We’re starting with this post because it perfectly encapsulates what this website is all about: early retirement or at least, getting ahead financially. A little extra thought goes a long way in understanding exactly what we’re working toward, so let’s begin on a high note and one of the best results we have to offer.
Today, we’re working toward a very intuitive retirement calculator. If you’re asking yourself how soon retirement is actually possible, then this post is for you.
Savings Rate
The importance of the Savings Rate is very well understood and often repeated in F.I.R.E. literature (Financial Independence Retire Early). While it’ll be used nearly everywhere on this site, let’s briefly define it here. Your savings rate p is the following.
p=1-\frac{\textrm{what you spend}}{\textrm{what you earn}} = \frac{\textrm{what you keep}}{\textrm{what you earn}}Let’s say your spending is what you have control over (so exclude taxes and benefits you wouldn’t choose to opt into), but your earnings include your take-home pay, 401k contributions (or equivalent), employer 401k contributions (match), and benefits you intend to keep purchasing post-retirement. Then p is simply the proportion of your earnings you keep each month (or year).
By way of example, someone who has a base pay of $3000/mo with 5% going into 401k to get the employers 5% match but doesn’t save anything outside the 401k has a savings rate of p_1\approx0.1, calculated below. Someone else who earns a total of $8000/mo but only spends $2000/mo of it, has a savings rate of p_2=0.75.
p_1 = \frac{300}{3150}=0.095\approx 0.1 \textrm{~, and~~~}p_2 = \frac{6000}{8000}=0.75Our 401k saver above with p_1\approx0.1 will have a standard length career of 50-some years, but p_2=0.75 guy will be able to retire only 7 years after he began furiously saving. This MMM article (same link as above) shows a table of other values, most notable being that p_3=0.5 savings rate can retire us in 17 years. Your length of time to retirement is determined entirely by your savings rate, but not so much by your income. In a subsequent post, we’ll show where these time estimates come from, but today we’ll begin to build a solid intuition (in tandem with a mathematical framework) for why this is true.
Savings Ratio
Let’s take it one step further than everyone else. If p is your savings rate, then your savings ratio R is the following.
R = \frac{p}{1-p} = \frac{\textrm{what you save}}{\textrm{what you spend}}~,~~0< p<1The savings ratio is an interesting value. While it is a unitless quantity, we can legitimately think of it as multiples of expenses. It works both as a multiple of your monthly expenses and a multiple of your annual expenses. Whatever timeframe you’re thinking in terms of, you’re saving R times more than you’re spending.
Examples. When p_1\approx0.1 is the savings rate, then the savings ratio is R_1\approx\frac{0.1}{0.9}= \frac{1}{9}. If p_2=0.75, then R_2=\frac{0.75}{0.25}=3 and you’re saving 3 times more than you’re spending per year. Finally, for p_3=0.5 we have simply R_3=\frac{0.5}{1-0.5} = 1 in which case you’re saving a month of expenses for each month worked.
Easiest Retirement Calculator
What does all this math buy us? Insight into freedom. Every time you accumulate (save) an extra month of expenses, you can exist without the job for one more month. When R=1, you’re spending as fast as you’re saving, and every month you save another month of freedom. When R=2, then you’re saving twice as fast as you’re spending and every 6 months at the job buys you 12 months of freedom. When R_1=\frac{1}{9}, then every 9 months at work buys you one month of freedom.
When you collect 25 years (or 300 months) of living expenses in your savings account, then you can retire whenever you want. The 4% rule (which is a big topic to be covered in more detail later) says that when you have a pile of savings invested appropriately, then you can withdraw 4% of that every year (inflation-adjusted) and the remainder will continue to grow larger over time (even outpacing inflation).
What happens when you collect R times your expenses every month over time? Well, they add up. After N months (or years), you have the following.
\underbrace{R + R + R + \cdots + R}_{N\textrm{ of these}} = N\cdot RAfter N months (or years) of saving at a ratio R accumulates into N\cdot R multiples of expenses. When you reach 300 months (or 25 years) of expenses saved up, then you’re effectively F.I.R.E. Simply solve N=300/R for how many months it takes until optional retirement (N = 25/R for years). The larger R is, the sooner you can break up with your boss.
Same examples. If R_2=3, then N=300/R_2=300/3=100\textrm{ months} or 8 years. When R_3=1, retirement can happen in N=25/R_3=25\textrm{ years}. These numbers are slightly larger than what was said above (7 years and 17 years, resp) because this equation ignores interest on your savings (the R values) pre-retirement.
Summary
There it is. The internet’s easiest back-of-the-napkin math for early retirement. It assumes
- No interest or capital gains on your savings pre-retirement (unrealistic),
- 4% withdrawl post-retirement (generally conservative), and
- Consistent spending post-retirement (generally conservative).
In a later post, we’ll overthink things further and let the R values collect their own interest pre-retirement for a much more realistic retirement calculation. The understanding we just built above will make the addition surprisingly easy.