How Compound Interest Works: Formula, Examples, Rule of 72
What compounding frequency actually changes, why starting early beats saving more, and how to check the math behind your savings yourself.
Put $10,000 into something earning 7% a year and leave it alone for 30 years. With monthly compounding you end up with about $81,165. Your deposits? Still just the original ten grand. The other $71,000 is interest earning interest — which sounds like a banking cliché until you see it laid out year by year in the Compound Interest Calculator.
The formula, without the mystery
Every compound interest calculation runs on one line of math:
A = P × (1 + r/n)^(n·t)
P is your starting amount, r is the annual rate as a decimal, n is how many times per year interest compounds, and t is the number of years. For the $10,000 example: 10,000 × (1 + 0.07/12)^360. The exponent is what does the damage — 360 monthly compounding periods, each one building on the last.
The calculator uses exactly this formula, and adds any monthly contributions at the end of each month so they start compounding from that point. Type four numbers and the final amount, total deposits, and interest earned appear as you type.
Compounding frequency matters less than you think
Banks love to advertise “daily compounding” as if it were a gift. Here’s what it’s actually worth on $10,000 at 5% over 10 years:
- Yearly compounding: $16,289
- Monthly compounding: $16,470
- Daily compounding: $16,485
Going from yearly to monthly earns you an extra $181. Going from monthly to daily? Fifteen dollars. Over a decade. The rate and the time do almost all the work; the frequency is a rounding error by comparison. If you’re choosing between a 5.0% account with daily compounding and a 5.1% account with yearly compounding, take the 5.1% — you can verify it in the calculator in under a minute.
Starting early beats saving more
This is the part I find genuinely hard to internalize, even knowing the math. Two people save $200 a month at 7%:
- Anna starts at 25 and stops at 65. She deposits $96,000 and ends with about $525,000.
- Boris starts at 35 and stops at 65. He deposits $72,000 and ends with about $244,000.
Anna put in $24,000 more but finished $281,000 ahead. Those first ten years of contributions had four decades to compound, and nothing Boris does later catches up — he’d need to save roughly $430 a month to match her. Run your own age and numbers through the year-by-year table and watch where the curve starts to bend. For most people it’s depressingly late, around year 15 or 20. That’s normal. The back half is where compounding actually pays.
The rule of 72
Quick sanity check you can do in your head: divide 72 by the interest rate and you get roughly the number of years it takes money to double. At 7%, that’s about 10 years. At 3%, 24 years. At 12%, six.
It’s an approximation, but a surprisingly good one for rates between 4% and 12%. I use it to gut-check calculator results — if $10,000 at 7% shows $80,000 after 30 years, that’s three doublings (10K → 20K → 40K → 80K), one per decade. Checks out.
One caveat for investments: the calculator assumes a steady rate, which is true for savings accounts and CDs but not for stocks. Using a long-term average return gives you a useful estimate, not a promise.
Everything you enter stays in your browser — no server, no logging, no account. Open the Compound Interest Calculator, plug in your real numbers, and see what time is worth.