APR to APY Converter & Interest Rate Calculator
Convert nominal Annual Percentage Rate (APR) to effective Annual Percentage Yield (APY) and vice versa with compounding frequencies.
APR to APY — interactive calculator, computed instantly in your browser.
In personal finance and banking, interest rates are quoted under two distinct metrics: Annual Percentage Rate (APR) and Annual Percentage Yield (APY). The crucial distinction lies in compound interest: APR reflects the simple nominal rate without factoring in compounding, whereas APY reveals the true effective annual interest earned or paid once intra-year compounding is incorporated.
1. Algebraic Conversion Formulas
To convert a stated nominal APR to an effective APY compounded $n$ times per year:
Under mathematical continuous compounding ($n \to \infty$), the formula converges to Euler's constant $e$:
Conversely, to convert an effective APY back to its underlying nominal APR:
2. Practical Worked Example: Credit Card APR vs. Real APY
Most credit card issuers compound interest daily (n = 365). If your credit card carries a stated 24.99% APR:
- Decimal Rate: $\text{APR} = 0.2499$.
- Daily Periodic Rate: $0.2499 \div 365 = 0.000684657$ (0.0685% per day).
- Formula Substitution: $$\text{APY} = \left(1 + \frac{0.2499}{365}\right)^{365} - 1 = (1.000684657)^{365} - 1 = 1.2835 - 1 = \mathbf{28.35\%}$$
- The Consumer Takeaway: Revolving a balance for one year at 24.99% APR actually costs you 28.35% in effective interest charges—an additional 3.36% in compounding penalties.
3. Regulatory Framework: TILA vs. TISA
| Regulatory Statute | Governing Federal Law | Mandated Rate Disclosure | Marketing Objective |
|---|---|---|---|
| Truth in Lending Act (TILA) | Applies to credit cards, mortgages, auto loans, personal debt | Must quote APR prominently | Standardizes debt costs across lenders by preventing hidden fee manipulation |
| Truth in Savings Act (TISA) | Applies to bank deposit accounts, CDs, money market, savings | Must quote APY prominently | Ensures savers see the full benefit of intra-year compounding on their savings |
🔗 Interest Rate Dynamics Cross-References
Lenders quote APR on loans to indicate nominal annual interest costs, while banks quote APY on deposit accounts to reflect the compounding boost. Access our 💰 Financial Hub for complete interest calculation solvers.
Model certificate of deposit yields or analyze compound interest schedules using the related tools below.
Frequently Asked Questions (APR to APY)
APY incorporates interest earned on previously accumulated interest (compounding). When interest compounds more than once per year (n > 1), APY will always mathematically exceed APR. APY only equals APR when interest compounds exactly once per year (n = 1).
Financial institutions highlight the figure that looks most advantageous to the consumer. For savings accounts and CDs, APY is higher, making investment yields look more attractive. For loans and mortgages, APR is lower, making borrowing costs appear cheaper.
Many commercial banks and business lenders historically use a 360-day year (twelve 30-day months, known as the commercial or bank year) to calculate daily interest. A 360-day compounding schedule produces a slightly higher effective APY than a standard 365-day calendar year.
Continuous compounding represents the mathematical limit where interest accrues and compounds at every instantaneous infinitesimal fraction of a second. It is calculated using the natural exponent e (e^r - 1) and represents the absolute theoretical maximum APY achievable for a given rate.