Compound Interest Calculator: How It Works
Compound interest pays you interest on your interest. It is the reason a modest, boring, consistent investment beats a large, late one — and the reason a carried credit card balance is so hard to shift. This page covers the formula, the frequency effect, and the one variable that matters most.
The formula
A = P × (1 + r/n)n×t
A is the final amount, P the principal, r the annual rate as a decimal, n the number of compounding periods per year and t the time in years. Interest earned is A − P.
10,000 at 8% compounded quarterly for 10 years: A = 10,000 × (1 + 0.08/4)40 = 10,000 × 1.0240 = 22,080.
Frequency matters — but less than people assume
100,000 at 10% for 10 years:
| Compounded | n | Final amount | Effective annual rate |
|---|---|---|---|
| Annually | 1 | 259,374 | 10.000% |
| Half-yearly | 2 | 265,330 | 10.250% |
| Quarterly | 4 | 268,506 | 10.381% |
| Monthly | 12 | 270,704 | 10.471% |
| Daily | 365 | 271,791 | 10.516% |
| Continuously | ∞ | 271,828 | 10.517% |
Moving from annual to daily compounding adds about 4.8% to the final amount. Moving from daily to continuous adds almost nothing — there is a mathematical ceiling, and it is ert. When comparing two accounts, the effective annual rate in the last column is the only fair comparison, because it already contains the frequency.
Time is the dominant variable
Investing 5,000 a year at 8%:
| Years invested | Total contributed | Final value | Growth |
|---|---|---|---|
| 10 | 50,000 | 78,227 | 28,227 |
| 20 | 100,000 | 247,115 | 147,115 |
| 30 | 150,000 | 611,729 | 461,729 |
| 40 | 200,000 | 1,398,905 | 1,198,905 |
Doubling the years from 20 to 40 does not double the outcome — it multiplies it by 5.7. Nearly all of the final figure in the 40-year row is growth rather than contribution. This asymmetry is why starting early outperforms contributing more later, and it cannot be recovered afterwards by any realistic increase in savings rate.
The Rule of 72
Divide 72 by the annual return to estimate the years to double. At 6%, roughly 12 years. At 9%, roughly 8. At 12%, roughly 6. It is accurate enough for mental arithmetic between about 4% and 15%, and it works on inflation too: at 6% inflation, prices double in about 12 years.
Compounding works against you too
The same curve applies to debt. A credit card at 24% APR compounded daily has an effective rate near 27%. Left untouched, a balance roughly doubles in under three years. Any strategy that clears high-interest debt before investing is really just choosing which side of the compounding curve to stand on.
What the formula quietly assumes
It assumes a constant rate, no fees, no tax and no withdrawals. Real returns vary year to year; fees compound against you exactly as returns compound for you — a 1% annual fee over 30 years typically consumes a quarter of the final balance; and tax on interest reduces the amount left to compound. For a realistic projection, use your expected return after fees and tax.