Okay, you math geniuses, riddle me this:

[MrScorpio]

You have $1,000,000 in a bank savings account. It has a standard fixed 3.5% APR.

However, you are limited to withdrawing a stipend of $2,000 per week. No more, no less.

The question is, how long does your $1,000,000 last until you deplete the account?


BTW, I don't know the answer.

Show your math

[mcctatas]

1. What fresh hell is this?

Sadist! :scared:

[MrScorpio]

2. Five hundred weeks would be too easy

Gotta factor in that interest, baby!

[mcctatas]

3. The math makes me cry...

way to go big man, making the girls cry!





;)

[MrScorpio]

7. Listen to my show tonight and I'll make you feel better

[mcctatas]

8. I should probably know this...

but how do I do that? :dunce:

[MrScorpio]

9. Double click my face located in my sig line?

go for it

[mcctatas]

13. Doh...

should have read the fine print! Bookmarked now though :hi:

[KitchenWitch]

4. How often is the interest compounded?

[MrScorpio]

5. Annually...

Of course, it's divided by each month

[mcctatas]

6. Oh no...

not you too! Will you fly to WI and take my stats final for me? ;)

[KitchenWitch]

10. It has been way too long

I used to be really good at this type of thing. I may have to go get the Pre Calc book out for this one.

[MrScorpio]

14. The only way I can do this is with a calulator and a lot of paper

Calculate the interest, divide it by 12, add that to the principal and subtract the monthly stipend... Rinse and repeat

Eventually, I'll get to zero.

[Critters2]

11. Where are you in Wisconsin? My dad's a math whiz and he's in Wisconsin.

If you paid for his fish tomorrow night, he might be talked into it.

[mcctatas]

15. Fox Valley area...

and I would pay for a years worth of Friday fish nite if I can pull off a B in stats!

[Critters2]

32. Hey! I'm in the Fox Valley, too. At the very southern end of the Fox in Illinois. nt

Am I right that there are 2 Fox Rivers in WI...one up by Neenah-Menasha, and one west of Milwaukee (that's the one I live on). We lived in Winneconne, on the Wolf River for about a year when I was a kid.

Oh, and my dad's math skills are more physics/engineering geared, than stats. Still, from what I can tell, math is math. It's all evil. :grr:

[4 t 4]

12. Do you take out 2,000 every week starting from week one?

1,000,000 - 2,000 per week = 8,000 month+ = 104,354.00 per year OMG! you do the math. My head hurts Hehehehehehhe

[MrScorpio]

16. I'll make it easy, add the interest before subtracting the stipend

So the first month will start you at $1,002,916.66

[mwooldri]

17. If you had said you can't withdraw a stipend of $2,000 a month you'd never deplete it.

... but $2,000 a week? It'll go eventually.

This is dead rough maths, and I'm cheating big time since I am at work and they supply us with a compound interest calcuator.

With an APR of 3.5%, turns into a weekly percentage of 0.0671%. $1,000,000 in a savings account will earn $671.00 a week in interest just for 7 days.

therefore first week is easy: $1,000,000 + 671.00 - $2,000 = $998,671.. and we would continue like this longhand until we get it.

But I don't want to go on that long... so I'm going to cheat and give a guessm which is an educated guess but still a wrong guess I bet.

With 0% APR that 1,000,000 will last me 500 weeks.
Just in interest on a depleting 1,000,000 balance without compounding I should expect to earn 167,750 over those 500 weeks. That's 83 more payouts possible... and then 167750 earns 4671.24.

Therefore my "educated but most likely wrong" guess is that if you are investing $1MM at a 3.5% APR with a $2K withdrawal a week it should last you about 585 weeks.

Mark.

[MrScorpio]

21. Right, it'll deplete, that's why I chose $2,000 a week

But of course, the result of 3.5% div by 12 varies monthly... it's only compounded per month not by week

[flvegan]

18. You should be able to do this with an amortization schedule.

The mortgage is $1,000,000.00 with a 3.5% interest rate (principal growth) and make your payment $2,000 x 52.

