NEW FORMULA for early retirement

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frugal
Posts: 72
Joined: Thu Sep 06, 2012 11:35 pm

NEW FORMULA for early retirement

Post by frugal »

Hello !

The new and safe formula to retire early is:

CAPITAL needed = Number of YEARS you will live x YEARLY EXPENSES x (1+ average %inflation)^years

Example:

Minimum Capital = 60 years x 15.000 USD x 1,02^60

= 60 x 15.000 x 3,3 =

= 2.952.000 USD


This assumes you will only have cash, to be on the safe side.

The return of your cash would be ZERO.

What is your opinion about my math?


In the end you will spend:

2.952.000 / 60 / 12 = 4.100 USD per month on average


2% inflation causes a lot of damage!


Without considering inflation, which is not real, it would be:

15.000 x 60 = 900.000 USD

1.250 USD per month


Waiting your advises I remain.

Regards!
:idea: :idea: :idea:

phil
Posts: 45
Joined: Thu Jan 09, 2014 10:05 am

Re: NEW FORMULA for early retirement

Post by phil »

your math is wrong. The formula assumes that all cash is spent after 60 years of inflation. I suggest you put this in Excel; with x being the capital needed and expenses in year i being (current yearly expenses)*1.02^i, find x so that cash left after 60 years equals zero. There is no simple formula to calculate x AFAIK.

Laura Ingalls
Posts: 668
Joined: Mon Jun 25, 2012 3:13 am

Re: NEW FORMULA for early retirement

Post by Laura Ingalls »

How exactly is anyone supposed to accomplish such an early retirement with such a conservative asset allocations? If you want to retire after 15 years of working you are going to have to save six figures every year.

To me one of the points of ER in general is that market appreciation works for you both in the accumulation and retirement phases. My money does the work so I can work less :D .

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fiby41
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Re: NEW FORMULA for early retirement

Post by fiby41 »

The math is right (for 100% drawdown on principal.) This is probably how they calculate to price the annuity of the type which have fixed monthly payouts.

The requirement number is so large because frugal assumes real rate of return (expected appreciation of principal minus inflation) to be -2%

Here's my journal entry in which I had done this calculation:
...so l made a rough back of the textbook estimate (which cost me in resale value of the textbook.)

It took into account 8% inflation and no capital gains.
Life expectancy: 100 years.
Since I made it ~1.5 years ago ...
Go to post: viewtopic.php?t=6084#p94916

Frugal's formula is special case of the Compound Interest Formula, which I had used, for n=1,

A=P*{1+r/n}^(nt)

Where
P is principal
r is rate of interest
t time
n is yearly compounding
A is total

Laura's first paragraph above might be amussing to some but I seriously was depressed for 3-4 months by such a large number, especially as I took fiyear to be 26.

APY annualised percentage yeild formula can also be used instead, where you already know the APY and are solving for principal amount required:

APY=100*[({1+(Interest/Principal)}^365/Days in term)-1]

jacob
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Re: NEW FORMULA for early retirement

Post by jacob »

The formula is wrong or maybe rather not appropriate for what you intended to calculate. Your formula assumes that all the monies are withdrawn in the final year and not before; whereas for an annuity, you would want to withdraw fixed amounts at regular intervals. A proper annuity calculation would result in less required starting capital since you're not discounting the withdrawal in year n with inflation in years [N-n+1;N] because it's already spent.

The exact answer for an annuity (assuming constant returns---which is a bit of a stretch anyway) can be found analytically (see e.g. ERE book eq. 7.8 for the result and preceding eqs. 7.1-7.7 for the derivation) and it's not pretty. Since you're assuming no yield and inflation, simply use a negative value for i. You do not need to solve this numerically.

frugal
Posts: 72
Joined: Thu Sep 06, 2012 11:35 pm

Re: NEW FORMULA for early retirement

Post by frugal »

hi JACOB,

how are you?

Can you please let me know a link with the correct FORMULA(s) ?

Thanks


Fish
Posts: 570
Joined: Sun Jun 12, 2016 9:09 am

Re: NEW FORMULA for early retirement

Post by Fish »

@frugal - You want the “PV of annuity with growth” formula (source: http://financeformulas.net/Present_Valu ... nuity.html):

PV = P/(r-g) * [1 - ((1+g)/(1+r))^n]

Where:
P = initial payment,
r = investment yield (= 0 in this case)
g = payment growth rate (= 0.02 with 2% inflation assumption)
n = number of payment periods

This equation derives from the geometric series if you’re familiar with that. If not, you can read a math textbook or the internet to learn more.

For your example, if we set P=1, r=0, g=0.02, and n=60, we get the result that a fund size of 114.1 years is needed to provide 60 years of inflation-adjusted withdrawals with zero yield and 2% inflation. For P=15,000 USD the required fund is 1,710,000 USD.

The conclusion is that with such pessimistic assumptions, extreme early retirement still relies heavily on yield unless you can manage a very high savings rate (90%+). This might be a safe approach to planning for retirement but is extremely conservative and not practically attainable by most.

On a similar note, JL Collins recently had a guest post on the ”Wasting Asset Retirement Model” which presumes 0% SWR. This is suggested as an alternative for those who don’t have the temperament for a 100% stock portfolio. As expected, the accumulation target (in years of expenses) = years of retirement in this model. For long retirement periods, say 60 years, it represents a significant increase over the commonly used 25-33x expenses.

Actually I think devising these simple, safe, conservative accumulation targets is a very good thing given the popularization of FI/RE in the general population. Even the usual 3-4% SWR requires some investing knowledge, competence and temperament. Some very conservative target of 60+ years of expenses should be the initial goal, and being able to go down to 25-33x should be the reward for figuring out the investing part of the retirement puzzle.

Edit: Fixed formula
Last edited by Fish on Mon Oct 09, 2017 4:10 pm, edited 1 time in total.

frugal
Posts: 72
Joined: Thu Sep 06, 2012 11:35 pm

Re: NEW FORMULA for early retirement

Post by frugal »

Bravo FISH!

Well done.

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