Compounding: There is no magic without saving (now!)

Date published: November 18, 2018

Many people have heard of the magic of compounding, and if you look at examples of historical charts (often using a 10% or so annual return for demonstrative purposes) it is indeed magical. However, when you next see one of these charts, have a quick squiz at the X-axis (the one along the bottom). What you will probably find is something along the lines of ‘0, 5, 10, 15, 20, 25, 30, 35, 40’.  What do these numbers refer to? Yes, indeed – FORTY YEARS.

So, yes, you can have a lot more money than you started with if you achieve a 10% return annually for forty years. I don’t know about you, but the Count and Countess will be well into their 70s at this point.

Waiting for the magic of compounding to achieve retirement at the tender age of 70? Well, that’s certainly not our plan! Additionally, fluctuations in investments often result in a return lower than 10% per annum.

An image that displays the Count awakening just in time to momentarily enjoying his compounded investments before dying of old age.
40 years on and mere seconds before dying of old age, the Count awakens just in time to momentarily enjoy his compounded investments.

You and your savings rate – a great team!

If, like us, your timeline to achieve financial freedom is a bit shorter – say, 10 to 20 years – what are your other options? The answer is… your savings rate! It is not the easy nor the sexy option, and it is definitely not often associated with the word ‘magic’.

However, with most wealth creation strategies that combine ‘easy’, ‘quick’, and ‘sexy’, financial disaster is probably just around the corner.

Savings rate is a simple calculation – it is the proportion of your after-tax income that you save (i.e. your income that is not spent on necessary or discretionary costs). For example, after tax we see about ~$85k of our combined ~$140k income (the Germans sure know how to tax!), and we spend ~$50k and save ~$35k annually.

That means that we have a savings rate of 35/85 = 40%. Below is a visualisation of our savings over the last 3 months of data (made using www.sankeymatic.com). Just bear in mind that we have removed income/expenses associated with investment (e.g. property rent, maintenance, dividends from shares etc.) to simplify things a little:

A figure showing our savings and expenses - made using www.sankeymatic.com
Savings and expenses – made using www.sankeymatic.com

Of course, the more months of data tracked, the better: any single month can fluctuate wildly. For example, one month this year we bought two return airfares from Europe to Australia scheduled for Christmas time and beachside accommodation. This resulted in a savings rate of about -50% for that month. Another month we decided to limit our spending (by not booking trips away or dining in restaurants), and we were able to achieve 55%.

Tracking your savings is a winner’s strategy

We believe that tracking your spending/savings is hugely beneficial to financial success. It creates awareness of where your dollars actually disappear to, it lets you set realistic savings goals, and it gives you get a warm fuzzy feeling when you see that a change in your spending decisions is reflected in a higher savings rate.

It’s not that difficult, either. The Count, in particular, could not stomach the idea of tracking every dollar on every day, or making a budget in which he felt restricted, so we track our spending retrospectively by adding up the items from bank statements/credit card bills at the end of each month.

Saving the maximum amount you can is crucially important, particularly in the early stages of your investment (more on this later). Investment returns alone cannot generate wealth, you need something to invest at the beginning, as well as ongoing further investment over the decades.

Let the demonstrative figures begin!

Consider the following examples. We will use two hypothetical couples in these examples; we have put a lot of thought and effort into naming them, and our brilliant creative minds have produced ‘Couple 1’ and ‘Couple 2’.

Thankfully, both Couple 1 and Couple 2 are savvy investors, and amazingly their investments both achieve the same annual return of 7%! How convenient for us…

Let’s first take a look at Couple 1, who has a savings rate of 40%. Note that the starting net worth here is $0, so these results are achievable for anyone or any couple who can save a fair proportion of their wage annually. Let’s track their progress over 10 years and see how they did.

A table showing Couple 1's net worth, who had a 40% savings rate over 10 years

What is immediately obvious from the above is that the the vast majority of the heavy lifting was done by savings. Specifically, 67% of the 10-year net worth is purely savings, with an additional 33% given by investment returns.

Sure, the extra $191,343 from compounding investment returns is nice, but this is the icing on the cake. In this example, your savings is well and truly the cake.

An image of a cake showing that the savings make up the bulk of the cake - the compounding returns are simply the icing!
The full recipe for the compounding cake can be found by reading this post a few times.

For comparison’s sake, let’s see take a look at Couple 2, whose annual savings is a little lower at $10,000 per year, but with the same annual after-tax income. Interestingly, this savings rate of 10% is often recommended and regarded as a good target, and it might be for those who currently have a 0% (or negative!) savings rate. We, of course, have our sights set a little higher.

