Fun Question For Our Math Geniuses

[TSATSO]

When I retired (5-31-2008), I took the "Series of Monthly Payments" withdrawal option from my TSP account. As I approach 2 years retired, so far it has worked perfectly. My plan was to keep the account value level - removing only what it gained each month. I started out taking a little too much, then had to lower it a bit at the end of 2008. Since then it has been "just right" and my total account value is now almost exactly the same as when I retired. I hope to be able to continue this process until I reach age 70.5, at which time the IRS mandatory witdrawal rules kick in. But (and now we come to my FUN QUESTION) what if there wasn't any such IRS rule? What if I could keep up this withdrawal process forever? How long would it take for my SHARE balance to get down to one single share? If you need numbers to work with, assume this situation: start with $400,000 in the TSP (G Fund) account. Assume the account "earns" a constant 3.00% per year, forever. (Ignore any effect from taxes and inflation.) I withdraw $1000 per month ($12,000 per year) forever. The starting share price is $13.13 per share, and you start out with (about) 30465 shares in the account. Obviously, even though the account value remains constant, the actual number of shares in the account drops each month. Where I run into trouble is calculating the exact number of shares "sold" each month. As the share price goes up (daily), the number of shares sold (monthly) goes down. Following this to a logical conclusion, at some point in the future, you would only have one share left in the account, and it would be worth $400,000! I figure somebody who is really clever with spreadsheets could figure this out pretty easily, but I could be wrong. Anyway, it is fun to consider this senario, and if anyone can come up with a answer, I would love to hear it. Thanks, Chuck Avery (TSATSO)

 

[Frixxxx]

Anyway, it is fun to consider this senario, and if anyone can come up with a answer, I would love to hear it. Thanks, Chuck Avery (TSATSO)

Impossible to answer, even though the "G" moves upward continually, it does not move at a rate that is constant. At that value it would be well into the future. So arguing:

So 13.13 at 3% a year would take 344 years 10 months.

Or I'm not seeing the whole question?

 

[TSATSO]

Thanks, Frixxxx, for taking the time to respond to my frivolous question. If I am correct, you simply calculated how long it would take $13.13, compounded annually at 3%, to reach the sum of $400,000. Very cool, very simple...a neat solution. See, I got all tied up in trying to compute numbers of shares sold, etc. I suppose you could guess that I was a English major several decades ago. Anyway, thanks for the reply.

Chuck Avery (TSATSO) (NOT a math major)

 

[Frixxxx]

Thanks, Frixxxx, for taking the time to respond to my frivolous question. If I am correct, you simply calculated how long it would take $13.13, compounded annually at 3%, to reach the sum of $400,000. Very cool, very simple...a neat solution. See, I got all tied up in trying to compute numbers of shares sold, etc. I suppose you could guess that I was a English major several decades ago. Anyway, thanks for the reply.

Chuck Avery (TSATSO) (NOT a math major)

Well, to be honset, that's only half your question.

If you are taking money out of the fund I think you would actually half that number....My excel skills reached the capacity of Googling calculations, so I can't really take all the credit yet.:suspicious:

 

[peterson82]

If you don't touch your money the whole year you would have 12,000 more in the account, but if you take it out monthly you would not be able to take out 12,000... more like 11750 (987 per month).