Understanding the Curvy Nature of Compound Interest

4 min read

Suppose you invest $10,000 per year for 30 years.

Consider three scenarios: you earn 3%, 5%, or 7% annual returns on your investments. Here’s how much you would have after 30 years in each scenario:

By earning 7% annual returns, your ending amount is more than double the amount you would have by earning 3% returns. 

I’m sure you have seen plenty of graphs like this one before, but I’d like to point out a specific piece of it that often gets overlooked: the early years.

Let’s zoom in on the first 10 years:

Notice how the difference in net worth for the 7% and 3% scenarios is less than $30k after the first 10 years. 

Also notice how the net worth lines are more linear than the previous graph. They lack that signature upward curve that comes as a result of compound interest. This is because the amount you save matters far more than your investment returns in your early financial years. 

To illustrate this, compare someone who saves $20k per year and earns paltry 2% annual returns with someone who saves $10k per year and earns stellar 12% annual returns:

The person who saves $20k per year comes out ahead by $27k despite earning significantly lower investment returns.

The takeaway here is simple: investment returns matter most when you have a significant amount invested. In the early years, it’s unlikely that you have enough money invested for returns to move the needle. In the later years, however, investment returns matter a lot. 

To see this, let’s jump back to our original graph. Notice how net worth growth is linear in the early years, but becomes more “curvy” towards the later years:

To understand the curvy nature of compound interest, let’s check out the raw numbers for this graph:

Check out the “7%” annual return column. From year 9 to year 10, net worth increases by $19,672. Only $9,672 of that increase comes from investment returns while the other $10,000 comes purely from savings.

But then from year 29 to year 30, net worth increases by $76,123 and only $10,000 of that increase comes from savings. In the later years, with hundreds of thousands of dollars at work, investment returns become incredibly important. 

As I illustrated in this post, investment returns begin to take over net worth growth in later years:

Notice how investment returns account for 86% of net worth growth when you move from $900k to $1 million (assuming $10k annual savings, 7% annual investment return).

The Takeaways

Don’t be anxious about investment returns early on in your financial journey. The amount you save matters far more than your returns in the early years.

Over time, investment returns will account for more and more of your net worth growth. 

The real power of compound interest is revealed in the later years. Compound interest will not make you rich in the short-term (<10 years), but when you give it several decades to work, its “curvy” nature in the later years can generate real wealth.

Grind it out in the early “linear” years. Enjoy the ride in the later “curvy” years. As Charlie Munger said, the first $100,000 is a b*tch, but once you cross that six-figure threshold and beyond, the curvy nature of compound interest begins to propel your net worth higher at a faster rate than you would expect.

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Spreadsheet: Curvy Nature of Compound Interest

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