Question

Problem #7 (TVM): Tom's brother has $950,000 (today) and wants to retire. He expects to live for another 25 years and to cam 7.5% on his invested funds. How much could he withdraw at the end of cach of the next 25 years and end up with zero in the account?

Answer 1

Assume R = Cash withdrawal of each Year

R = Investment (today) ÷ Present value annuity factor (25 years, 7.5%)

R = $950,000 ÷ 11.14695

R = $85,225

Thus, Tom's brother can withdraw $85,225 each year for 25 years.

Calculations:

Calculation of present value annuity factor

Year	Formula	Present value
1	1/(1.075)^1	0.93023
2	1/(1.075)^2	0.86533
3	1/(1.075)^3	0.80496
4	1/(1.075)^4	0.74880
5	1/(1.075)^5	0.69656
6	1/(1.075)^6	0.64796
7	1/(1.075)^7	0.60275
8	1/(1.075)^8	0.56070
9	1/(1.075)^9	0.52158
10	1/(1.075)^10	0.48519
11	1/(1.075)^11	0.45134
12	1/(1.075)^12	0.41985
13	1/(1.075)^13	0.39056
14	1/(1.075)^14	0.36331
15	1/(1.075)^15	0.33797
16	1/(1.075)^16	0.31439
17	1/(1.075)^17	0.29245
18	1/(1.075)^18	0.27205
19	1/(1.075)^19	0.25307
20	1/(1.075)^20	0.23541
21	1/(1.075)^21	0.21899
22	1/(1.075)^22	0.20371
23	1/(1.075)^23	0.18950
24	1/(1.075)^24	0.17628
25	1/(1.075)^25	0.16398
Total		11.14695