Question

1. Your uncle is 70 years old. Over the years, he has accumulated savings of $400,000. He estimates that he will live another 10 years at the most and he wants to spend his savings by then. He places his $400,000 into an account earning 8% annually and sets it up in such a way that he will be making 10 equal annual withdrawals.

How much will he be able to withdraw each year?

2. Your mother is planning to retire this year. Her firm has offered her a lump-sum retirement plan of $120,000 or a $10,000 lifetime annuity, whichever she chooses. Your mother is in reasonable good health and expects to live for at least 20 more years. Which option should she choose, assuming that a 7% interest rate is appropriate to evaluate the annuity?

3. You just won $200,000 in the lottery. You have decided to invest this amount and to withdraw an equal amount each year for 5 years. How much can you withdraw each year if you invest the $200,000 at 10% compounded annually?

4. You want to spend $15,000 on a vacation at the end of each of the next 5 years. What lump sum do you have to invest now to take the 5 vacations, assuming that your minimum desired rate of return is 5% compounded annually.

5. If you desire to have $50,000 for a down payment for a house that you plan to buy in three years, what amount would you need to deposit today? Assume that your money will earn 8 percent.

Present value interest factor of $1 per period at i% for n periods, PVIF(i,n). (TABLE #1) Period 1% 2% 3% 4% 5% 10.990 0.990 0.980 0.971 0.962 0.952 2 0.980 0.980 0.961 0.943 0.925 0.907 3 0.971 0.942 0.915 0.889 0.864 4 0.961 0.924 0.888 0.855 0.823 wooo wo 5 0.951 0.906 0.863 0.822 0.784 we vide 6 0.942 1:24 0.888 0.837 0.790 0.746 7 0.933 0.871 V. Dom 0.813 0.01 0.760 0.711 8 0.923 0.853 viac 0.789 0.731 wo 0.677 400 wer 9 0.914 0.837 0.766 0.703 Vio SO 0.645 10 0.905 0.820 0.02 0.676 Doc 0.744 0.11+ 0.org 0.614 0.014 11 0.896 0.804 0.722 0.650 0.585 12 0.887 0.788 0.701 0.625 0.557 . re ! - 20 13 0.879 0.773 0.681 0.601 0.530 wo ! 14 0.870 0.758 0.661 0.577 0.505 we 15 0.861 0.743 0.642 0.555 vice Vart JU 0.481 Video 16 0.033 0.853 0.728 0.623 0.023 0.534 20 0.458 17 0.844 0.044 0.714 0.605 0.513 0.436 0.439 18 1o 0.836 0.030 0.00 0.700 0.587 0.494 0.484 0.416 0.419 19 0.020 0.828 0.686 0.000 0.570 0.475 0 0.413 0.396 www 20 0.820 0.673 0.554 0.012 0.456 1.430 0.377 V. 25 0.780 0.610 0.478 0.375 0.295 30 0.742 0.552 0.308 0.231 35 0.706 0.500 0.355 0.253 0.181 40 0.672 0.453 0.307 0.208 0.142 50 0.608 0.372 0.228 0.087 6% 7% 0.943 0.935 0.890 0.873 0.840 0.816 0.792 0.763 0.747 0.713 0.705 0.666 1.000 D. 0.665 0.623 0.003 0.02 0.627 0.582 De 20 0.592 0.544 0.558 0.508 0.300 0.527 0.475 0.497 0.444 11 0.469 0.415 0.442 0.388 0.417 0.362 Van 0.394 0.594 0.339 0.339 0.371 0.317 0.350 Die 0.296 0.331 0.277 Ver 0.312 0.258 V.230 0.233 0.233 0.184 0.174 0.131 0.130 0.094 0.097 0.067 0.054 0.034 8% 9% 10% 11% 0.926 0.917 0.909 0.901 0.857 0.842 0.826 0.812 0.794 0.772 0.751 0.731 0.735 0.708 0.683 0.659 0.681 0.650 0.621 0.593 e 