Convert between nominal, effective, APR, APY, periodic, and continuous interest rates. Supports any compounding frequency for loans and investments.
Interest rates come in many forms — nominal (stated), effective (APY), periodic, APR, and continuously compounded. Comparing financial products requires converting them to the same basis. A 6% APR compounded monthly is not the same as 6% compounded daily or 6% simple interest.
The Interest Rate Converter instantly converts between all common rate formats. Enter any rate with its compounding frequency and see the equivalent rate expressed every other way — nominal, effective annual, periodic, and continuous.
This utility calculator is essential for comparing loans, savings accounts, CDs, and investments that quote rates differently. No more manual calculations or confusion about which rate is the "real" rate. The difference between nominal and effective rates matters more than most borrowers realize. A credit card advertising 24% APR compounded daily actually carries an effective annual rate of 26.82%, and savings accounts compound at different frequencies too. Converting all rates to a common basis is the only way to make accurate comparisons across financial products.
Financial products deliberately quote rates in the most favorable format. Savings accounts advertise APY (which looks higher), while loans advertise APR (which looks lower). To make fair comparisons, you need all rates converted to the same basis. This converter does that instantly for any compounding frequency. Without a common baseline, you cannot accurately compare a mortgage APR to a credit card rate or a savings account APY.
Effective rate = (1 + nominal/n)^n − 1. Nominal rate = n × [(1 + effective)^(1/n) − 1]. Continuous rate = ln(1 + effective). Periodic rate = nominal / n. Effective from continuous = e^r − 1.
Result: 6.168% APY, 0.5% monthly, 5.991% continuous
A 6.0% nominal rate compounded monthly has an effective annual rate (APY) of 6.168% — the extra 0.168% comes from earning interest on interest each month. The equivalent periodic (monthly) rate is 0.5%, and the equivalent continuously compounded rate is 5.991%.
Lenders and banks choose the rate format that looks most attractive. Savings banks advertise APY because compounding makes it higher than the nominal rate. Loan providers advertise APR because it excludes compounding effects and looks lower. Understanding the conversion between these formats is essential for making informed financial decisions.
For a 6% nominal rate: Annual compounding yields 6.000% effective. Quarterly yields 6.136%. Monthly yields 6.168%. Daily yields 6.183%. Continuous yields 6.184%. The difference between monthly and daily is just 0.015% — but between annual and monthly it is 0.168%, which matters on large balances.
Credit cards typically compound daily on a monthly billing cycle. Mortgages compound monthly. Savings accounts compound daily or monthly and disclose APY. Treasury bonds use semi-annual compounding. This converter handles all these conventions so you can compare any two products fairly.
A quick mental shortcut: divide 72 by the interest rate to estimate doubling time. At 6% effective, money doubles in approximately 12 years (72 ÷ 6 = 12). This works best for rates between 4-12%.
APR (Annual Percentage Rate) is the nominal rate without compounding — it is the periodic rate multiplied by the number of periods. APY (Annual Percentage Yield) includes the effect of compounding within the year. APY is always ≥ APR. For a 6% APR compounded monthly, the APY is 6.168%.
A nominal rate is the stated annual rate before accounting for compounding. If a credit card charges 1.5% per month, the nominal rate is 18% (1.5% × 12). The effective rate is higher (19.56%) because monthly compounding means you pay interest on interest.
Continuous compounding is the mathematical limit of compounding infinitely often. It uses the formula A = Pe^(rt). In practice, no financial product compounds truly continuously, but the concept is used in options pricing (Black-Scholes), certain bonds, and academic finance.
For typical consumer rates (3-10%), the difference between monthly and daily compounding is small — usually 0.01-0.05% APY. Between annual and monthly compounding, the difference is more noticeable (0.1-0.5%). At high rates (20%+ credit cards), compounding frequency matters more.
Use APR for comparing loans of the same type with the same fee structure. If fees differ, use the effective APR (which factors in fees). For savings products, always compare using APY. The key is comparing the same type of rate across products.
For APR (nominal): monthly rate × 12. For APY (effective): (1 + monthly rate)^12 − 1. Example: a 1.5% monthly rate equals 18% APR but 19.56% APY. The APY is the true annual cost because it includes compounding.