%
Enter APR between 0.01 and 100.
Annual Percentage Rate (nominal rate)
How often interest is compounded
APY
—
⚠️ Disclaimer: Results are mathematical estimates. Actual loan costs and savings yields may include fees and other factors not captured here. Consult a financial advisor for specific financial decisions.
Was this calculator helpful?
Sources & Methodology
APR/APY formulas per Truth in Savings Act (TISA) and Truth in Lending Act (TILA). Standard finance textbook formulas for effective annual rate.
FDIC — Truth in Savings Act (TISA) Regulation DD
Federal reference defining APY as the effective annual rate including compounding, per the standard formula used in this calculator: APY = (1 + r/n)^n − 1.
CFPB — Truth in Lending Act (Regulation Z)
Consumer Financial Protection Bureau reference for APR disclosure requirements for loans, confirming the nominal rate basis used in this calculator.
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)
Rate difference: APY − APR = the compounding premium (always positive when n > 1)
Continuous: APY = e^APR − 1 (theoretical limit of increasing n)
APY to APR: APR = n × ((1 + APY)^(1/n) − 1)
Rate difference: APY − APR = the compounding premium (always positive when n > 1)
Continuous: APY = e^APR − 1 (theoretical limit of increasing n)
⏱ Last reviewed: April 2026
APR vs APY — What’s the Difference?
APR (Annual Percentage Rate) and APY (Annual Percentage Yield) are two ways to express an interest rate. APR is the nominal rate — the simple annual rate before accounting for compounding. APY is the effective rate — the actual return or cost after compounding is applied. For the same nominal rate, APY will always be higher than APR when interest compounds more than once per year.
The Formulas
APY = (1 + APR/n)^n − 1
APR = n × ((1 + APY)^(1/n) − 1)
n = number of compounding periods per year (365 for daily, 12 for monthly, 4 for quarterly)
Example: 6% APR compounding monthly (n=12):
APY = (1 + 0.06/12)^12 − 1 = (1.005)^12 − 1 = 6.168% APY
The 0.168% difference is the compounding premium earned above the nominal rate.
Example: 6% APR compounding monthly (n=12):
APY = (1 + 0.06/12)^12 − 1 = (1.005)^12 − 1 = 6.168% APY
The 0.168% difference is the compounding premium earned above the nominal rate.
APY vs APR by Compounding Frequency
| APR | Daily | Monthly | Quarterly | Annual |
|---|---|---|---|---|
| 1% | 1.005% | 1.004% | 1.003% | 1.000% |
| 3% | 3.045% | 3.042% | 3.034% | 3.000% |
| 5% | 5.127% | 5.116% | 5.095% | 5.000% |
| 10% | 10.516% | 10.471% | 10.381% | 10.000% |
| 20% | 22.134% | 21.939% | 21.551% | 20.000% |
| 24% | 27.115% | 26.824% | 26.248% | 24.000% |
Why It Matters for Borrowers and Savers
- For savings accounts: Look at APY. Banks must disclose APY per the Truth in Savings Act. A higher APY means you earn more money. Daily compounding is slightly better than monthly for savers.
- For loans and credit cards: Lenders advertise APR. But if interest compounds daily (as with most credit cards), the actual cost is higher than the stated APR. A 24% APR credit card compounding daily costs an effective 27.1% APY.
- Comparing products: Always compare APY to APY or APR to APR, not one to the other. A savings account with 4.8% APR (daily compounding = 4.917% APY) pays more than one with 4.9% APR (annual compounding = 4.9% APY).
💡 Credit Card Tip: Most credit cards compound interest daily on the outstanding balance. A card with 24% APR = 27.1% APY in true annual cost. The daily periodic rate = 24% ÷ 365 = 0.0658% per day. Even a 30-day delay in paying off a $1,000 balance costs roughly $19.75 in interest at this rate.
Frequently Asked Questions
APR is the nominal annual rate without compounding. APY is the effective annual rate including compounding. APY is always higher than APR when compounding occurs more than once per year. Lenders advertise APR (lower-looking); savings accounts advertise APY (higher-looking). Always convert to the same measure when comparing financial products.
APY = (1 + APR/n)^n − 1, where n is compounding periods per year. For 6% APR monthly (n=12): APY = (1 + 0.06/12)^12 − 1 = (1.005)^12 − 1 = 6.168%. Use the APR → APY tab above for instant conversion.
APR = n × ((1 + APY)^(1/n) − 1). For 5% APY monthly compounding (n=12): APR = 12 × ((1.05)^(1/12) − 1) = 12 × 0.004074 = 4.889%. APR is always lower than APY when compounding is more frequent than annual.
More frequent compounding earns interest on interest more often, increasing the effective yield. At 6% APR: annual compounding APY = 6.000%; monthly = 6.168%; daily = 6.183%. The difference grows with higher rates and longer periods, making compounding frequency a key factor in long-term savings and loan comparisons.
For savings: want HIGH APY (more earnings). For loans: want LOW APR (lower cost). Banks advertise APR on loans and APY on savings for this reason. When comparing products, always use the same metric. A savings account with 4.9% APY versus one with 4.85% APY earns more, regardless of underlying APR.
Most US savings accounts compound daily (365/year). CDs compound daily or monthly. Mortgages compound monthly. Credit cards compound daily on the balance. Bonds typically don’t compound within periods. The Truth in Savings Act requires APY disclosure; the Truth in Lending Act requires APR disclosure.
Continuous compounding is the mathematical limit as compounding frequency approaches infinity. Formula: APY = e^APR − 1. For 6% APR: APY = e^0.06 − 1 = 6.184%. This is nearly identical to daily compounding (6.183%) — beyond daily compounding, gains are negligible in practice.
For mortgages and many consumer loans, the legally required APR disclosure includes origination fees, points, and certain insurance, making it higher than the base interest rate. For credit cards, APR typically equals the periodic rate times periods. Always check the loan disclosure to understand exactly what is included in the stated APR.
EAR is synonymous with APY — the actual annual interest rate accounting for compounding. EAR = APY = (1 + r/n)^n − 1. Finance textbooks use EAR; US banking regulations require APY. They are the same concept and the same formula.
A 24% APR credit card compounded daily has APY = (1 + 0.24/365)^365 − 1 = 27.11%. This means you effectively pay 27.11% per year when interest compounds daily. The daily periodic rate is 24% ÷ 365 = 0.0658% per day, which seems tiny but compounds to a much higher effective annual cost.
In 2026, high-yield savings APYs run approximately 4–5%. Mortgage APRs are approximately 6–7%. Credit card APRs average 20–24%. The spread between savings and loan rates is the interest margin that banks use to profit. For borrowers, APR matters; for savers, APY is the key metric to maximize.
Related Calculators
Popular Calculators
ATV Loan Calculator
Finance
Bitcoin DCA Calculator
Finance
3D Printing Cost Calculator
Finance
Car Lease Calculator
Finance
Stripe Fee Calculator
Finance
Pain & Suffering Calculator
Legal
TDEE Calculator
Health
Roofing Calculator
Construction
GPA Calculator
Education
Mortgage Refinance Calculator
Finance
CPM Calculator
Marketing
Markup Calculator
Finance