How Compound Interest Works

What compound interest actually means

Simple interest is calculated only on your original amount, every time. Compound interest is calculated on your original amount plus whatever interest has already been added — so once interest has been credited once, it starts earning interest of its own. That's the entire mechanism, and it's why the U.S. Securities and Exchange Commission's investor education site defines it simply as "interest paid on principal and on accumulated interest."

The standard formula for a lump sum is A = P(1 + r/n)ⁿᵗ, where P is the amount you start with, r is the annual interest rate as a decimal, n is how many times per year interest compounds, and t is the number of years. If you're also adding money regularly — say, a monthly contribution — the formula extends to add the future value of those contributions on top of the lump sum growth. That's exactly the calculation behind the Compound Interest Calculator on this site: enter an initial amount, a monthly contribution, a rate, and a term, and it runs this formula for you.

Compound interest vs. simple interest, with real numbers

The difference sounds abstract until you run one example. Put $10,000 in at 7% for 20 years. With simple interest, you earn a flat 7% of $10,000 every year: $700 × 20 = $14,000 in interest, for a final balance of $24,000. With annual compounding, each year's interest is calculated on the growing balance, not the original $10,000 — and the final balance comes out to $38,696.84, meaning $28,696.84 in interest. That's more than double what simple interest would have earned, from the exact same rate and the exact same 20 years.

Nothing about the rate changed. What changed is that, starting in year two, you're earning 7% on a balance that already includes year one's interest — and that effect keeps stacking every year after.

Does compounding frequency actually matter?

It matters far less than most people assume. Take $10,000 plus $100/month at 4% APY over 5 years: compounding it monthly comes out to $18,861.96, and compounding it daily comes out to $18,867.01 — a difference of about $5 over five years. The rate, the amount you're contributing, and how long you leave it invested do almost all of the work; whether your bank compounds monthly or daily is close to a rounding error by comparison.

Where frequency does matter is in how a rate gets disclosed. Two accounts can advertise the same interest rate but compound at different frequencies, which changes what you actually earn — which is exactly why U.S. banking regulation (Truth in Savings, enforced by the CFPB) requires banks to disclose an Annual Percentage Yield (APY): a standardized figure that already accounts for compounding frequency, so you can compare accounts on equal footing without doing this math yourself.

The Rule of 72 — a shortcut, not a law

The Rule of 72 estimates how many years it takes an investment to double: divide 72 by the interest rate (as a whole number, not a decimal). At 9%, that's 72 ÷ 9 = 8 years to roughly double your money. It's an approximation that holds up best for rates in the rough 6%-10% range — outside that band it drifts further from the exact answer, which you'd get from the full compound interest formula. Use it for quick mental math, not for a number you're relying on to the dollar.

Putting it to work

The most useful thing to do with this concept isn't to memorize the formula — it's to run your own numbers and see how much of your outcome comes from rate versus time versus contribution size. Try the same scenario in the calculator with the term extended by 5 or 10 years, or the monthly contribution raised by even a small amount, and compare the result. Because later growth compounds on everything that came before it, small changes made earlier tend to matter more than the same change made later.