The Surprising Math Behind Compound Interest
Most people have heard that compound interest is powerful. Far fewer have actually sat down and worked through what it does to a specific number over time. Once you do, the advice to “start early” stops sounding like a platitude.
What compound interest actually means
Simple interest pays you a return on your original investment each year. Compound interest pays you a return on your original investment plus all the returns you’ve already earned. That difference sounds minor. Over decades, it isn’t.
Take $5,000 invested at 7% annual return — roughly the long-run real return of a broad stock index after inflation.
| Years | Simple interest | Compound interest |
|---|---|---|
| 10 | $8,500 | $9,836 |
| 20 | $12,000 | $19,348 |
| 30 | $15,500 | $38,061 |
| 40 | $19,000 | $74,872 |
At 10 years the difference is noticeable. At 40 years, compound interest has produced nearly four times the outcome of simple interest on the same initial amount.
The Rule of 72
A useful mental shortcut: divide 72 by your annual interest rate to estimate how many years it takes for an investment to double.
At 6%, money doubles every 12 years. At 8%, every 9 years. At 4%, every 18 years.
This rule makes it easy to think about sequences of doublings. $10,000 at 8% becomes $20,000 in 9 years, $40,000 in 18, $80,000 in 27. The doubling periods don’t get longer — they stay the same — which is exactly why the later years produce such outsized results.
Starting early vs. investing more
Here’s a comparison that illustrates the effect more starkly. Two investors both earn 7% per year:
- Investor A puts in $5,000 at age 25 and never adds another cent
- Investor B puts in $5,000 at age 35 and never adds another cent
By age 65, Investor A has $74,872. Investor B has $38,061. A single decade’s head start roughly doubles the outcome — without any additional money invested.
The practical implication: for long time horizons, when you start often matters more than how much you invest. An extra $1,000 today is worth more than an extra $1,000 ten years from now, even if the interest rate stays the same.
Inflation: the compound interest working against you
Compound interest also works in reverse. Inflation compounds the reduction in your purchasing power just as steadily as a good investment compounds its growth.
At 3% inflation, $50,000 today buys the same as $41,199 in ten years, $33,819 in twenty, and $27,797 in thirty — in today’s dollars. The erosion is gradual enough to be easy to ignore year-to-year, but significant over the long run.
This is why financial projections often talk about real returns — the return after subtracting inflation. A 7% nominal return during a 3% inflation period is really a 4% real return. That’s still good. But it’s worth knowing what you’re actually working with.
Running your own numbers
The examples above use round figures and a fixed rate. Your situation will be different — different starting amount, different rate, different time horizon, possibly regular contributions.
The compound interest calculator lets you plug in your own numbers and see a year-by-year breakdown. If you want to stress-test how inflation affects the real value of an investment, the inflation calculator is a good complement to it.
The math won’t tell you what to invest in. But it will make the stakes of starting now versus later a lot clearer.