Formula for/to calculate independently wealthy

[SpicyF]

Don't know if this is the right forum but i'll give it a shot. But it has something to do with stock market probarbly so why not.
Anyways, i'm looking for a forumla that will calculate how much money u need be able to invest and "live" on over a period of time. Let's say 50 years.
So 50 years you will need X amount of money each month. Let's say this amount is $3000, of course this amount must be changed accordingly to inflation.
So for 50 years, $3000 each month, with inflation, tax and everything how much would u need to invest to make it? (calculated with the growth % of the stock market in mind)

Replies would be appreciated as a 2 part answer, one for how much money you need if you still want to have the money left after 50 years and/or if your money is depleted in 50 years.

I sure hope someone understands and can help me with this problem. Sorry for bad english.

[Dan Mezick]

10 million in investment cash is generally considered "entry level rich" in the USA. Inflation may take that to 15 million shortly.

[crazy canuck]

Lets assume your starting capital is X. Now assume that the stock market gives you a constant return of r, and assume you take out an amount A in each period pre tax.

So in period 0 you have X.

After 1 year you have (1+r)*X-A.

After 2 years you have (1+r)^2*X-A*(1+r)-A.

After 3 years you have (1+r)^3*X-A*(1+r)^2-A*(1+r)-A.

So after n years u have:

(1+r)^n*X - A*(1+r)^(n-1) - A*(1+r)^(n-2) .... - A.

Now u can use geometric sum formula for:

A*(1+r)^(n-1) + A*(1+r)^(n-2) .... + A =

= A*[1-(1+r)^n]/[1-(1+r)]=-A*[1-(1+r)^n]/r

So the final formula is:

(1+r)^n*X + A*[1-(1+r)^n]/r = (1+r)^n*(X-A/r)+A/r

So if after 50 years you want to have B, then set above to

B and you're starting capital is:

X=(B-A/R)/(1+r)^50 + A/r

So suppose you want to have 100K left (remember to readjust this amount for inflation) and stock market returns 4% above risk free interest rate and want to take out 30K each year then (in thousands):

X=(100-30/0.04)/(1.04)^50 + 30/0.04 = -91.5 + 750

=658.5 K

If you want to have 0 left then the starting amount is:

X=(0-30/0.04)/(1.04)^50 + 30/0.04 = -105.5 + 750 =

=644.5 K


Now there are several problems with this type of calculation.

First, of all it is hard to tell what the stock market return is going to be. Over the last 100 years in the US it was 6% above risk free interest rate. Many financial planners use this stupidly. However, economist studied other international markets and concluded it should be 3% (this is called equity premium puzzle), becasue the US had a phenomenal century.

And also the stock market return is not constant. This can ruin the above calculation. So the above calculation is kind of like planning based on the assumption that your poker earnings are the same each month. So if you start out with a disasterous year in which stock market drops 10% then you need way more initial capital than the above formula suggests to make up for this initial loss.

[KaneKungFu123]

This formula excludes tax/fees.

[crazy canuck]

This formula excludes tax/fees.

As I said A stands for pre-tax. So if u want to have 3K each month and u pay 30% tax on 36K/year, then let A=3K/0.3

Fees are easy to adjust for also.

[Sniper]

You are independently wealthy... when your passive income exceeds yours expenses!!!

[SpicyF]

Great reply, thank you! This was exactly what I was looking for!

[BradleyT]

Well Snipers response was the correct one though.

[ QUOTE ]
Formula for/to calculate independently wealthy


[/ QUOTE ]

If liquid assets > $10M (net of debt), you are independently wealthy. If >$20M, you are stinkin rich.

[Sniper]

[ QUOTE ]
If liquid assets > $10M (net of debt), you are independently wealthy. If >$20M, you are stinkin rich.

[/ QUOTE ]

The problem with using a fixed dollar amount as a generalization is that everyones expenses are different. In fact, for most people, the more they make, the higher their expenses.

$10 million may sound like alot to you, but to someone with 1 million/month in expenses its probably not looking so hot!

It costs alot to keep the castle, yacht and private jet running smoothly [img]/images/graemlins/wink.gif[/img]