Retirement Planning Revisited

I'm facinated by retirement. If I had enough money I'd retire tomorrow. By retire, I mean not working in the corporate sector just to make my ends meet. I'll splurge money on my pet projects that no one but me will benefit from. Alas! I'm not there yet and don't seem to be getting there anytime soon either.

About 5 years ago I blogged about retirement planning. I wrote about projecting your retirement money remaining at the end of any year. Just to refresh here is the formula

i = Rate of return on your investment (post tax)
i_f = Inflation
P₀ = Initial Savings
B = Annual expenses (burn rate)
R = (1 + i_f )/(1+ i)
n = Time in years

Money remaining at the end of n^th year

P_n = P₀ X (1+i)ⁿ – B X (1+i)^n-1 X (Rⁿ-1)/(R-1)

Its another one of those useless things that no one but I found any value in. But over the years as I fantasized retirement, I noticed an interesting trend. 

What I noticed was that in most cases I'd finally run out of money. Dh!

But then if I save till a point I'm calling "inflection point" everything will change. 

The inflection point is the initial amount P₀ you being with and if the other variables are held constant, namely inflation, interest you earn on your savings, you'll never ever run out of money. 

Not in 100 years and not in 1000 years. Never. Just like escape velocity, you'll never return to earth.

That value can be derived from the above equation with n-> Infinity. Assuming i_f(inflation) is lower than i(interest earned) of course. 

Calculating the dream P₀ 

P₀ = B/(R-1)(1+i) 

gives you the initial amount that will NEVER run out....

An interesting point :)