A time value of money question?

you have decided to start planning for your retirement by analyzing different retirement plans. The plan offered by an insurance manager requires you to deposit $5000 at the beginning of each of the next 30 years. The retirement plan guarantees a 10 percent annual compounding rate over the 30 years period. when you retire at the end of the thirtieth year, the interest earned on the money in the account is guaranteed to increase to a 12 percent annual rate. if you plan on making 20 equal withdrawals at the beginning of each year from the account(with the first withdrawer made at the end of the 30th year), how much can you withdraw?





can you help me ? i dont know how to do it .....|||This an Annuity Due problem, since payments are made for 30 yrs on the first day of the year, and withdrawals start on Dec 31, Yr 30, or the first day of Yr 31.





Annuity Amount (Payment) - 5,000. N 30 R 10%. Future Value = 904,717





Then with a PV of 904,717, N 20 R 12% Annuity = 108,145|||You got 121,122 because you calculated an Ordinary Annuity, but this is an Annuity Due.





Either find the tables for Annuity Due, or if using a financial calculator, convert PMT to BGN.

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|||Since you have a computor, why don't you put the problem on a spreadsheet?





I do that with all of my finances.|||Below is a computation of cash flow based on 30 years contribution of $ 5000 per year at 10% interest

and 20 years of withdrawal of $ 108,415 at 12% interest.



column 1 - year number

column 2 - annual contribution/withdrawal at beginning of year.

column 3 balance at beginning of year ( balance of previous year plus annual contribution)

column 4 interest at 10% up to 30th year, 12% on 31th to 49th based on column 3

column 5 balance at the end of year





1 5000 5000 500 5500

2 5000 10500 1050 11550

3 5000 16550 1655 18205

4 5000 23205 2321 25526

5 5000 30526 3053 33578

6 5000 38578 3858 42436

7 5000 47436 4744 52179

8 5000 57179 5718 62897

9 5000 67897 6790 74687

10 5000 79687 7969 87656

11 5000 92656 9266 101921

12 5000 106921 10692 117614

13 5000 122614 12261 134875

14 5000 139875 13987 153862

15 5000 158862 15886 174749

16 5000 179749 17975 197724

17 5000 202724 20272 222996

18 5000 227996 22800 250795

19 5000 255795 25580 281375

20 5000 286375 28637 315012

21 5000 320012 32001 352014

22 5000 357014 35701 392715

23 5000 397715 39772 437487

24 5000 442487 44249 486735

25 5000 491735 49174 540909

26 5000 545909 54591 600500

27 5000 605500 60550 666050

28 5000 671050 67105 738155

29 5000 743155 74315 817470

30 5000 822470 82247 904717

31 -108145 796572 95589 892161

32 -108145 784016 94082 878098

33 -108145 769953 92394 862347

34 -108145 754202 90504 844706

35 -108145 736561 88387 824948

36 -108145 716803 86016 802820

37 -108145 694675 83361 778036

38 -108145 669891 80387 750278

39 -108145 642133 77056 719189

40 -108145 611043 73325 684369

41 -108145 576224 69147 645371

42 -108145 537226 64467 601693

43 -108145 493548 59226 552773

44 -108145 444628 53355 497984

45 -108145 389839 46781 436619

46 -108145 328474 39417 367891

47 -108145 259746 31170 290916

48 -108145 182771 21932 204703

49 -108145 96558 11587 108145

50 -108145 0 0 0