Convert between nominal (APR) and effective annual rates (EAR/APY). Compare compounding frequencies: daily, monthly, quarterly, continuous, and custom periods.
The Effective Interest Rate Calculator converts between nominal (APR) and effective annual rates (EAR/APY) across different compounding frequencies. The effective rate reflects the true annual cost or yield after accounting for intra-year compounding — the more frequently interest compounds, the higher the effective rate compared to the nominal rate.
Banks advertise APR (annual percentage rate) for loans and APY (annual percentage yield) for savings — both are correct but serve different purposes. APR is the nominal rate; APY is the effective rate. For a credit card charging 24% APR compounded monthly, the effective annual rate is 26.82% — you actually pay 2.82% more than the stated rate. Understanding this difference is critical for comparing financial products.
Enter a nominal rate and compounding frequency to see the effective annual rate, or enter an effective rate to find the equivalent nominal rate. The comparison table shows how compounding frequency affects your money. It is a quick way to see what the stated rate really means in practice.
Compare financial products on an equal basis. Understand the true cost of borrowing and the true yield of savings after compounding. Use this when comparing APRs, APYs, and any product where compounding frequency changes the result. It helps you compare rates that look similar but compound differently. That is the cleanest way to spot the real annual effect.
EAR = (1 + r/n)ⁿ - 1. Where r = nominal annual rate (decimal), n = compounding periods per year. Continuous: EAR = eʳ - 1. Reverse: r = n × [(1 + EAR)^(1/n) - 1]. Periodic Rate = r/n. Daily Rate = r/365.
Result: EAR = 12.683%, monthly rate = 1.000%
Nominal rate 12% compounded monthly: EAR = (1 + 0.12/12)¹² - 1 = (1.01)¹² - 1 = 0.12683 = 12.683%. The periodic monthly rate is 12%/12 = 1.000%. Compounding adds 0.683% to the effective rate.
Einstein reportedly called compound interest "the eighth wonder of the world." The power comes from earning interest on interest. $10,000 at 10% for 30 years: simple interest = $40,000. Annual compound = $174,494. Monthly compound = $198,374. The difference ($24,000) comes entirely from intra-year compounding growing the effective rate from 10.0% to 10.47%.
For long time horizons, even small differences in effective rate compound dramatically. A 0.5% EAR advantage over 30 years turns $10,000 into $16,000 more wealth.
In the US, Regulation Z (Truth in Lending Act) requires lenders to disclose APR. Regulation DD (Truth in Savings Act) requires depository institutions to disclose APY. The European Union uses the Annual Equivalent Rate (AER), which is essentially the same as EAR.
These regulations ensure consumers can compare products, but they don't eliminate confusion. Many people still don't understand that 24% APR on a credit card means paying 26.82% effectively.
Effective rates apply anywhere growth compounds: population growth (doubling times), radioactive decay (half-lives), inflation (purchasing power erosion), investment returns (CAGR vs average return), and even bacterial growth in biology. The same math underlies all exponential processes.
APR (Annual Percentage Rate) is the nominal rate without intra-year compounding. APY (Annual Percentage Yield) is the effective rate including compounding. For savings, banks advertise APY (higher number looks better). For loans, they advertise APR (lower number looks better). By law, both must be disclosed (Truth in Lending Act / Truth in Savings Act).
More frequent compounding increases the effective rate. 10% APR: annually = 10.00% EAR, semi-annually = 10.25%, quarterly = 10.38%, monthly = 10.47%, daily = 10.52%, continuous = 10.52%. The difference grows with higher rates. At 24% APR: monthly compounding gives 26.82% EAR — a 2.82% difference.
Continuous compounding is the mathematical limit as compounding periods approach infinity. EAR = eʳ - 1. It's used in theoretical finance, Black-Scholes option pricing, and some bond calculations. In practice, daily compounding (365×/year) is very close to continuous and is the most frequent real-world compounding.
Credit cards compound daily on the average daily balance and charge monthly. A 24% APR card effectively charges 26.82% per year. Additionally, the APR doesn't include late fees, over-limit fees, or cash advance surcharges, making the true cost even higher.
Always compare using the effective annual rate (EAR). A loan at 11.5% compounded daily (EAR = 12.19%) is actually more expensive than a loan at 12% compounded annually (EAR = 12.00%). The nominal rate alone is misleading when compounding frequencies differ.
The real (inflation-adjusted) effective rate: Real EAR ≈ EAR - Inflation Rate, or more precisely: (1 + EAR)/(1 + Inflation) - 1. A 5% APY savings account with 3% inflation gives a real return of about 1.94%, not 2%.