Retirement Planning (Corollary)

Starting where I left off. What do I do, I had 2 more days to kill.

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)
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)

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%
i_f = 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?

Retirement Planning

Being lazy is my way of life. The idea of getting up every day, shaving, bathing, dressing in formals and showing up for work is not my favorite fantasy of how life should be. If I could, I'd love to retire today and spend my life in creative pursuits such as blogging, bidding for junk on ebay, updating my queue on Netflix, ripping CDs in lossless format and having orgasms listening to them on my Harman Kardon. No, Gaming and cybersex do not interest me yet.

So here I was, Friday night, fretting over my retirement and planning my life beyond, tinkering with excel, projecting my future finances blah, blah.

As I did "What If" toying with the spreadsheet, I observed something amusing. It was a simple equation. When put on paper it looked something like this.

i = Rate of return on your investment (post tax)

i_f = Inflation

p = Savings

b = Annual expenses (burn rate)

∆ = Difference in invest rate and Inflation (i - i_f)

Money you need to support yourself for ever without running out of it ever

p = b / ∆

For example

i = 0.08 (8% returns on your investment)

i_f = 0.03 (3% based on last 20 years)

b = $ 30,000 (excluding house, all other expenses or $2,500 monthly)

∆ = 0.05 (i - i_f)

Then

p = $600,000 ($30,000 / 0.05)

The secret here is to keep beating the inflation by 5 points, year on year. I'd bet that shouldn't be any tougher than breaking 128 bit encryption or hacking into NASA on your dell laptop. Hollywood does it every other Friday.

If I had $600,000 invested @ 5% better than inflation, I will never ever run out of money, no matter how long I live. I could be the longest living blogger @1000 years and like "Baba Moze" (In Hindi version of Phantom, he used to tell stories of 5th to 15th generation Phantom. He was only 400 yrs old though) read out this blog to my Android Generation-X.

If anything, the thought of never running out of money did make me feel lighter. Needless to say, I slept better that night.

The next to-do items are to get $600,000 and to find an investment opportunity that gives a stable 8% return.

You can try this out to your hearts content. Let me figure out if I can upload the excel so that all you lazy bums out there can retire tomorrow betting on my path breaking discovery to bring home the bacon. I'm sure when I'm 547 years old they will offer me a Nobel for my contribution to the lazy planet in 2008.

If you figure out that this theorm was proved 1300 years ago by Aryabhatta in his crib, pls keep it to yourself. I live in my cacoon and light of wisdom can't penetrate it.

Aaaaahhh!! This is the same as Annuities with growing cash flow. How Dumb of me!