0.519 0.497 0.476 | 0.456
0.790 0.746 0.705 0.666 0.630 0.596 0.564 0.535 | 0.507 0.480 0.456 | 0.432 0.410 0.390
0.792 0.763 0.735 0.708 0.683 0.659 0.636 0.613
0.423 0.410
0.855 | 0.823
0.822 0.784 0.747 0.713 0.681 0.650 0.621 | 0.593 | 0.567 0.543
0.516 | 0.499| 0.482
0.437 0.419 0.402 0.386 0.370 0.355 0.341 0.328
0.370 0.352 0.335 0.319 0.303 0.289 0.275 0.262
4
0.467
0.451 | 0.437
5
6.
7
0.760 0.711 0.665 | 0.623 0.583 0.547 0.513 | 0.482 | 0.452 0.425 | 0.400 0.376 | 0.354 0.333 |0.314 | 0.296 | 0.279 |0.263 | 0.249 0.235 | 0.222 | 0.210
0.731 0.677 0.627 | 0.582 0.540 0.502 0.467 | 0.434
0.703 0.645 0.592 | 0.544 0.500 0.460 0.424 0.391
0.404 0.376 0.351 | 0.327 0.305 0.285 0.266 | 0.249
0.225 | 0.209
0.233 0.218 0.204 |0.191 0.179 0.168
0.194 0.180 0.167 |0.155 0.144 0.134
0.361 0.333 0.308 0.284 0.263 0.243
0.676 0.614 0.558 0.508 0.463 0.422 0.386 0.352 0.322 0.295 0.270 0.247 0.227 | 0.208 0.191 | 0.176 | 0.162 0.149 0.137 0.126 | 0.116 0.107
0.650 |0.585 | 0.527 | 0.475 0.429 |0.388 0.350 0.317 0.287 | 0.261 | 0.237 | 0.215 | 0.195 | 0.178 | 0.162 | 0.148 0.135 0.123 | 0.112 | 0.103 | 0.094 0.086
10
11
12
0.625
0.557 0.497 0.444| 0.397 0.356 0.319 0.286 | 0.257 0.231
0.208 0.187 0.168 | 0.152 0.137 0.124 0.112 | 0.102
0.092 0.083
0.076 0.069
13
0.601 0.530 0.469 0.415 0.368 0.326 0.290 0.258 | 0.229 0.204 0.182 0.163 0.145 0.130 0.116 | 0.104 0.093 0.084 0.075 0.068 0.061 0.055
0.577 0.505 0.442 0.388 0.340 0.299 0.263 0.232 0.205 0.181 0.160 0.141 0.125
15
0.555 0.481 0.417 0.362 0.315 0275 0.239 0.209
0.534 |0.458 0.394 0.339 0.292 |0.252 0.218 | 0.188 0.163 | 0.141 | 0.123 | 0.107 | 0.093 0.081
0.099 0.088 0.078 0.069 0.062 0.055 0.049 0.044
0.040 | 0.035
0.071 0.062 0.054 0.047 0.042 | 0.036 0.032 0.028
14
0.111
0.183 0.160 0.140 | 0.123 0.108 0.095
0.084
0.074 | 0.065
0.057 0.051 | 0.045
16
17
0.513 0.436 0.371 0.317 0.270 0231 0.198 0.170 0.146 0.125 0.108 0.093 0.080 0.069 0.060 0.052 0.045 0.039 0.034 0.030 | 0.026 0.023
0.095 | 0.081
0.494 0.416 0.350 0.296 0.250 0212 0.180 0.153 | 0.130 0.111
0.475 0.396 0.331 0.277 0.232 0.194 0.164 0.138 0.116
0.456 0.377 0.312 0.258 0.215 0.178 0.149 0.124 | 0.104 0.087 0.073 0.061 0.051 0.043
0.051 0.044 0.038 0.032
0.098 0.083 0.070 0.060 0.051 0.043 0.037 0.031
0.028 0.024 0.021 | 0.018
0.027 0.023 0.020 | 0.017 0.014
0.037 0.031 | 0.026 0.022 0.019 |0.016 0.014 0.012
18
0.069
0.059
19
20
21
0.439 0.359 0.294 0.242 0.199 |0.164 0.135 | 0.112| 0.093 0.077 0.064 0.053 | 0.044 0.037 0.031 0.026 0.022 0.018 | 0.015 | 0.013 | 0.011 0.009
0.422 0.342 0.278 0.226 0.184 0.150 0.123 0.101 | 0.083
0.406 0.326 0.262 | 0211| 0.170 0.138 0.112 0.091 | 0.074 0.060 0.049 0.040 0.033
0.068 0.056 0.046 0.038 0.032 0.026 0.022 0.018 0.015 | 0.013
0.027
0.011 0.009 0.007
0.022 | 0.018 0.015 | 0.012 0.010 | 0.009 0.007 0.006
22
23
24
0.390 0.310 0.247 | 0.197 0.158 | 0.126 0.102 0.082 0.066 | 0.053 0.043 0.035 | 0.028 0.023 | 0.019 0.015 | 0.013 0.010 | 0.008 | 0.007 | 0.006 0.005
25
0.375 | 0.295 | 0.233 | 0.184 0.146 | 0.116 0.092 0.074 0.059 | 0.047 0.038 0.030 | 0.024 | 0.020 | 0.016 | 0.013
0.361 0.281
0.347 0.268 0.207 | 0.161 | 0.125 | 0.098 0.076 | 0.060 0.047 | 0.037 0.029 0.023 | 0.018 0.014 | 0.011 | 0.009
0.010 0.009 0.007 0.006 0.005 0.004
0.004 | 0.003
0.003 0.002
0.006 0.005
0.004
26
0.220 |0.172 0.135 0.106 0.084 0.066 0.053 0.042 0.033 |0.026 0.021 0.017 | 0.014 | 0.011 | 0.009 0.007
27
0.007 0.006 0.005
28
0.333 0.255 0.196 0.150 0.116 0.090 0.069 0.054 | 0.042 0.033 0.026 | 0.020 0.016 0.012 | 0.010 0.008 0.006 0.005 | 0.004 0.003 0.002 0.002
29
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 0.004 0.003 0.002 0.002 0.002
30
0.308 0.231 0.174 0.131 0.099 0.075 0.057 0.044 0.033 0.026 0.020 0.015 | 0.012 0.009 0.007 0.005 | 0.004 0.003 0.003 0.002 | 0.002 0.001
40
0.208 0.142 0.097 0.067 0.046 | 0.032 0.022 0.015 0.011 | 0.008 | 0.005 0.004
0.003 0.002
0.001 0.001 0.001
0.000 0.000 0.000 0.000 0.000

Accepted Answer

The goal of retirement planning is to provide a steady stream of income once you retire. It entails…