# A tale of two graphs

Today, how about a couple of simple graphs.  Starting with;

On the x-axis the percentage of your income saved.

On the y-axis how long you would be able to take off work for each year of saving.  Or to make it easier Years-Saved-per-Year-of-Saving (“YSpYoS”).  YSpYoS =  % of income saved / (1-% of income saved)

The graph is really just Y = X/(1-X), and it’s a beauty.

The Finance Zombies – Years Saved per Year of Saving (YSpYoS)

The graph gives us a  visual relationship between annual savings rates and annual expense.  For example, each year spent saving 20% of your income allows you to take a quarter of a year off work.

• Saving 33.3% of your income for a year = 1/2 a year off work
• Saving 50% of your income for a year = 1 year off work
• Saving 66.67% of your income for a year = 2 years off work
• Saving 75% of your income for a year – 3 years off work

There is an exponential kick in the tail of this graph, meaning the gradient gets steeper as you move further along the x-axis.  Initially you need to move all the way from saving 0% right up to saving 50% annually to hit one year of savings being equal to one year of living expenses.  The point of savings parity.  Then save an additional 16.67% and you have netted yourself another year of freedom for each year worked, that’s 2 for the price of 1.  That first year required you to save 50% of your income, the second ‘only’ an additional 16.67%.

It gets better, an extra 7.33% on top of that and you’ve got yourself three years of freedom for every year worked.  That’s right, save 75% of your income in one year and you could take three years off work spending at the same rate, or be absolutely belting along the path towards financial independence.

No doubt about it, saving 75% of your income is tough.  Realistically it requires earning a fairly large wage.  It requires a fairly large wage, but not a ridiculous wage, it is more achievable than many realise.  Saving 75% of your income will require a strong resolve as it is going against the social norm of seemingly trying to spend all that you earn.  Aiming for a savings rate of 75% and placing it to work as capital to later buy freedom is far more enticing than chasing payrises to buy another car.

Phew, take a step back, things were about to get heated there.  Let’s refresh.  Cranking up your savings rate and reducing your outgoings has an exponential impact on the relative size of your savings to your outgoings because you are simultaneously saving more whilst requiring less to live off.

We could argue tax and expenses, how you define your savings rate and other semantics.  Regardless, the shape of the graph would stay similar.  We can argue about asset allocations, invest strategies, passive or active investing.  Despite all the complications available to us, this graph is a nice reminder that a lot of the times it’s best to Keep It Simple.  Our savings rate is the biggest contributor to wealth during much of the accumulation phase and so it makes sense to focus on it.

Point being, save more of your income and your expenses must be dropping (assuming you aren’t being an idiot and resorting to credit to boost your savings).  Or decrease your expenses and the amount available to save increases.  Savings of £300k mean more to someone with outgoings of £15k compared to the guy chewing through £100k a year.  One has security and happiness, the other a stupid boat called Boaty McBoatface.

Of course, it’s a balancing act.  Get caught up in simply just maximising your savings rate (or your income) and you will start to actually reduce happiness along the way.  Happiness is an ethereal thing that doesn’t lend itself well to measurement.  Luckily I am an ethereal being, allow me to enter the other dimensions and measure it for you;

The savings rate happiness curve

We’ll start this by assuming we can save, i.e. income is greater than fixed expenses.  At the bottom left we have mindless consumption. Somewhere in the middle we reach a peak on the happiness-saving curve.  And at the very top right we have mindless & obsessive saving.  Once we reach the point where we are eating dirt and wearing bin bags in the name of thrift, things start to descend with terrible rapidity.

Savings bring us security, freedom and happiness.  And a higher savings rate brings this about faster.  But this needs to be balanced with enjoying life whilst saving.  Saving and increasing your savings rate can get addictive, possibly all consuming.  Foregoing living just to save a bit more is bad.  This is advanced level personal finance shit we are talking here, if you are still carrying credit card balances, mindlessly walking about shopping centres and buying stuff you don’t need, sort that out first before you start to worry about saving too much.

These two graphs are not the same shape.  The first tears a path upwards towards infinity, while the second has a turning point.  Blindly chasing the endless more is a recipe for failure.  More being either endless consumption or the ever higher savings rate.  Somewhere in between these two lies the happiness turning point, where the gradient momentarily hits 0, the peak is reached before the gravity of the function pulls it southwards once again.

If we could define our own happiness function, Happiness = f(Savings Rate), we could differentiate it, set it equal to zero and solve to find our peak savings rate.  Sadly, this is not possible.

You will notice on the graph that the savings rate that provides peak happiness is not defined, that’s because it will be depend on the individual.  We need to find our own savings happy medium, it’s not something that is fixed.

On our tight rope walk across to the Utopia of Financial Independence we need to balance enjoying living in the now with saving so that the future you can enjoy the freedom provided by a large chunk of capital.

I want to be able to look wistfully into the past as say “Thank you past Mr Z for all your hard work, you truly are a top chap“.  Or perhaps have large mural of the historic Mr Z in my house, captured perfectly, hunched over a terminal, frantically typing shit into Excel, a constant reminder of the hard work that was put in and the good financial decisions made.

The freedom brought by not having to live pay check to pay check, or having to go to work just for the income, shouldn’t be understated,  Either should the happiness brought about by a simpler life, free from the endless consumption of the shopping mall lifestyle.  Simplify your life, work for a short few years and bank the difference.  End result, freedom and happiness.  That’s the plan, at least 🙂

Mr Z

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## 7 thoughts on “A tale of two graphs”

1. Income Surfer

Well said Zombie. We’re just beginning to sample F.I., and it’s outstanding. We saved and invested hard upfront, and now we have the flexibility do work on projects we want…..and to follow our passions. Hope we don’t screw it up 🙂
-Bryan

1. Mr Zombie Post author

Thanks Bryan 🙂

It sounds amazing. And I am following with a keen (jealous) interest!

All the best,

Mr Z

2. Tawcan

Well said Mr. Z. It’s a balancing act when it comes to how much you save and how much you spend to enjoy life now. If you just save and Ave but not enjoy life, do you really think you can do that once you reach FI? Vice versa, YOLO mentality is definitely not the right approach either.

1. Mr Zombie Post author

There’s a fine balance that’s for sure.

Keep on cranking buddy – I know you smashed through \$10k of divi income and have been building side income too. You’ll be there soon!

3. ZJ Thorne

It is definitely hard to walk this line. For right now, my girlfriend is working even more than I am, which means that building up all these side hustles, when it does not mean taking time away from us, is a great use of my current time. That’ll change when here work downshifts in a few months. Hopefully, then I’ll be in a good groove.