I was lying awake last night thinking about all the financial math problems I couldn't solve and ...
>Couldn't solve? That's not unusual. Besides, I thought you were giving up on financial stuff.
In an earlier tutorial
(Equation [4A]), we ran across the expression:
SQRT[(1+S2/M2) - 1]
SQRT[(1+S2/M2)2 - 1]
SQRT[(1+S2/M2)n - 1].
I never could sum this series, so tried to simplify and approximate and ...
That's the question I asked myself. My approximations resulted in another series which was no better than the one above.
>And that kept you awake? Besides, weren't you through with financial stuff?
Don't keep reminding me!
Anyway, it occurred to me that I might just as well use the series [4A].
>What was the approximation?
1+M SQRT+M2 SQRT+...+Mn-1SQRT[n]
Anyway, since the formula was my attempt to calculate a Safe Withdrawal Rate (avoiding a jillion Monte
Carlo simulations), I decided to modify the spreadsheet by allowing the user to pick either [4B] or [4A]
... which, in the modified spreadsheet, I call Formula #1 and Formula #2, respectively.
>And does Formula #2 give a better value for SWR?
Who knows. Try it yourself ... and decide. The (modified) spreadsheet looks like this:
To download a .ZIPd file, RIGHT-click on the picture above and Save target.
>What's the point of all this?
Well ... uh, I just figured that if you wanted to see how the SWR changed when you changed from 30 years to 35 or
maybe 8% return to 9% or 3% inflation to ...
So you wouldn't have to do a jillion Monte Carlo simulations for each new set of parameters.
>And that's good?
Sure. Don't you think so?
Here's some examples, with various inflation rates (that's i), Years (that's N) and Standard Deviations (that's S) :