Simple interest pays you on your original deposit, forever. Compound interest pays you on the deposit plus every bit of interest you have already earned - and that one difference is why long-term savers end up with multiples of what they put in. This guide walks through the mechanics with real dollar figures you can verify yourself in our Compound Interest Calculator. (This article is educational only and is not financial advice.)
Simple vs Compound: The Same $10,000, Two Very Different Curves
Put $10,000 at 5% per year. Simple interest adds a flat $500 every year. Compound interest adds 5% of the current balance - $500 the first year, $525 the second, $551 the third, and so on. Small differences at first, then not small at all:
| Year | Simple interest (5%) | Compound interest (5%, annual) | Gap |
|---|---|---|---|
| 5 | $12,500 | $12,763 | $263 |
| 10 | $15,000 | $16,289 | $1,289 |
| 20 | $20,000 | $26,533 | $6,533 |
| 30 | $25,000 | $43,219 | $18,219 |
By year 30, compounding has produced $33,219 of growth versus $15,000 - more than double - from the identical deposit and rate. The curve is not a straight line; it bends upward, and the bend gets steeper the longer you leave it alone.
The Formula, Translated into Plain Words
A = P (1 + r/n)n·t- P is what you start with (the principal).
- r is the annual rate as a decimal (5% → 0.05).
- n is how many times per year interest is added (12 for monthly).
- t is the number of years, and A is the final amount.
In words: each compounding period, your balance is multiplied by a number slightly bigger than 1 (for 5% monthly, that is 1 + 0.05/12 ≈ 1.00417). Do that 12 times a year for t years - n·t multiplications in total - and the formula is just all those small multiplications collapsed into one expression.
Worked example: $10,000 at 5% compounded monthly for 20 years: A = 10,000 × (1 + 0.05/12)240 ≈ $27,126. Now add a $200 monthly contribution on top and the balance reaches roughly $109,000 - of which only $58,000 is money you deposited ($10,000 + 240 × $200). The remaining ~$51,000 is growth. Change any input in the calculator and the year-by-year table shows exactly where the curve bends.
Run Your Own Numbers
Principal, monthly contributions, rate, and years - see the final balance and a year-by-year growth table instantly
Open the Compound Interest Calculator →Why Starting 10 Years Earlier Beats Contributing Twice as Much
Compounding rewards time more than it rewards money. Compare two savers earning 7% per year (a common long-run stock-market assumption), both stopping at age 65:
| Saver | Contributes | Total deposited | Balance at 65 (7%) |
|---|---|---|---|
| Early starter | $200/month from age 25 to 65 | $96,000 | ~$525,000 |
| Late starter | $400/month from age 35 to 65 | $144,000 | ~$490,000 |
The late starter deposits $48,000 more of their own money and still ends up behind, because the early starter's first decade of contributions gets 30-40 years to compound. Those earliest dollars do the heaviest lifting - which is the real, unsentimental meaning of "start early".
The Rule of 72: Doubling Time in Your Head
Divide 72 by the annual rate to get the approximate years to double: 12 years at 6%, about 10 at 7.2%, 8 at 9%. Chain it for long horizons - at 7%, money doubles roughly every 10 years, so 30 years means three doublings: 8× the original amount. (For the general math behind percent changes, see our percentage guide.)
Compounding Frequency: A Reality Check
Banks sometimes advertise daily compounding as if it were a major perk. The honest numbers, for $10,000 at 5% nominal over one year:
- Annually: $10,500.00
- Monthly: $10,511.62
- Daily: $10,512.67
Daily beats monthly by about one dollar per $10,000 per year. The lesson: compounding frequency is a rounding error next to the two inputs that dominate everything - the rate you earn and the years you stay invested. When comparing accounts, look at the APY (which already folds compounding in) and ignore the frequency marketing.
Frequently Asked Questions
What is the rule of 72?▼
Divide 72 by your annual return to estimate how many years your money takes to double. At 6%, doubling takes about 72 ÷ 6 = 12 years; at 9%, about 8 years. It is an approximation, but between 4% and 12% it lands within a few months of the exact answer - close enough for any mental estimate.
Does daily compounding earn much more than monthly?▼
Barely. At 5% nominal, $10,000 for one year grows to $10,511.62 with monthly compounding and $10,512.67 with daily - about a dollar apart. Compounding frequency matters far less than the rate itself and how long the money stays invested. Compare APY (which already includes compounding) rather than compounding frequency.
What is the difference between APR and APY?▼
APR is the nominal annual rate before compounding; APY (also called effective annual rate) is what you actually earn after compounding is included. A 5% APR compounded monthly is a 5.116% APY. Banks tend to advertise APY on savings accounts (bigger number) and APR on loans (smaller number) - always compare like with like.
Does compound interest work against me on debt?▼
Yes, and faster than most people expect. Credit cards often charge around 20-24% APR compounded daily; by the rule of 72, an unpaid balance at 24% doubles in roughly 3 years. The same math that builds savings grows debt, which is why paying off high-interest balances is usually the best guaranteed "return" available.
Are the calculator’s projections guaranteed?▼
No. A fixed-rate savings account or bond behaves close to the math, but market investments do not return the same percentage every year - a projection at 7% is a long-run average scenario, not a promise. Real results also depend on fees, taxes, and inflation. Use projections to compare scenarios, not to predict a balance to the dollar.
See Your Money's 20-Year Curve
Enter a starting amount, monthly contribution, and rate - get the final balance, total interest, and a year-by-year table. Free and private.
Try the Compound Interest Calculator →