How Compound Interest Works: The Complete Guide
Albert Einstein reportedly called compound interest "the eighth wonder of the world." Whether or not he actually said it, the concept is genuinely powerful — and understanding it is one of the most important steps in building financial literacy.
What Is Compound Interest?
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. This is in contrast to simple interest, which only calculates interest on the original principal.
The result is that your money grows at an ever-increasing rate — the more it grows, the faster it grows. This is what makes compounding so powerful over long time periods.
Simple: $10,000 at 5% for 10 years = $5,000 interest → $15,000 total
Compound (annually): $10,000 at 5% for 10 years = $6,289 interest → $16,289 total
Compound (monthly): $10,000 at 5% for 10 years = $6,470 interest → $16,470 total
The Compound Interest Formula
A = P × (1 + r/n)^(n×t)
A = Final Amount · P = Principal · r = Annual Interest Rate (decimal) · n = Compounding Frequency per Year · t = Time in Years
If you're also making regular contributions (like monthly savings), the formula extends to:
A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) - 1) / (r/n)]
PMT = Regular contribution per compounding period
Worked Example: Step by Step
Let's say you invest $5,000 at 7% annual interest, compounded monthly, for 20 years:
- P = $5,000
- r = 0.07 (7% as a decimal)
- n = 12 (monthly compounding)
- t = 20 years
Monthly rate: 0.07 / 12 = 0.005833
Total periods: 12 × 20 = 240 months
A = $5,000 × (1 + 0.005833)^240 = $5,000 × 4.0387 = $20,194
Your $5,000 grew to over $20,000 — you earned $15,194 in interest without adding a single dollar more.
How Compounding Frequency Affects Growth
The more frequently interest is compounded, the more you earn (though the difference shrinks at higher frequencies):
| Frequency | Times/Year | $10,000 at 6% for 20 years |
|---|---|---|
| Annually | 1 | $32,071 |
| Semi-annually | 2 | $32,620 |
| Quarterly | 4 | $32,907 |
| Monthly | 12 | $33,102 |
| Daily | 365 | $33,198 |
Monthly and daily are very close — monthly compounding is the most common for savings accounts and most investments.
The Rule of 72
A quick mental math trick: divide 72 by your interest rate to get an approximate doubling time.
Doubling Time ≈ 72 / Annual Interest RateExample: At 6% interest, your money doubles in 72/6 = 12 years.
This is an approximation — actual doubling times vary slightly based on compounding frequency — but it's remarkably accurate for most practical purposes.
Compound Interest and Debt
The same effect that grows your savings works against you with debt. Credit card debt at 20% APR compounds (usually daily) against your balance. If you only make minimum payments, the interest compounds and your debt can grow rapidly.
This is why financial advisors consistently recommend paying off high-interest debt as quickly as possible before investing — the guaranteed 20% "return" from paying off a 20% credit card beats almost any investment.
Try Our Compound Interest Calculator
See compounding in action with your own numbers:
Compound Interest CalculatorKey Takeaways
- Compound interest earns interest on both principal and accumulated interest
- More frequent compounding = slightly more growth
- Time is the most powerful factor — start early
- The Rule of 72 estimates how long it takes to double your money
- Compound interest works against you in debt — pay it down fast