Compound Interest vs CAGR - Not the Same (But We Use Them Interchangeably)

There's a phrase repeated ad nauseam in the investing world: "Compound interest is the eighth wonder of the world" (supposedly said by Einstein, though probably not). The problem is that when we talk about stock market investing, technically we're not talking about compound interest. We're talking about CAGR.

So why does everyone keep using the term "compound interest" anyway? Because it's become the standard. It's incorrect, yes, but it is what it is. Let's unravel this little white lie of the financial world.

What is compound interest really?

Compound interest is a mathematical concept applied to fixed-rate debt instruments. Think of:

• A savings account that gives you a guaranteed 2% annually
• A bond that pays a fixed 3% coupon annually
• A fixed-term deposit with a known interest rate

The magic of compound interest is simple: you earn interest on your interest. If you have $1000 at 5% annually:

• Year 1: $1000 × 1.05 = $1050
• Year 2: $1050 × 1.05 = $1102.50 (not $1100)
• Year 3: $1102.50 × 1.05 = $1157.63

The formula is straightforward:

Final Value = Initial Capital × (1 + interest)^years

The important thing here is that the interest is known, fixed, and predictable. You know exactly how much you'll have in 10 years.

So what is CAGR then?

CAGR stands for Compound Annual Growth Rate. It's a measure used to calculate the average annual return of an investment whose value fluctuates.

The key difference: CAGR is calculated backwards, looking at the past. It doesn't predict the future, it simplifies the past.

Imagine you invest $1000 in stocks:

• Year 1: +20% → $1200
• Year 2: -10% → $1080
• Year 3: +15% → $1242

What was your average annual return? This is where CAGR comes in:

CAGR = (Final Value / Initial Value)^(1/years) - 1

CAGR = (1242 / 1000)^(1/3) - 1 = 7.49% annually

CAGR tells you: "If you had grown at a constant rate each year instead of having those ups and downs, you would have grown at 7.49% annually." It's a useful simplification, but it doesn't reflect the reality of what happened.

The fundamental difference

Here's the crux:

Why do we misuse the term?

Because it sounds good. "Compound interest" has that air of mathematical magic that attracts. Plus, the formula looks the same on the surface:

• Compound interest: 1000 × (1.05)^10
• Projected CAGR: 1000 × (1.08)^10

Visually they're identical, but conceptually they're different worlds. In the first case, that 5% is guaranteed. In the second, that 8% is a hope based on historical data.

The problem with applying compound interest to stocks

When someone says "If you invest $10,000 at 8% annually for 30 years you'll have $100,626," they're using the compound interest formula for something that doesn't have a fixed interest rate.

The stock market doesn't guarantee you 8% annually. It might give you +30% one year and -20% the next. The end result might be similar, but the journey is completely different. And that journey matters because:

1. It affects your psychology: Seeing your investment drop 40% hurts, even if it recovers "in the long run"
2. Timing matters: If you need the money in a bad year, you're screwed
3. Volatility has a cost: It's not the same to grow at a constant 8% as to go up 50% and down 30%

So what term should we use?

Technically, when talking about stock market investing we should say:

• "Annualized compound return" (more precise)
• "Historical CAGR" (if talking about the past)
• "Expected return" (if projecting into the future)

But let's be realistic, everyone says "compound interest" and everyone understands what we're talking about.

Conclusion: use the term, but understand the difference

Will I continue using "compound interest" when talking about stock market investing? Probably yes. Is it wrong? Technically yes. Does it matter?

Yes, it matters to understand the difference. Not because you need to correct everyone on the Internet (please don't), but because it changes how you invest:

• Compound interest is predictable → plan with certainty
• CAGR is descriptive → plan with uncertainty

When you project your retirement assuming a 7% annual "compound" return, you're not making an exact mathematical projection. You're making an estimate based on historical averages that may or may not hold true.

And that's fine, as long as you're aware of it.

So yes, keep using the term "compound interest" in your investment discussions. But keep in mind that you're simplifying. Reality is more volatile, more uncertain, and honestly, more interesting.

In the end, what matters isn't using the 100% correct term, but understanding what's behind that compound growth. And now, if someone corrects you at a family dinner because you said "compound interest" instead of "CAGR," you know what to say: "Technically you're right, but socially you're being annoying" 😄