The Math Checks Out

The math behind financial freedom is simple. It all boils down to one thing: your savings rate.

Your savings rate determines when you become independent. It determines how much freedom you are building up every month. It is what you should focus on. Everything else is secondary to this number. Your income, current worth, return on investment, and any other metric you can think of are all less important.

Savings rate = savings / income * 100

Why does your savings rate matter so much?

Let’s start with a simple example: (source)

As you can see, increasing your savings rate significantly reduces the time it takes to save. Makes sense.

But somehow these numbers are often a bit surprising. Maybe it is because we have been told that a reasonable savings rate is somewhere in the 10 - 15% range. So we never stopped to consider what would happen if we instead saved 66% of our income. The answer is that we would only need to work ~ 6 months ((1-0.66)/0.66 = 0.52) to save for 1 year of living expenses.

Work 6 months, take off 1 year. Sounds pretty damn good, no?

How Much Do You Need?

To continue our journey we need to determine how much we need to become independent. When does work become optional?

Maybe you don’t care much about retirement/independence right now - that’s fine. But take some time to absorb this information still. It is part of a bigger point and without it you’ll miss the full picture.

Estimating how much money you need to stop working is not an exact science. We don’t know what the future brings and we can’t plan for the unknown. Maybe AI will take over and we’ll all be retired with UBI in a few years, who knows?

With that said, there are some rough guidelines - based on historic data - we can follow.

The 4% Rule

A general guideline is the 4% rule - based on a study often referred to as the Trinity Study (a 1998 paper by three professors at Trinity University). The rule suggests that 4% can be used as a rough guideline for a safe withdrawal rate. This 4% is based on the initial portfolio value at the start of retirement. So whatever value your portfolio has, 4% of that is your annual budget in dollars.

This is a useful way to think about retirement portfolio value as we can estimate the required size based on our current expenses. We just need a portfolio big enough that 4% covers our annual spending.

According to the Trinity Study, a 4% withdrawal rate keeping up with inflation has a very low failure rate. Using historical data from 1926 to 1995, the study shows a retiree would be able to withdraw for 30 years with a low risk of exhausting the entire portfolio and thereby running out of money. For a 100% stock-based portfolio the success rate was 95% and for a 75/25 stock/bond portfolio it was 98%. For a 50/50 portfolio the success rate was also 95%.

The Trinity Study suggests 4%. But it is by no means a guarantee. High success rate does not mean guaranteed success. There was a risk the portfolio would deplete (2-5%). And if your retirement is longer than 30 years the risk of depletion increases (although probably not by much).

But as mentioned before, nobody knows what the future will bring. 3% is safer than 4%. But it will also take you longer to accumulate. So you risk working longer building up a bigger portfolio you may never need.

Finally, the 21st century is bound to be different than the 20th century.

All of this is is to say the 4% rule is a debated topic. (This post argues for the 4% rule and this series has a lot of information arguing against blindly following it.)

I’ll use 4% in the following calculations. If you prefer another number you should be able follow along and redo the examples with another safe withdrawal rate.

Portfolio value

Using the 4% rule we can now estimate our retirement portfolio value.

What we want is:

Retirement portfolio * 4% = annual spending

As this means we can satisfy our annual spending with 4% of our portfolio.

So to get our retirement portfolio value:

Retirement portfolio = annual spending / 4%

And as dividing by 4% is the same as multiplying by 25 (4% = 4/100 = 1/25) we get:

Retirement portfolio = annual spending * 25

To be financially independent we need a portfolio 25 times the size our our annual spending.

Years to retirement

We can now go back to our example and add our 25 multiplier:

At this point it should be quite clear how much of an impact the savings rate has.

But something seems a bit off - a “normal” savings rate is usually in the 10-25% range and most people expect to work less then 75 years (and certainly less than 225!) before they retire. What is missing?

What we don’t account for yet is investment returns. In our current example our money simply follows inflation without any excess returns (note that this isn’t the same as just keeping our money in a bank account - if we did that we would not even reach financial independence after 225 years!)

Investment returns

The reason it takes 225 years to retire on a 10% savings rate in our example above is that we don’t do anything with our money in those 225 years. We just put them in something that follows inflation. If we instead invested our money in something that had a better return than inflation, we’d be financially free a lot earlier.

The historical average annual return, adjusted for inflation, is around 6.37% for the S&P500 according to Investopedia and according to moneychimp:

Over the very long run, the stock market has had an inflation-adjusted annualized return rate of between six and seven percent.

Another factor that impacts our real investment returns is tax. A complicated topic with lots of different nuances depending on your jurisdiction. Our simplifying assumption here will be a 33% tax which gives us a nice round number for our return after tax and inflation: 4%.

Our assumptions:

• Overall return: 10%
• After adjusting for inflation: 6%
• After adjusting for inflation and tax: 4%

4% is maybe a bit pessimistic. Here is the example with 6%:

I have used this tool to compute the final scenarios. I suggest you play around with it a bit. It gives you a good feel for how the different metrics influence your time-to-retirement. Also, on the graph you can see the fun begins at the higher savings rates and each percentage point matters quite a bit.