0.630 0.000 0.596 9.00 0.564 0.535 Dado 0.583 0.547 0.513 0.347 0.313 0.482 0.540 0.002 0.502 0.467 0.434 0101 1.404 0.500 0.460 0.424 0.391 0.463 0.400 0.422 0.386 0.422 V.300 0.352 Devel 0.429 0.388 0.350 0.317 0.397 0.356 0.319 0.286 0.368 we 0.326 0.290 0.258 0.340 0.299 0.263 0.232 0.315 0.275 0.239 0.209 Der Service 0.292 0.252 0.210 0.108 0.218 0.188 0.270 0.270 0.231 0.198 0.170 0.250 0.212 0.214 0.180 0.100 0.153 0.13 V.202 0.232 0.194 0.164 0.138 D. 0.215 0.178 0.110 0.149 0.124 0.127 0.146 0.116 0.092 0.074 0.099 0.075 0.057 0.044 0.068 0.049 0.036 0.026 0.046 0.032 0.022 0.015 0.021 0.013 0.009 0.005 12% 0.893 0.797 0.712 0.636 tes 0.567 0.307 0.507 0.452 0.404 1.404 0.361 0.322 Dave 0.287 0.257 0.229 0.205 0.10 0.183 0.163 0.163 0.146 0.130 Side 0.116 0.104 0.109 0.059 0.033 0.019 0.011 0.003 13% 14% 0.885 0.877 0.783 0.769 0.693 0.675 0.613 0.592 0.543 0.519 . 0.480 0.456 0.425 0.400 0.42 0.400 0.376 0.351 0.333 0.308 Vio 0.295 0.270 0.21 V.2 0.261 0.237 0.231 0.208 0.204 0.182 w 0.181 0.160 0.160 0.140 Dance . 0.141 0.123 0.12 0.125 0.111 0.095 0.098 0.098 0.083 9.00 0.087 0.00 0.073 More 0.047 0.038 0.026 0.020 0.014 0.010 0.008 0.005 0.002 0.001 15% 0.870 0.756 0.658 0.572 4 0.497 0.432 1:22 0.376 0.327 0.284 0.247 0.24 0.215 0.187 10 0.163 0.141 0.123 . 0.107 0.093 0.093 0.081 0.070 voru 0.061 0.001 0.030 0.015 0.008 0.004 0.001 16% 17% 0.862 0.855 0.743 0.731 0.641 0.624 0.552 0.534 w 0.476 0.456 114 0.410 0.390 0.419 20 0.354 0.333 0.33 0.034 0.305 0.285 0.263 0.243 wa 4 0.227 0.208 V.22 Vicce 0.195 0.178 0.168 0.152 100 0.145 0.130 war 0.125 0.111 w 0.108 0.095 Valvo a 0.093 0.081 0.001 0.09 0.000 0.080 0.069 0.069 0.059 0.060 0.051 0.051 0.043 0.043 0.024 0.020 0.012 0.009 0.006 0.004 0.003 0.002 0.001 0.000 18% 19% 20% 0.847 0.840 0.833 0.718 0.706 0.694 0.609 0.593 0.579 0.516 0.499 0.482 w 0.437 0.419 0.402 ve! 12 vre 0.370 0.10 0.334 0.352 V.233 0.335 0.314 0.296 0.14 9.2 0.279 22 0.266 0.249 0.233 2:00 0.249 Vio 0.225 0.209 0.194 194 0.191 0.19 0.176 0.170 0.162 0.162 0.148 0.135 0.137 0.124 0.112 0.116 0.104 0.093 0.099 0.088 0.078 0.084 0.074 0.065 Vivo vor 0.071 0.064 0.062 0.054 0.060 0.052 0.045 0.051 0.03 0.044 0.038 0.043 0.037 1.04 0.031 0.0" 0.037 0.031 0.00 0.00 0.026 V.UZ 0.016 0.013 0.010 0.007 0.005 0.004 0.003 0.002 0.002 0.001 0.001 0.001 0.000 0.000 0.000 0.108 0.412 0.141

Answer 1

Hi, As per the HOMEWORKLIB RULES, in case of multiple questions, I need to solve the first question.

The amount is computed as shown below:

Present value = Annual withdrawal x [ (1 – 1 / (1 + r)ⁿ) / r ]

So, the annual withdrawal is computed as follows:

$ 400,000 = Annual withdrawal x [ (1 - 1 / (1 + 0.08)¹⁰ ) / 0.08 ]

$ 400,000 = Annual withdrawal x 6.710081399

Annual withdrawal = $ 400,000 / 6.710081399

Annual withdrawal = $ 59,611.80 Approximately

I request you to please post remaining questions separately, since as per the guidelines in case of multiple questions, I need to solve the first question.

Feel free to ask in case of any query relating to this question