# 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

• 5% annual return
• \$10,000 per month net income (please don’t get hung up on amount, the results are scalable, so if you want to use \$6,000 instead the number of months to retirement to replace a certain % of consumption are still the same)
• Abe saves “only” 20% (actually more than most Americans) and consumes \$8,000 per month
• Ben saves 60% and consumes \$4,000 per month, actually still a lot of money compared to how little many turbo savers and early retirees have to spend. So, we’re not even going completely rustic like the 75% savings rate recommended by some. But we have those results too, further below!

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:

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.

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):

• Assume 1,740 cohorts (145*12) that each start saving in Jan-1871 until Dec-2015
• Save 60% of net income and invest in the S&P500 stock index. Assume 0.08% annual fees from ETF/Mutual Fund
• Net income grows by inflation
• No tax-loss harvesting
• Using a 3.92% withdrawal rate (4% less annual fees), how many months does it take to get to the crossover point, where withdrawals are as high as monthly real consumption?

Results:

• On average these cohorts would have retired after only 136 months. The median is even a bit lower at only 132 months, or 11 years
• The fastest cohort started saving in Sep 1923 and needed only 72 months during the roaring 1920, only to retire in Sep 1929, right before the great market meltdown. The path to reaching the savings goal was just one straight line up, see chart below
• The slowest cohort started saving in May 1961. It needed 219 months and retired in August 1979. You almost made it in around the median time, but the setback  of the 1973-75 recession brought you back to just above 50% progress
• The most recent cohort that could have retired by December 2015, started saving in June 2005 and needed only 126 months, 10.5 years, to reach the crossover point. Astonishing, because they were hit by the global financial crisis, visible as a small setback between months 36 and 48, but of course also participated in the strong rebound
• If you stared saving in October 2007 (peak before last recession) you are making very good progress now, almost 80% there!

## 11 thoughts on “Early Retirement Math 101”

1. Great post! I really like all of the in-depth calculations. I’m going with the “save as much as possible and hope that the market doesn’t crash at the end” plan. How terrible would it be to almost at FI in 1973 and then have a huge bear market and have to work an additional six years? That would be difficult for me to swallow.

1. Thanks!
We’re worrying about the bear market scenario too. But then again, it turns out that a quick bear market right at the beginning of retirement will likely not derail your retirement. 1929-1933 did, but that was exceptionally bad. The more insidious outcome would be a situation like 1966, with flat returns for 7 years, then a bear market. That would wipe out your savings under a 4% rule.
But being flexible with the spending, using the CAPE-based withdrawal rule (https://earlyretirementnow.com/2016/04/15/pros-and-cons-of-different-withdrawal-rate-rules/), additional sources of income including rental income, one should be able to weather that storm too.

1. Good points. Early retirement is all about being flexible and it’s much easier to be flexible when younger and healthy anyway.

2. Amy G says:

I discovered FIRE 4 days ago and am devouring the blogs and data. Simple question: is the saving rate taken from gross income or net?

3. Amy G says:

NET income! Found the answer. Thanks!

1. For this particular calculation, net would be more appropriate. True! 🙂

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