One question we get quite a bit is related to the fundamentals of saving: *is there a magic savings rate?*

In the past we’ve looked at the ideal savings rate. There we suggested 20% as a minimum savings rate, with the caveat you should save more if you can.

Interestingly, there are also some *magical savings rates*. These rates are mathematically elegant: *without even worrying *about returns, they help you reason about savings and amounts. Let’s discuss those magical mathematical breakpoints and savings rates today.

## The Most Magical Savings Rate

The most magical of all the savings rates is **50%**.

When you save 50%, for every year you work you’re saving one year’s worth of spending. In essence, *you’re paying for the entire next year by working during this one*.

Importantly, this property doesn’t require any investment gains whatsoever*.*

Presumably, you’re earning some interest on your savings. Even if you’re only being paid a small return, everything on top of 50% is gravy.

**Savings Rates vs. Whole Years of Spending**

*20%*, *25%, *and* 33%* are also magical savings rates. Although they don’t provide a spending buffer for an entire year, they also make the math easy on income replacement:

**20%**savings rate: for every 4 years of work, you save 1 year of spending.**25%**savings rate: for every 3 years of work, you save 1 year of spending.**33%**savings rate: for every 2 years of work, you save 1 year of spending.

*How does it work so cleanly?*

It
boils down to a simple fact: **money you
save is money you aren’t spending. **Without knowing any more about your
situation, I know if you save money you didn’t pay it in tax or spend it.

## Extremely High Rates and Spending Breakpoints

Because of the above property that *saving is non-spending*, extremely high savings rates make the financial picture even better. For this article, **we’re calling a savings rate over 50% extremely high savings rates**.

That makes the *inversion* of the above magical rates interesting. Flip the above rates for spending and
here’s what you get:

**80%**savings rate: every year, you save 4 year of spending.**75%**savings rate: every year, you save 3 year of spending.**66%**savings rate: every year, you save 2 year of spending.

Sometimes it helps to look at **savings** really as **spending buffer building**.

**The Deceiving Top End**

Now, undoubtedly, extremely high rates are… extremely hard to sustain. However, they cover up an interesting mathematical property: **savings rates aren’t linear**, they’re closer to exponential.

Take 50% savings, for example, which saves one year worth of spending. It takes an additional 16.7% savings to turn *1 year of savings* in a single year to *2 years of savings*.

Now you can see the curve…

Respectively, it takes *8.3%*, *5%*, then *3.33%* to add another year of spending buffer in a single year. These high rates are deceiving – by the time you get to 90% savings, *that’s 9 years of savings buffer for a single year of spending*.

## Capturing the Magic of High Savings Rates

The best part about reasoning about savings rates in this way? It doesn’t require coming up with investment gains or interest returns. All of these numbers are achievable with money under your mattress.

*(Don’t store money there…)*

The key takeaway: people tend to group these rates together, especially at the top end. However, because savings is “not spending”, extremely high savings rates are volatile.

The difference between 80% savings and 90% savings is **a whole 5 years of spending buffer** at 90%. Stated differently: a 90% savings rate is more than twice as effective as an 80% rate.

Now, the magic makes more sense. If you’re targeting financial independence, your goal should be as high a rate as possible. The more you save, the more years of buffer you build at once… and the less you need to worry about investment returns.

Celia Johnson says

This is the single most interesting piece of math I’ve ever seen in the personal finance arena. THANK YOU! 🙂

PK says

Thank you Celia, glad you enjoyed this piece!

spintwig.com says

I never had the inclination to explore the “why” behind the rapidly increasing difficulty of achieving higher and higher savings rates. Your graph answers that question nicely. Simple and elegant indeed.

Clint says

The other part of “why” it gets more difficult as you go up in savings rate is starting from no savings, you can go to 50% by cutting your spending in half. If you cut your spending in half again, you only gain 25% more on your savings rate, but your “replacement years” goes from 1 year to 3 years (making 2 years spending in one year at 50%, up to making 4 years spending in one year at 75%). When you think of it that way, it makes intuitive sense, but you have to add back the year of spending while earning in order to make the half/double relationship work.

PK says

Great explanation Clint, and it definitely shows why the ‘cut expenses’ side is harder and limited when you get down to it (kinda why I followed on with the post today, too – that switch to an income focus).

PK says

Thank you, glad you enjoyed it!