Well I started with a little introspection. What are the odds that I'd not live to see the next millennium. Pretty much 100% I guess. Living to be 80 is perhaps closer to reality, though still pretty far from where I am.
Obvious part of perpetual cashflow is that it requires higher initial base. When I plan for a more realistic life expectancy, anything less than infinite, one new variable springs up. Time.
Adding time to the equation made it a little more challenging. I had to brush up my class XI maths. Sum of Geometric Progression and Finding nth term of a series was something I had not done for a long time. After a rusty start and scribbling on sheets of paper for some time here is what I got
i = Rate of return on your investment (post tax)
if = Inflation
P0 = Initial Savings
B = Annual expenses (burn rate)
R = (1 + if )/(1+ i)
n = Time in years
Money remaining at the end of nth year
Pn = P0 X (1+i)n – B X (1+i)n-1 X (Rn-1)/(R-1)
That’s kind of lengthy equation. To solve this I needed excel. I’ll see if I can upload the excel so that anyone can try this out.
If I wanted to know how much do I need to last 50 years I could use above equation.
Lets complete the example. Please notice that all the values are the same as previous example except a new variable “n”
i = 8%
if = 3%
B = $30,000
n = 50 years
I’m now solving for P50 = 0 (as I plan to spend my booty in 50 years)
P0 X (1+i)n = B X (1+i)n-1 X (Rn-1)/(R-1)
Solving for P0 we get
P0 = $543,918
This is interesting. Comparing between perpetual cashflow (P0 = $600,000) and one lasting just 50 years I find the "Initial Savings" differ by just about $56,000. Less than 10% of perpetual cashflow requirements.
Given this, I’d rather work another couple of years to save an additional $56K than run the risk of running out of money just in case… What do you prefer?
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