APY & Interest Calculator
Turn a nominal interest rate into what it actually earns once compounding is applied, convert back the other way, and project a balance forward. Every result shows the formula it came from, because APR and APY are quoted interchangeably and are not the same number.
Effective annual yield (APY)Enter a rate to see both numbers side by side
What a stated rate is really worth once it compounds.
APR and APY are not the same number. APR ignores compounding; APY includes it. A 5% rate compounded monthly yields 5.116%, and compounded daily it yields 5.127%: same stated rate, different money. Lenders quote the lower figure and savings accounts quote the higher one, for identical arithmetic, which is why both are shown above rather than one standing in for the other. Everything on this page is arithmetic; it has no opinion about what anyone should do with their money.
Common questions
- What is the difference between APR and APY?
- APR is the nominal annual rate and ignores compounding. APY is the effective annual rate and includes it. A 5% nominal rate compounded monthly earns 5.116% over a year, because each month's interest itself earns interest. The gap widens with the rate and with compounding frequency. Savings products advertise the higher APY; loans advertise the lower APR; the underlying arithmetic is identical.
- How is APY calculated?
- APY = (1 + r/n)^n − 1, where r is the nominal annual rate as a decimal and n is the number of compounding periods per year. For 5% compounded monthly: (1 + 0.05/12)^12 − 1 = 0.05116, or 5.116%. For continuous compounding the limit is e^r − 1. The tool prints the substituted formula alongside the answer.
- Does compounding more often always earn more?
- Yes, but with sharply diminishing returns. At 5% nominal, annual compounding yields 5.000%, monthly 5.116%, daily 5.127%, and continuous 5.127%. The entire gap between daily and infinitely often is under a thousandth of a percentage point. Beyond monthly, compounding frequency is close to a marketing detail.
- Can I work backwards from an advertised APY?
- Yes. The reverse mode solves for the nominal rate: r = n × ((1 + APY)^(1/n) − 1). This is the useful direction when comparing an account advertising 4.5% APY compounded daily against one advertising a 4.45% nominal rate, which are nearly the same product described two ways.
- Does it handle negative rates?
- Yes. Negative nominal rates compound the same way and the tool computes them rather than erroring, which matters for modelling real-terms returns after inflation or the negative-rate environments some central banks have run. A zero rate returns exactly zero rather than a floating-point artefact near it.
- Is this financial advice?
- No. This is an arithmetic tool: it computes what a rate does under a compounding schedule you specify, and nothing more. It does not know your tax position, does not model fees, introductory rates or early-withdrawal penalties, and offers no opinion on any product. For decisions about your money, talk to a qualified adviser.
Exact arithmetic for the formula shown. It does not model fees, tax, introductory rates or penalties, and it is not financial advice.