A table showing Couple 2's net worth, who had a 10% savings rate over 10 years

Above, you can see that although the rate of return is still 7%, Couple 2 would only have a 10-year investment return of only $48k, compared to the $191k of Couple 1. Thus, the ‘magic’ of compounding is directly related to the hard work of saving, particularly in a short investing time frame.

This is clearly demonstrated by the below chart, which compares the investment return consequences of adding $40,000 versus $10,000 to an investment portfolio annually. Note: the values in the below chart ignore the actual added capital from the savings/investment contribution, and only represent the investment returns:

An image showing how compounding returns are dependent on savings contributions

The importance of ‘savings rate’ as opposed to ‘savings’

Now that you understand the importance of saving money (you probably knew it already, otherwise you wouldn’t be here…), let’s kick this mother up a notch and see how savings rate, rather than simply savings, is of mega importance.

An estimate of how much money you need in order to retire is calculable. Research has demonstrated that 4% is a rough guide for a safe withdrawal rate in most models of market returns (see here for a more detailed analysis).

Some believe that this is too high, while others believe that it is too low. Either way, this helps us calculate an estimate of what one’s target net worth must be to retire. From this, the rule of 25 was born. If you multiply your current annual spending by 25 (the inverse of 4%), you can work out what you will need in order to safely withdraw 4% annually to cover your living expenses.

Crucially, your living expenses and savings are directly related to each other. As one goes up, the other goes down. This can drastically affect the number of years it will take you to become financially free. We demonstrate this below.

Couple 1 have expenses of $60,000 each year, so they would need $60,000 x 25 = $1.5 million to be financially free. We can then calculate that, saving $40,000 per year, Couple 1 would need to save and invest for 19 years if they are getting a 7% annual return to retire (see figure below).

Remember, this is from starting at a net worth of $0! For an excellent summary of this concept, check out ‘The shockingly simple maths of early retirement’ by Mr Money Mustache.

This is all well and good for Couple 1 – they will be financially free at the age of 49, as they were 30 years at the start of their saving extravaganza. However, the age of financial freedom is incredibly sensitive to your cost of living.

Think about it, the higher your cost of living, the more capital you will need to retire using the 4% withdrawal rate. Not only that, but a higher cost of living, given no difference in income (i.e. still $100,000 per annum), will be associated with a lower savings rate.

For our second couple, Couple 2, who have living expenses of $90,000 per year (so much smashed avocado on their toast…), they require a net worth of $90,000 x 25 = $2.25 million to retire. And, unfortunately for them, their savings rate is only 10%.

So just how much later will Couple 2 retire than Couple 1, remembering that Couple 1 had living expenses of $60,000 per year and a savings rate of 40%?

A figure showing how spending less means freedom sooner

Couple 2 are on track to retire 43 years after starting their investment journey at the ripe(r) old(er) age of 73. Compared with Couple 1, this is a difference of 24 years. It is worth noting that if Couple 1 decided that they wanted to retire in a bit more luxury, they would achieve the same $2.25 million at the age of 55 – almost 20 years sooner than Couple 2.

Of course, it’s unlikely that Couple 2 would continue working and saving until the age of 73. They would more likely work until whatever the government decides is retirement age is at that point in time (probably 70), and have a net worth of a little over $1.5 million. Then, they can supplement their annual retirement income with whatever small pension they may be entitled to.

Not a bad outcome by any means, and probably why it is recommended by financial planners!

In the example here, we talk about couples, but for the singles out there, there is no reason that this cannot work for you too. Just divide the numbers above by 2 (although living expenses and rent will take up a greater proportion of your spending).

Can’t I start saving later on?

Let’s say things didn’t go exactly to plan for either of these couples.

Couple 1 managed to save 40% for the first 10 years of their investment journey, but after this they had children and spent a little more. This resulted in them only being able to save 10% from then on until retirement.

Couple 2 saved 10%, and upon reaching 56, they realised they were only 10 years out from retirement and decided to save more to improve their situation.

Both couples were on $100k after tax, saved the same total amount ($650k), and retired at age 65:

A figure showing how saving now and not later is the way to go!

By the time both couples retire at 65, Couple 1 has $4 million and Couple 2 has $2 million. Keep in mind that both of these couples saved exactly the same amount, the only difference is when they saved. By saving earlier rather than later, Couple 1 ended up with DOUBLE the amount of money at retirement. If you want to talk about the magic of compounding, this is it!

The take-home message

Although compounding is useful in the journey towards financial freedom, it is also directly dependent on: (i) the amount that you start with and (ii) the amount that you regularly contribute. For the majority of people, who haven’t been born into vast riches, these additional contributions come from savings.

Without ongoing savings, your quest for financial freedom may arrive a lot later than desired, or maybe never at all.

And if you are going to save, don’t wait until tomorrow.

Start today!

The Count and Countess