The formula and the test case
Compound interest is calculated with A = P(1 + r/n)^(nt), where P is the principal, r is the nominal annual rate, n is the number of compounding periods per year, and t is the number of years. Only n changes between compounding frequencies; P, r and t stay the same. That isolates exactly how much the compounding frequency alone contributes.
To compare frequencies on equal footing, we hold everything else constant: a principal of $10,000, a nominal annual rate of 5%, and a term of 10 years. The only thing that changes from row to row in the table below is how often interest is added.
The comparison table
Each row uses the same $10,000 principal, 5% nominal rate and 10-year term. The effective annual rate (EAR) column shows the true annualised yield once compounding is accounted for.
| Compounding frequency | Effective annual rate | Balance after 10 years |
|---|---|---|
| Annual (n = 1) | 5.0000% | $16,288.95 |
| Semi-annual (n = 2) | 5.0625% | $16,386.16 |
| Quarterly (n = 4) | 5.0945% | $16,436.19 |
| Monthly (n = 12) | 5.1162% | $16,470.09 |
| Daily (n = 365) | 5.1267% | $16,486.65 |
| Continuous | 5.1271% | $16,487.21 |
What the numbers show: diminishing returns
The gain from compounding more frequently shrinks rapidly as frequency rises. Moving from annual to monthly compounding adds $181.14 over the decade. Moving all the way from monthly to daily adds only a further $16.56, and moving from daily to continuous compounding — the mathematical limit — adds just $0.56 more. There is a hard ceiling (continuous compounding) that daily compounding already sits within a dollar of.
The practical takeaway is that the rate and the time horizon dominate. Doubling the term or gaining even a fraction of a percentage point on the rate changes the outcome far more than any change in compounding frequency. When comparing two accounts, the effective annual rate (EAR) — not the compounding frequency in isolation — is the number that lets you compare them fairly.
Why banks quote nominal rates and EAR separately
A nominal rate of 5% compounded daily is not the same as 5% simple interest — its effective annual rate is 5.1267%. This is why regulators require lenders and savings providers to disclose an effective or annual equivalent rate: it lets two products with different compounding frequencies be compared on a single, honest number. When you see two accounts advertising the same nominal rate, the one compounding more frequently has the marginally higher EAR, but the gap is small.
Sıkça Sorulan Sorular
Is daily compounding much better than monthly?
Only marginally. On $10,000 at 5% over 10 years, monthly compounding yields $16,470.09 and daily yields $16,486.65 — a difference of $16.56 across the entire decade.
What is the most compounding can ever add?
Continuous compounding is the mathematical maximum. On the test case it reaches $16,487.21, only $0.56 more than daily compounding, so daily is effectively at the ceiling.
What matters more than compounding frequency?
The nominal interest rate and the length of time invested both have a far larger effect on the final balance than how often interest is compounded.
How do I compare two accounts with different compounding?
Compare their effective annual rates (EAR), not their nominal rates or compounding frequencies. The EAR folds compounding into a single annual figure you can compare directly.
Kaynaklar
- U.S. Securities and Exchange Commission (Investor.gov) — Compound Interest Calculator and definition. https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator
- Consumer Financial Protection Bureau — Annual Percentage Yield (APY) and how compounding is disclosed. https://www.consumerfinance.gov/
- Federal Reserve — Regulation DD (Truth in Savings), disclosure of annual percentage yield. https://www.federalreserve.gov/