Financial Independence, simply defined, is when your passively produced income
is enough to pay for your life’s expenses. But how do you get
there? When at the beginning of the path, it can seem daunting.
Even imaging enough wealth to generate that kind of passive income is a
challenge. However, the good news, and the real point of this blog, is
that the decisions we make along this path drive non-linear results.

A mathematician would tell you that a linear function is defined by the output
being directly proportional to the input. Your elementary school teacher
would say they make a straight line on a graph. Fortunately, on the
quest for Financial Independence, we leverage the power of non-linear
mathematics. Maybe the most powerful, the exponential effect of compound
interest when investing, we will get to later. However, it starts with
the disproportional effect of saving versus spending. Let’s explore that
now.

A useful metric to track is the ** Savings Rate**, commonly defined as the amount you save in a year divided by the total
amount you make in a year. So, as an example, let’s say you had
take-home pay of $50,000 in a year and spent $40,000 on expenses that same
year. That gives you $10,000 left over, which by definition you have
saved since you didn’t spend it.

$$Income\ per\ Time\ -\ Expenses\ per\ Time=Savings\ per\ Time$$

Your savings rate would then be calculated as:

In fact, as long as the time period is the same between the income and savings, you could evaluate the Savings Rate over any period of time, from a single paycheck to years. A year is a common choice because many of our life’s expenses come in chunks that repeat annually. For example, looking at the first few months of the year might not give a clear picture if a bunch of tax payments, insurance premiums, and holiday spending skews the result later in the year. So more generally, the equation is:

Being dimensionless makes it easier to compare. Two people with
different incomes may have very different savings goals, but they can
compare savings rates to give them a common language to discuss Financial
Independence. However, there are some issues with this
calculation. Is it before tax or after-tax income? Where do 401k
contributions go? Ask these questions of different experts and you
will get different answers. It’s also not immediately clear what
effect different saving rates have on your path to Financial
Independence.

A related calculation I use is the ** Stash Rate**. Much like the savings rate, this is a dimensionless number.
It is defined as:

$$Stash\ Rate={Savings\ per\ Time \over Expenses\ per \ Time}$$

Notice in using this equation that we have eliminated the income term. When looking at a year, for example, you now take the total amount of money you stashed away in any savings or investing vehicles (we will dig into the different types in future articles and why they all count) and divide it by your expenses for the year.

The result can again be interpreted as a percent, but it may be more useful to think of it as a multiple. Let’s look at some numbers to see what I mean. Using the same example as before:

$$Stash\ Rate={Savings\ per\ Time \over Expenses\ per \ Time} = {$10,000 / year \over $40,000 / year} = 0.25$$

This time, instead of $50,000 of income in the denominator, you have
$40,000 of expenses. The important result is that
**you have saved 0.25 of a year’s worth of expenses.** This is
meaningful on the journey to financial independence. If you can save
0.25 of a year’s worth of expenses, then the message is simple. You
can work for 4 years and afford to take
one yearFor the time being, we'll ignore inflation and earning a return
on our money that will outpace it. That concept will help our
money last longer and we will cover it in future articles. For
now, let’s keep the math simple and pretend we are just going to live
off of what we have saved.
off (0.25 + 0.25 + 0.25 + 0.25 = 1.0). Some people with
aspirations to take a year to travel the world or dive into a startup may
do exactly that. The rest of us may instead choose to work many
years and take the remainder off.

But the numbers here aren’t very promising yet. In the example, you
would have to work 40 years just to take 10 off. The compounding
returns of investing our savings will certainly help, but compounding
takes time. For those of us looking to reach financial independence
earlier, there must be a better a way.

Fortunately, non-linear math comes to our rescue! The way to
accelerate this path is to ** Grow the Gap**. To grow the gap, we must put as large a gap between our income
and our expenses as possible. To continue with the example in this
article, let’s say your income is fixed (a common scenario of W-2 job
where we expect modest raises, just keeping up with inflation over the
years) so we focus on your expenses. In other articles we will
tackle different methods and life hacks to do this. For now, let’s
just focus on the numbers. Let’s say you can reduce your expenses by
10%. What happens? Expenses were $40,000, now they drop to
$36,000. By definition, that means your savings now increases to
$14,000. Therefore, your Stash Rate climbs to:

$${$14,000 / year \over $36,000 / year} \approx 0.39$$

Now that’s interesting: you reduced our expenses by 10% but your stash rate went up over 55%0.39 / 0.25. Instead of working four years to have one free, we’ve brought it down to just over two and half. Let’s try another example. What if you can decrease our expenses by 25% all the way to $30,000?

$${$20,000 / year \over $30,000 / year} \approx 0.67$$

The stash rate tells us how many years of freedom we’ve bought. In this case, you’ve bought a full two-thirds of a year in just one year. If you can get your savings to match your expenses, then not surprisingly you have bought yourself a year of freedom in just one yearFor example: $25,000 / $25,000 = 1.0 of working.

As we approach and then cross a stash rate of 1.0, the impact flips.
We can now take more than a year off for every year we’ve worked. If
we can save 3 dollars for every dollar we spend, we can work a year and
then take 3 off. You could work 15 and take 45 off, flipping
traditional retirement on its head!

*Remember the Stash Rate definition: the vertical axis can also be
interpreted as years of expenses saved per year worked. Note
the crossover point at 50% Stash Rate accumulating one year's worth of
expenses.*

What’s your financial situation? Can you save a dollar for every
dollar you spend? Can you save three? It might be hard in our
$50k example to imagine spending only $12,500 per year, but it’s not
impossible. More realistically, we’ll pull both levers of ** Grow the Gap** and try to increase our income at the same time. Making
$100,000 and spending $25,000 so we can save $75,000 doesn’t seem as
farfetched.

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