[flvegan]

19. I get 11.73 years.

Principal borrowed: $1000000.00
Annual Payments: 52 Total Payments: 610 (11.73 years)
Annual interest rate: 3.50% Periodic interest rate: 0.0673%
Regular Payment amount: $1999.39 Final Balloon Payment: $0.00

[MrScorpio]

23. This sounds like the best answer

I think

[flvegan]

27. Wait...correction

On edit:

Nope, scratch that. You'd pay capital gains out of the $104k you pulled over the course of the year. Nevermind.

[MrScorpio]

28. I didn't factor in Uncle Sam, 1. Because I have no idea what the marginal tax rate is

Thanks for the adjustment

[flvegan]

29. Heh I just unadjusted it.

Technically, you'd pay the capital gains out of the $104k you pulled over the year. I'm all debate wound up and not thinking.

The marginal, without any other cap gains is 25% for this amount, I believe.

[Ptah]

20. I think 20 years, 11 months.

Using this formula:
start with $1,000,000 in the first line.

Next line is
Previous balance+(.035/12)-$4333

in an Excell spreadsheet and repeating until a negative balance.

[MrScorpio]

22. That seems an awful lot

Eight grand gets subtracted every four months

[A HERETIC I AM]

24. 12.5 years.

Year      Desired     Beginning       Earnings       Needed          End 
           Income      Balance         @3.50%      Withdrawals    Balance
1          96,000    $1,000,000        $34,012       $-96,000     $938,012
3          96,000      873,819          29,524        -96,000      807,343
5          96,000      738,503          24,711        -96,000      667,214
7          96,000      593,390          19,550        -96,000      516,940
9          96,000      437,771          14,015        -96,000      355,786
11         96,000      270,885           8,079        -96,000      182,964
13        $96,000      $91,917          $1,714       $-93,631         $0

http://www.financialcalculators.com/AdvisorCalcs.htm

BTW, If you're only getting 3.5% yield on your million, you are invested wrong.

One more BTW...I'm no math genius, I just knew about that handy dandy website.

[MrScorpio]

26. Yeah, I just pulled that amount out my butt

If I had said 4.9% I'd start a riot

Uncle Sam notwithstanding, I'm at a point in my life now that I can live on 3.5% interest interest alone. I'm just missing the million


Ideally, I'd rather have five mil @ 5%, even after taxes, I'll never run out of money.

[A HERETIC I AM]

30. 30 Year Treasuries will pay you $45,000/yr on a million.

Thing is, if you bought them today, you would buy them at a premium so your yield is lower. Yield at the end of today was 4.15%.

[MrScorpio]

31. I could live on that and never touch the principal

Even after taxes

[some guy]

33. why $96,000?

you have desired income and needed withdrawals both as $96,000 - but the scenario was $2,000 per week, which would be $104,000 per year.

[A HERETIC I AM]

34. I used a 4 week month......

The calculator asked for monthly income. I multiplied two grand times 4.

My apologies, I'm short 4 weeks worth.

[some guy]

35. ok

I was just curious. We can blame MrS for making up the question badly. :D

[PfcHammer]

25. 155 months or about 12yrs 11 months

:shrug:

[Dr. Strange]

36. That's what I get.

With the present value formula:

PVoa = PMT ((1 - (1 + i)^-n) / i)

http://www.getobjects.com/Components/Finance/TVM/pva.html

[Orrex]

40. He's a witch! Burn him!

You and your maths can go straight back to Hell, you demon-spawn!

[pokerfan]

37. 609.77 weeks

http://www.zenwealth.com/BusinessFinanceOnline/TVM/TVMCalculator.html">Time Value of Money Calculator

PV = 1,000,000
PMT = -2,000
Rate = 3.5%
FV = 0
solve for # of periods

[Dem2theMax]

38. I read the entire thread.

Tell you what. Someone just give me the million and I'll report back to you once it's gone.

How's that sound? ;)

(I REALLY like this idea.) LOL.

[PfcHammer]

39. I suggest we have a thread with math problems or financial problems

like this for those inclined. Could be here or in some other group.:think:

[meegbear]

41. 1 week ...

your bank failed due to running up bad loans and they don't have FDIC insurance, so you don't even get the $100,000 coverage.