APR vs APY Comparison Calculator
Convert APR (Annual Percentage Rate) to APY (Annual Percentage Yield) and back, with any compounding frequency. See exactly how much compounding adds to a savings account or to your loan cost.
APR vs APY: What's the Real Difference?
APR (Annual Percentage Rate) and APY (Annual Percentage Yield) describe the same thing — an interest rate — but APY includes the effect of compounding, while APR does not. The Federal Reserve Board's Regulation Z (Truth in Lending Act) requires lenders to disclose APR on loans and credit cards. The Federal Reserve's Regulation DD (Truth in Savings Act) requires banks to disclose APY on savings accounts, CDs, and money market accounts.
For a 5% nominal rate compounded monthly, the APR is 5.00% but the APY is approximately 5.116% — a difference of 0.116 percentage points that compounds over years into significant dollar amounts.
The Math: APR to APY Formula
The formula to convert APR to APY is:
APY = (1 + APR/n)^n − 1
where n is the number of compounding periods per year (12 for monthly, 365 for daily, etc.). For continuous compounding, the formula becomes APY = e^APR − 1 where e is Euler's number (≈2.71828).
Why APY Matters for Savings Accounts
When comparing high-yield savings accounts (HYSA) and CDs, always compare APY-to-APY, not APR-to-APR. The CFPB warns that some banks advertise APR (the lower number) to seem competitive, when the regulatory standard for deposit accounts is APY. If Bank A advertises 4.95% APR with daily compounding and Bank B advertises 5.00% APY with monthly compounding, Bank A actually pays more — its APY is roughly 5.075% vs Bank B's 5.00%.
Why APR Matters for Loans
For loans and credit cards, the regulatory standard under TILA is APR — which includes finance charges and certain fees in addition to the nominal interest rate. The CFPB requires lenders to disclose the APR in the Loan Estimate within 3 business days of application. For a 30-year mortgage, the APR is typically 0.05%–0.25% higher than the nominal rate due to closing costs.
Credit cards are different — their APR is typically the same as the nominal rate (no fee inclusion), but because credit card interest compounds daily on average daily balance, the effective APY can be 0.30%–0.40% higher than the stated APR.
How Compounding Frequency Affects Your Money
For a 5% APR:
- Annual compounding: APY = 5.000%
- Semi-annual: APY = 5.063%
- Quarterly: APY = 5.095%
- Monthly: APY = 5.116%
- Daily: APY = 5.127%
- Continuous: APY = 5.127%
The jump from annual to daily compounding adds 0.127 percentage points — meaningful but not life-changing. The bigger lever is the rate itself.
Sources: Federal Reserve Regulation Z (Truth in Lending Act, 12 CFR Part 1026), Regulation DD (Truth in Savings Act, 12 CFR Part 1030), Consumer Financial Protection Bureau (consumerfinance.gov). Last updated: May 2026.
Frequently Asked Questions
What is the difference between APR and APY?
APR (Annual Percentage Rate) is the simple annualized interest rate without accounting for compounding. APY (Annual Percentage Yield) is the rate including the effect of compounding within the year. For a 5% APR compounded monthly, the APY is approximately 5.116%. Federal regulations require APR disclosure on loans (TILA) and APY disclosure on deposits (Truth in Savings Act).
Why do banks advertise APY for savings but APR for loans?
It is a regulatory disclosure requirement, not marketing. The Federal Reserve's Regulation DD (Truth in Savings Act) mandates APY disclosure on deposit accounts because APY is the higher, more accurate number for what you earn. Regulation Z (Truth in Lending Act) requires APR disclosure on loans because APR includes some fees and gives the true cost of credit including those charges.
Is daily compounding really better than monthly?
Yes, but the difference is small. On a 5% APR, monthly compounding yields APY 5.116% while daily compounding yields 5.127% — a difference of only 0.011 percentage points. On a $10,000 balance, that is $1.10 more per year. The compounding frequency matters far less than the underlying rate when shopping for savings accounts.
How does credit card APR compare to APY?
Credit card statements show APR, but most credit cards compound daily based on the average daily balance. A card with a 24.99% APR effectively has a 28.34% APY. The CFPB recommends paying credit card balances in full each month to avoid this compounding entirely — if you pay in full by the grace period due date, no interest accrues regardless of APR or APY.
Does APR include mortgage fees?
Yes — for mortgages, the APR includes certain closing costs (origination fees, mortgage broker fees, discount points). This makes the APR higher than the note rate (the nominal interest rate). On a 30-year mortgage with 1% in fees, the APR is typically 0.05%–0.25% higher than the note rate. Compare APR-to-APR across lenders to compare true cost of borrowing.
What is continuous compounding?
Continuous compounding is the theoretical upper limit where interest is computed every instant — equivalent to compounding infinitely often. The formula is APY = e^APR − 1 where e ≈ 2.71828. In practice, daily compounding is almost identical to continuous compounding (5.127% vs 5.127% for a 5% APR). It is used in physics, biology growth models, and some financial derivatives but rare in retail banking.