Question

Today is your 22^nd birthday, and your grandmother just gave you $5000. G-ma’s gift comes with the condition that you must invest the money and save it for your retirement. You’ve found an investment that is expected to earn an annualized rate of return of 8.4% per year forever.
In 8 years, in order to save even more money for retirement, you will begin making annual deposits into the investment account. The first payment will be $6500, and subsequent payments will grow at 3% per year. These deposits will continue until your 50^th birthday (the last deposit is on your 50^th
birthday).
No more deposits are made into the account after your 50^th birthday, but the money continues to earn a rate of return of 8.4% per year, each year thereafter.

HINT: Draw a timeline which has both time and age labels. For example, at t = 0, your timeline should also say (just below t = 0), age = 22. At t = 1, your timeline should say age = 23, etc. Double-labeling your cash flow timeline in this manner helps to avoid mistakes. Notice that the delta between time and age will always be 22. i.e. t = 50 implies age = 72.

How much money will you have in the investment account 43 years from today?

Now assume that you will begin withdrawing money from the investment account 44 years from today (i.e. on your 66th birthday). You are expecting to live to 100, and therefore the last withdraw you will need to make is on your 99^th birthday (which will fund your living expenses from the 99^th to 100^th
birthday). You have decided to have your annual withdraws decrease by 1% per year.

What is the size of the first withdraw?

What is the size of the 6^th withdraw?

What is the size of the last withdraw?​​​​​​​

Answer 1

Year can be written as t
Growth Growth Addition Amount Rate Withdrawal 32 Birthday Year 51 52 53) 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 Cash Flow 29 518,970 30 562,563 31 609,819 661,043 331 716,571 34 776,763 35 842,011 36 912,740 37 989,410 38 1,072,521 39 1,162,612 40 1,260,272 41 1,366,135 42 1,480,890 43 1,605,285 44 1,581,994 45 1,558,328 46 1,534,239 47 1,509,677 48 1,484,586 49 1,458,906 50 1,432,573 51 1,405,517 1,377,663 53 1,348,927 54 1,319,223 55 1,288,453 56. 1,256,515 57 1,223,295 Interest ROI 40,215 8.40% 43,593 8.40% 47,255 8.40% 51,225 8.40% 55,528 8.40% 60,192 8.40% 65,248 8.40% 70,729 8.40% 76,670 8.40% 83,110 8.40% 90,092 8.40% 97,659 8.40% 105,863 8.40% 114,755 8.40% 124,395 8.40% 134,844 8.40% 132,887 8.40% 130,900 8.40% 128,876 8.40% 126,813 8.40% 124,705 8.40% 122,548 8.40% 120,336 8.40% 118,063 8.40% 115,724 8.40% 113,310 8.40% 110,815 8.40% 108,230 8.40% 105,547 8.40% 158,135 156,554 154,988 153,438 151,904 150,385 148,881 147,392 145,918 144,459 143,014 141,584 140,168 138,767 52 78 79

Growth Growth Addition Amount Rate Birthday Year 80 81 82 83 84 85 86 87 88 89 90 91 Cash Flow 58 1,188,673 59 1,152,516 60 1,114,682 61 1,075,016 62 1,033,352 63 989,507 64 943,286 65 894,476 66. 842,846 67 788,147 68 730,108 69 668,436 70 602,814 71 532,898 72 458,313 73 378,658 74 293,492 75 202,343 761 104,695 77 0 78 Interest ROI 102,757 8.40% 99,849 8.40% 96,811 8.40% 93,633 8.40% 90,301 8.40% 86,802 8.40% 83,119 8.40% 79,236 8.40% 75,136 8.40% 70,799 8.40% 66,204 8.40% 61,329 8.40% 56,149 8.40% 50,636 8.40% 44,763 8.40% 38,498 8.40% 31,807 8.40% 24,653 8.40% 16,997 8.40% 8,794 8.40% Withdrawal 137,379 136,005 134,645 133,299 131,966 130,646 129,340 128,046 126,766 125,498 124,243 123,001 121,771 120,553 119,348 118,154 116,973 115,803 114,645 113,489 92 93 94 95 96) 97 98 991 100

Interest Growth Growth Addition Amount Rate ROI Withdrawal Birthday Year 22 23 241 25 26. 27 28 29 30 31 32 33 34 35 Cash Flow 5,000 5,420 5,875 6,369 6,904 7,484 8,112 8,794 16,032 24,074 32,992 42,866 53,783 65,836 79,128 93,768 109,879 127,590 147,043 168,392 191,804 217,461 245,560 276,314 309,955 346,734 386,926 430,825 478,754 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22. 23 24 25 26 27 28 36 37 38 39 40 41 421 43 44 45 46 47 48 49 50 420 8.40% 455 8.40% 494 8.40% 535 8.40% 5808.40% 629 8.40% 681 8.40% 739 8.40% 1,347 8.40% 2,022 8.40% 2,771 8.40% 3,601 8.40% 4,518 8.40% 5,530 8.40% 6,647 8.40% 7,877 8.40% 9,230 8.40% 10,718 8.40% 12,352 8.40% 14,145 8.40% 16,112 8.40% 18,267 8.40% 20,627 8.40% 23,210 8.40% 26,036 8.40% 29,126 8.40% 32,502 8.40% 36,189 8.40% 6,500 6,695 6,896 7,103 7,316 7,535 7,761 7,994 8,234 8,481 8,735 8,998 9,267 9,545 9,832 10,127 10,431 10,744 11,066 11,398 11,740 195 201 207 213 219 226 233 240 247 254 262 270 278 286 295 304 313 322 332 342 3% 3% 3% 3% 3% 3% 3% 3% 3% 3% 3% 3% 3% 3% 3% 3% 3% 3% 3% 3%