The Financial Magic of Compounding

There’s a wealth accelerator available to every single person in the world, and all you need to access it is a simple understanding of multiplication. Compounding is mathematical alchemy that feeds your savings, accelerating your income without you needing to make any effort at all.

Without it, you’ll likely never reach your financial goals.

Compounding is the mathematical effect that accelerates the growth in your invested savings. It’s the engine that makes it possible to pass the finish line of your financial independence journey.

Knowing what’s under your control

When we invest time and effort in improving our finances, we’re trying to influence two numbers: Our income, and our spending.

That’s it. There’s plenty of complexity when you unwrap those two things, but at its heart, it’s a very simple problem.

When your income is higher than your spending, then the money left over at the end of each month adds to your savings.

As your savings grow each month, you slowly build the pot of gold that will bring you financial independence and security.

If those savings are carefully placed, they grow on their own. Understanding how they grow, and how best to take advantage of that growth, is where compounding comes into the picture.

Where you put your savings

Hopefully, you do not keep your savings in a mattress.

Unfortunately, most “savings” accounts pay such low interest that they’re not really any better than a mattress.

Your savings should be invested somewhere that earns a decent return. What that return is depends on the economic climate and your personal situation and appetite for risk, but it should be above 4%.

The most obvious places to put your savings are government bonds and index trackers. This is because government bonds are almost completely risk-free, and index trackers don’t require you to make judgement calls on the quality of any given company. They’re good places for your money and most non-professional investors opt for a mix of these two investment types for their retirement savings.

When you buy government bonds, you’re basically lending money to the government.

When you buy shares in an index fund, it’s like buying shares in an entire stock market at once. Instead of betting on a single company, you’re betting on the overall performance of every company in that index. So if you buy the Vanguard All-Share Index, the value of your investment will go up and down with the stock market as a whole. This is not risk-free, obviously, but over the last hundred years, it’s earned a lot more than government bonds, despite all the ups and downs.

The math behind compounding

Why is compounding important?

Let’s say that you’ve invested $1000 in an index that returned 5% last year.

You will have earned $50 on that investment. That’s $1000 multiplied by 5 percent.

Add that income back to your total, and your account now has $1050 in it.

If you add another $1000 to your savings at the start of the second year, the balance increases to $2050. 5 percent interest on $2050 is $102.5. Even though you’ve only set aside $2000, you’ve received interest on the extra $50 that you earned in the first year.

$2.50 doesn’t go very far, but that’s only the first year. Keep doing the math for twenty years and the numbers begin to rise faster and faster. It adds up dramatically over time.

What compounding means for financial independence

When calculating your financial independence threshold (the amount you need to retire), you need a few numbers to base your calculations on.

What do I earn? What do I spend to live? What interest do I earn on my savings? What’s my safe withdrawal rate?

The last number is 4%. The reason why is the subject of a whole other post, but as a general rule of thumb, if you can live off 4% of your total capital every year, you’re golden and you can quit your job.

The interest rate is also not entirely up to you. A safe number is 5%. A slightly more aggressive number is 7%. These also are deserving of entire articles to explain them.

How much you earn, and how much you spend. Well, that’s up to you.

If you earn $70,000 and you spend $60,000 then you’re saving $10,000 each year. You can work out what that looks like for yourself, but here’s a little chart:

A chart showing how the interest earned on savings grows over time, demonstrating the effect of compounding.

Here’s a few interesting things about that chart.

By year 15, you’re earning more in interest each year than you’re contributing in savings.

In year 37, your savings are over a million dollars, even though you’ve only actually contributed $370,000. That means you’ve earned over $630,000 in interest. You’re also earning almost $50,000 per year in interest at this point.

In year 41, your interest earnings are above $60,000 for the first time. In year 44 (the first year after the end of the chart), you could withdraw 4% of your capital every year to live off (the withdrawal rate we mentioned above), and that would be more than the $60,000 you need to live.

This is a simple example that doesn’t take inflation into account. A full retirement calculation needs to go into more depth than this. 


What this exercise does show is that if you’re going to retire on your savings, you need compound interest to do the heavy lifting for you. If you let that happen, by saving regularly over time, your money works for you, rather than the other way around. This should be a feature of your financial planning, and the sooner you can start growing your savings, the sooner this effect starts working for you.