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Convert a nominal interest rate into true annual yield based on compounding frequency.
Convert a nominal interest rate into true annual yield based on compounding frequency.
Enter values above and click Calculate — results will appear here with the formula explained.
Two banks can quote the same nominal rate yet pay different interest, purely because of compounding frequency. APY — the effective annual rate — settles the comparison by answering: including compounding, how much does $100 become after exactly one year? Without APY, the higher APR doesn't always win — frequency can flip the ranking.
More frequent compounding nudges APY above APR. The effect is small at everyday rates (5% monthly-compounded becomes 5.116% APY) but grows with both rate and frequency, which is why promotional accounts love quoting whichever number flatters them more. At 10% the gap widens: monthly 10.47% APY versus daily 10.52% — small in one year, material when multiplied across large balances or decades of compounding.
Continuous compounding (e^r − 1) sets the mathematical ceiling banks approach but never quite reach: at 5% the ceiling is 5.127% — essentially the daily figure, which is why most institutions stop at daily compounding. The table is logarithmic: annual→semi-annual is the biggest jump; daily→continuous is negligible. Don't chase frequency past monthly unless the balance justifies the comparison effort.
Regulation requires banks to disclose APY precisely because nominal rate alone misleads: Reg DD (Truth in Savings) in the US mandates APY so savers can compare apples to apples. When an ad shouts a high APR but whispers compounding terms, the APY line is the truth — read it first, and run both offers through this calculator to expose any gap.
Loan-side, APR versus periodic rate is the parallel concept: credit-card issuers quote APR but charge monthly periodic rate (APR ÷ 12) on revolving balances, while mortgages fold certain upfront fees into loan APR. APY's lesson transfers — periodic rate × periods beats nominal ranking — and the effective cost of carrying a 24% APR balance compounded monthly is actually ~26.8% APY if unpaid.
Real return subtracts inflation from APY to measure purchasing power, and taxes on interest further reduce take-home yield. A 5.1% APY at 3% inflation is ~2% real; at a 24% marginal tax on interest it's ~3.9% after-tax nominal. Model after-tax real yield for honest long-run comparisons, especially for taxable savings versus tax-advantaged accounts.
Convert a nominal interest rate into true annual yield based on compounding frequency. Formula: APY = (1 + APR/n)ⁿ − 1, where n = compounding periods per year. Example: 5% APR compounded monthly yields (1 + 0.05/12)¹² − 1 = 5.116% APY.
Two banks can quote the same nominal rate yet pay different interest, purely because of compounding frequency. APY — the effective annual rate — settles the comparison by answering: including compounding, how much does $100 become after exactly one year? Without APY, the higher APR doesn't always win — frequency can flip the ranking.
More frequent compounding nudges APY above APR. The effect is small at everyday rates (5% monthly-compounded becomes 5.116% APY) but grows with both rate and frequency, which is why promotional accounts love quoting whichever number flatters them more. At 10% the gap widens: monthly 10.47% APY versus daily 10.52% — small in one year, material when multiplied across large balances or decades of compounding.
Continuous compounding (e^r − 1) sets the mathematical ceiling banks approach but never quite reach: at 5% the ceiling is 5.127% — essentially the daily figure, which is why most institutions stop at daily compounding. The table is logarithmic: annual→semi-annual is the biggest jump; daily→continuous is negligible. Don't chase frequency past monthly unless the balance justifies the comparison effort.
Regulation requires banks to disclose APY precisely because nominal rate alone misleads: Reg DD (Truth in Savings) in the US mandates APY so savers can compare apples to apples. When an ad shouts a high APR but whispers compounding terms, the APY line is the truth — read it first, and run both offers through this calculator to expose any gap.
Loan-side, APR versus periodic rate is the parallel concept: credit-card issuers quote APR but charge monthly periodic rate (APR ÷ 12) on revolving balances, while mortgages fold certain upfront fees into loan APR. APY's lesson transfers — periodic rate × periods beats nominal ranking — and the effective cost of carrying a 24% APR balance compounded monthly is actually ~26.8% APY if unpaid.
Real return subtracts inflation from APY to measure purchasing power, and taxes on interest further reduce take-home yield. A 5.1% APY at 3% inflation is ~2% real; at a 24% marginal tax on interest it's ~3.9% after-tax nominal. Model after-tax real yield for honest long-run comparisons, especially for taxable savings versus tax-advantaged accounts.
5% APR compounded monthly yields (1 + 0.05/12)¹² − 1 = 5.116% APY. The same 5% compounded daily yields 5.127% — slightly better despite the identical headline rate. A fee case: a 5.25% APR paid semi-annually yields 5.32% APY, beating a 5.20% daily account — higher nominal wins here, but only the APY comparison reveals it.
Formulas are standard public references (see our methodology). External standards are cited in the text where they apply.
Last reviewed: September 2026 · Report an error