Convert between APR and APY instantly. Understand how compounding frequency affects interest rates on loans and savings with this free calculator.
APR and APY are two of the most commonly quoted — and commonly confused — interest rate figures in personal finance. APR (Annual Percentage Rate) is the simple annual rate without accounting for compounding, while APY (Annual Percentage Yield) reflects the true annual return or cost after compounding is factored in. The difference matters because compounding can significantly increase the effective rate.
For savings and investments, APY shows you the real return you will earn. For loans and credit cards, APR is the rate typically advertised, but the effective cost may be higher depending on how often interest compounds. A credit card with an 18% APR that compounds daily has an effective APY of about 19.72% — nearly two percentage points higher than the stated rate.
This APR vs APY Calculator converts between the two rates for any compounding frequency — daily, monthly, quarterly, semiannually, or annually — so you can see exactly how compounding affects the true cost of borrowing or the real yield on savings.
Financial products advertise whichever rate looks more favorable: savings accounts promote APY (which is higher than APR) while credit cards and loans advertise APR (which is lower than APY). This calculator lets you convert between the two so you can compare products on equal terms and understand the true annual cost or return.
APR to APY: APY = (1 + APR/n)^n − 1, where n = compounding periods per year. APY to APR: APR = n × [(1 + APY)^(1/n) − 1]. Continuous Compounding: APY = e^APR − 1.
Result: APY = 19.72%
With 18% APR compounding daily (365 times per year), the effective annual yield is 19.72%. This means a credit card advertising 18% APR actually costs 19.72% per year when daily compounding is considered. The 1.72 percentage point difference is the compounding effect.
Compounding means earning (or paying) interest on previously accumulated interest. With annual compounding, interest is calculated once per year. With monthly compounding, interest is calculated twelve times per year, and each month's interest begins earning its own interest. The more frequently interest compounds, the greater the effective annual rate.
When you open a savings account, the bank pays you interest based on the APY. If a bank offers 5.00% APY with monthly compounding, the actual monthly rate applied is slightly less than 5%/12 because the compounded result must equal exactly 5%. When you carry a credit card balance, interest compounds daily at a rate derived from the APR divided by 365, but the effective annual cost is higher than the stated APR.
The APR-APY gap is most significant at high interest rates with frequent compounding. For a mortgage at 6% with monthly compounding, the APY is 6.17% — a small difference. For a payday loan at 400% APR with biweekly compounding, the effective APY can exceed 1,400%. The higher the rate, the more compounding frequency matters.
APR (Annual Percentage Rate) is the nominal interest rate that does not account for compounding within the year. APY (Annual Percentage Yield) includes the effect of compounding, showing the true annual rate. APY is always equal to or higher than APR — the more frequent the compounding, the larger the difference.
It depends on whether you are earning or paying interest. For savings and investments, a higher APY means more earnings — so higher is better. For loans and credit cards, a higher APR/APY means more cost — so lower is better. Always compare the same type of rate across products.
Banks advertise whichever rate is more favorable to attract customers. APY is higher than APR, making savings yields look better. APR is lower than APY, making loan costs look lower. Regulations require disclosure of both, but marketing emphasizes the more appealing number.
The impact depends on the rate. At 5%, monthly vs. annual compounding adds about 0.12 percentage points. At 20%, it adds about 1.94 points. Higher base rates amplify the compounding effect. Daily and monthly compounding produce very similar results; the biggest jump comes from annual to monthly compounding.
Continuous compounding is a theoretical concept where interest compounds an infinite number of times per year. It uses the mathematical constant e (approximately 2.71828). The formula is APY = e^APR − 1. In practice, daily compounding produces almost identical results to continuous compounding.
For loans, the regulatory definition of APR includes certain mandatory fees (like origination fees) in addition to the interest rate, making it slightly higher than the base rate. For credit cards, APR typically equals the interest rate since there are no origination fees. The exact fees included in APR vary by product type and regulation.