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Early Retirement Math 101

Here are some simple calculations to show the benefit of compounding and the power of turbo-charging your savings. If you don’t believe you too can get rich in 10-15 years keep reading!

The power of compounding

For the average retirement saver this effect is huge. Compounding your investments over 40 or so years works wonders with your savings. If we assume a real index return of 5% (net of inflation, dividends reinvested), the first dollar invested grows to $7.04 in real terms. Investing one dollar every month, adjusted by inflation and compounded with 5% annual return gives you almost $1,500 after 40 years.

For the turbo retiree who wants to retire after, say, 150 months (12.5 years), compounding has a lot less opportunity to unfold. That first dollar grows to only $1.84 in real, inflation-adjusted terms. Investing one dollar monthly (inflation adjusted) and getting 5% real return yields only around $206 after 150 months.

What we lose due to less compounding we have to make up with frugality!

The power of frugality

During the accumulation phase, every dollar we don’t spend every month accelerates the retirement date in two ways:

  1. You have an additional dollar every month to save and invest, obviously! About $206 over 150 months.
  2. Assuming you shoot for a 4% withdrawal rate you lower the target Portfolio Value by a full $25*12=$300 if you can keep up that reduced spending during retirement as well.

For the turbo investor that second effect is actually even more valuable than the first (300>206). Not convinced? Take a look at this example

After 150 months, Abe has accumulated $412,459. A respectable amount, but a far cry from being able to afford retirement; this cash stash can yield around $1,375 per month (real, inflation adjusted) at a 4% annual withdrawal rate, only about 17% of the consumption level Abe has gotten used to. In fact, it would take a total of 437 months, over 36 years, to be able to reach an inflation adjusted level of $8,000 per month in consumption.

Ben, on the other hand, has $1,237,377 after 150 months, exactly three times of Abe’s savings. This amount would be able to fund around $4,125 per month, more than enough finance the $4,000 in inflation adjusted consumption Ben has been accustomed to. By consuming only half of Abe’s monthly budget, Ben has slashed the time to retirement by about two thirds! Actually, the crossover-point occurs already after 147 months, 12.25 years, even with zero initial net worth. Intriguingly, most of closing the gap came from the lower consumption target. Out of the 83% shortfall that Abe experiences, Ben makes up 50 points from the lower consumption target and 33 points from the higher asset accumulation, see chart below:

Frugality vs. Compounding

 

So, to the people who don’t believe that a lot of people in the Early Retirement community are truly self-made (as opposed to getting an inheritance from some rich uncle), look at the numbers. It is perfectly possible for aggressive savers to have enough to retire in their 30s! Also notice that these results are scalable. Not everybody makes $10,000 per month after taxes, I know. So saving 60% of your $7,000 monthly income works just the same.

What if we go really, I mean really, frugal? Here’s the number of years needed to achieve the crossover point, as a function of the savings rate, again assuming 5% real return, 4% withdrawal rate. At 75% we’re looking at only about 7 years. At 80% savings rate only slightly above 5 years. On the other hand, if you save less than 40% you are looking at a multi-decade slog. At 20% we’re back to the 36 years. You might as well count on Social Security.

The power of frugality

What about actual returns?

Not surprisingly, actual returns would have generated even faster results. That’s because over the long-haul equity returns were quite a bit higher than 5%, closer to 6.75%. I did some simulations with equity return data starting in Jan-1871 (not a typo, that’s 145 years ago):

Results:

 

Fast, Slow and two other cohorts

 

 

 

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