How this APY calculator works
Annual percentage yield (APY) is the rate that tells you what a balance really earns in a year once compounding is taken into account. A stated, or nominal, rate — often called the APR — is the simple annual rate before compounding. But when interest is added to the balance several times a year, each later round of interest is calculated on a slightly larger balance, so the effective return ends up higher than the nominal rate. APY captures that effect in one number.
The formula is APY = (1 + r ÷ n)n − 1, where r is the nominal rate written as a decimal and n is the number of compounding periods per year — 365 for daily, 12 for monthly, 4 for quarterly, 2 for semiannual and 1 for annual. You divide the rate across the periods, grow the balance period by period, then subtract one to convert back into a rate. Multiplying by 100 turns it into a percentage. Because compounding only ever adds value, APY is always greater than or equal to APR, and equal only when compounding is annual.
This tool also works in reverse: given a target APY and a compounding frequency, it solves for the nominal APR using APR = n × ((1 + APY)1 ÷ n − 1). If you add a starting balance, it shows the interest earned over one year (balance × APY) and the ending balance, and it lists the APY you would get at each compounding frequency for the same nominal rate.
Reference note: these figures are simple APY and APR math and do not account for fees, taxes, introductory or promotional rates, minimum-balance rules, or rate changes over time. Results are an estimate, not financial advice.
Frequently asked questions
- What is APY?
- APY, or annual percentage yield, is the effective annual rate of return once compounding is taken into account. It tells you how much a balance actually grows in one year as a single percentage, assuming the rate and compounding frequency stay the same.
- What is the difference between APY and APR?
- APR is the nominal annual rate before compounding, while APY is the effective rate after compounding within the year. APR ignores how often interest is added to the balance; APY accounts for it, so APY more accurately reflects what you actually earn or pay over a year.
- How is APY calculated?
- APY equals one plus the nominal rate divided by the number of compounding periods per year, raised to the power of that number of periods, minus one: APY = (1 + r / n) ^ n − 1, where r is the nominal rate as a decimal and n is the compounds per year. Multiply by 100 for a percentage.
- Why is APY higher than the stated rate?
- Because of compounding. When interest is added to the balance during the year, later interest is earned on the earlier interest as well as the principal. The more frequently compounding happens, the larger this effect, so APY is greater than or equal to APR and equal only when compounding is annual.
- What compounding frequency is best?
- For money you earn interest on, more frequent compounding gives a slightly higher APY for the same nominal rate, so daily beats monthly, which beats annual. The gains shrink as frequency rises and approach a limit called continuous compounding. For money you owe, more frequent compounding works against you.
- Is this financial advice?
- No. This calculator is an informational tool that performs basic APY and APR math. It does not account for fees, taxes, introductory rates, minimum balances, or rate changes over time, and it is an estimate, not financial advice. Consult a qualified professional before making financial decisions.