Question on formula

[TexasAnnie]

I've seen this formula from MDM (who said it came from Heart of Tin):

Time in years to FI = Ln((S + i*E/WR) / (S + i*A)) / Ln(1 + I)

A =  amount currently invested in funds you will draw upon in retirement
E = total expenses in retirement (including taxes, in today's dollars)
I = Real return on invested retirement funds
S = Annual amount invested in funds you will draw upon in retirement
WR = withdrawal Rate planned for retirement (e.g. 4%)

I have a few questions regarding the definitions:
is E per year?  Or total for all years I plan to be retired?
For S, is it the amount that I will invest each year until retirement?
Does it assume that you want the principal to remain untouched?

I've also been using forum search and google site: search to try to find the post from someone whose money only needs to last x  years until their pension / defined benefit plan kicks in.  Anyone remember that?

Thanks,
TexasAnnie

[dandarc]

Yes - E is per year.
Yes - S is annual amount saved per year.

Does it assume that you want the principal to remain untouched?

This formula doesn't say anything about how long your money will last.  All it does is tell you how many years until you hit your "number" which is E / I.

[MDM]

This formula doesn't say anything about how long your money will last.  All it does is tell you how many years until you hit your "number" which is E / I.

The formula is based on the savings at retirement being E/WR.  That does lead to potential inconsistencies if one chooses a wildly different value for I, as the "Safe" WR of 4% is based on historical market returns, but for a one line formula it's not bad (and the answer "moves in the right direction" as one changes I).

[dandarc]

Blah - I meant WR.  Trying to be quick as I'm actually at the office right now - running new batch is often best done during low-use periods such as Sunday night.

[TexasAnnie]

Thanks, that helps a lot!

[MDM]

If you want the derivation details, see http://forum.mrmoneymustache.com/ask-a-mustachian/fire-in-8-years/.