APR vs APY Converter (Annual Percentage Rate vs Yield)
Convert between nominal interest rate (APR - Annual Percentage Rate) and effective annual rate (APY - Annual Percentage Yield).
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What Is the APR vs APY Converter (Annual Percentage Rate vs Yield)?
APR vs APY Converter (Annual Percentage Rate vs Yield) Formula
APY = (1 + APR/n)ⁿ − 1
APR = n × ((1 + APY)^(1/n) − 1)
How Is the APR vs APY Converter (Annual Percentage Rate vs Yield) Calculated?
APR is the stated annual rate before accounting for compounding. APY reflects the actual return or cost over a year once compounding is applied — the more frequently interest compounds (n), the larger the gap between APR and APY becomes.
APR vs APY Converter (Annual Percentage Rate vs Yield) Example
An 8% APR compounded monthly (n = 12) has an APY of (1 + 0.08/12)^12 − 1 = 8.30% — meaning the true annual cost or return is slightly higher than the advertised 8% rate.
How to Use the APR vs APY Converter (Annual Percentage Rate vs Yield)
Step 1
Choose whether you're converting APR to APY, or APY back to APR.
Step 2
Enter the rate as a percentage.
Step 3
Select how often the rate compounds — monthly and daily are most common for loans and savings accounts.
Step 4
Read off the converted rate instantly.
Benefits
- Lets you fairly compare two offers that quote rates using different compounding frequencies.
- Reveals the true cost of a loan or true yield of a deposit beyond the advertised headline rate.
- Works in both directions — APR to APY and APY to APR.
Common APR vs APY Converter (Annual Percentage Rate vs Yield) Scenarios
Scenario 1
Comparing credit card APRs or loan offers that compound monthly vs. daily.
Scenario 2
Checking whether a bank's advertised APY on a savings account matches its stated compounding.
Scenario 3
Financial coursework or CFA/finance exam preparation involving nominal vs. effective rates.
Understanding Your Result
APY is always equal to or higher than APR (for positive rates), because it reflects interest earning interest within the year. The more frequent the compounding, the bigger that gap — daily compounding produces a noticeably higher APY than annual compounding for the same APR.
Tips
- When comparing loans, always compare APY (or APR with compounding disclosed) — a lower headline APR with more frequent compounding can cost more than a slightly higher APR compounded annually.
- For savings accounts, APY is the number that reflects your actual annual return — that's the one to compare across banks.
- Daily compounding produces the largest APR-to-APY gap among common frequencies.
Common Mistakes
- Comparing one lender's APR directly against another lender's APY — always convert to the same measure first.
- Assuming APR and APY are the same thing — they're only equal when compounding is annual (n = 1).
- Forgetting that credit cards typically compound daily, making their true effective rate higher than the quoted APR.
Frequently Asked Questions
What's the difference between APR and APY?
APR is the nominal annual rate before compounding is applied, while APY (also called effective annual rate) reflects the actual annual return or cost after compounding.
Is APY always higher than APR?
Yes, for positive interest rates, APY is always equal to or greater than APR, and the gap grows with more frequent compounding.
Which one should I use to compare loans?
Use APY (or the effective rate) whenever possible, since it accounts for compounding frequency and gives a true apples-to-apples comparison.
Why do banks advertise APR instead of APY for loans?
APR appears lower than APY, so lenders often lead with it, while savings products often advertise APY since it appears higher — always check which measure you're being shown.
Does the compounding frequency (n) change the gap between APR and APY?
Yes — more frequent compounding (e.g. daily vs. annually) widens the gap between APR and APY, since interest is calculated and added to the balance more often.
Which rate do credit cards typically advertise?
Credit cards typically advertise APR, since that's the lower-looking number, even though the effective cost of carrying a balance (which compounds) is closer to the APY.
Is APY the same as CAGR?
They're related but not identical — APY specifically converts a compounding rate into an effective annual yield, while CAGR measures actual realized annualized growth over a historical period.
Does a savings account's advertised APY already include compounding?
Yes — APY by definition already accounts for compounding, which is why banks advertise APY (the higher number) for deposits and APR (the lower number) for loans.
What happens to the APR-APY gap as compounding frequency approaches continuous?
The gap approaches a mathematical limit — going from daily to continuous compounding makes very little additional difference compared to going from annual to monthly.
Important Information
Results are for informational purposes and do not account for fees, which can affect the true cost or yield of a loan or deposit.
Last updated: July 26, 2026