Annual percentage yield, or APY, answers a simple question: if you left money in this account for a full year, untouched, by what percentage would it grow? A 4.00% APY means $10,000 becomes $10,400 after one year. The reason APY is the number to compare — rather than the interest rate printed next to it — is that APY already includes compounding, so two accounts quoting APY can be compared directly even if one compounds monthly and the other daily. This guide shows the formula, works it at the specific rates savers search for, and ends with the one warning that matters: APYs on savings accounts are variable, so the rate you see today is not a promise about next year. Check the bank for the current rate before you decide.

What APY means, in plain terms

APY is a standardised measure of what a deposit earns in a year, with compounding counted in. The standardisation is the point. Banks compound interest on different schedules — monthly is the most common for savings accounts, daily is also used — and a plain interest rate does not tell you which schedule sits behind it. APY removes that ambiguity: it states the growth you actually get over a full year, whatever the schedule. That is why comparison sites, account pages and regulators all quote APY for deposit products, and why our high yield savings calculator takes APY as its input rather than a nominal rate.

Two cautions belong in the first section, not the last. First, the APY on a savings account is variable: the bank can raise or lower it at any time, and in practice the whole shelf of offers drifts with the wider rate environment. Treat every APY figure in this article as an illustrative example, not a current offer, and check the bank for the rate it pays today. Second, a headline APY can be tiered — paid only up to a capped balance, with a lower rate above it. The tiered case is priced in our guide to comparing high-yield savings accounts; the formula below assumes one rate on the whole balance.

The APY formula, worked step by step

The formula converts a nominal (stated) interest rate and a compounding frequency into the effective yearly yield. Written out: APY equals (1 + r divided by n), raised to the power n, minus 1 — where r is the nominal annual rate as a decimal and n is the number of compounding periods in a year. For monthly compounding n is 12; for daily compounding n is 365.

Work it for a nominal rate of 4.00% compounded monthly. Divide 4.00% by 12 to get the monthly rate, 0.3333%. Raise 1.003333 to the power 12, which gives 1.040742, and subtract 1: the APY is 0.040742, or 4.0742%. The extra 0.0742 percentage points over the nominal rate is the compounding itself — interest earned in earlier months earning interest in later ones. Compound the same 4.00% nominal rate daily instead and the APY is 4.0808%: daily compounding beats monthly, but only by a whisker, which is why the compounding schedule matters far less than the rate itself.

The pattern to remember: the APY is always a little above the nominal rate, and the gap grows with the rate. At 3.00% the monthly-compounding gap is about 0.04 percentage points; at 7.00% it is about 0.23. If you need the conversion rather than the explanation, our APY calculator runs it in both directions — nominal rate to APY, and APY back to the monthly rate.

APY examples at real balances

Because APY is already the effective yield, the one-year examples are simple multiplication — which is exactly why the specific-APY questions savers ask have clean answers. These are worked examples at illustrative rates, not current offers from any bank.

Stretch the same balances over five untouched years and compounding shows its weight. At 3.00% APY, $10,000 grows to $11,592.74. At 5.00% it reaches $12,762.82. At 7.00% it reaches $14,025.52. The five-year gap between the 3.00% and 7.00% cases is $2,432.78 on the same starting deposit — the reason rate shopping matters more the longer money sits. Add monthly deposits and the deposit does most of the work; that case is worked month by month in our guide to how savings account interest is calculated.

Monthly and daily APY calculators: the logic inside them

An APY calculator that works monthly is doing one conversion and then a loop. The conversion turns the APY back into a monthly rate with a 12th root: monthly rate equals (1 + APY) raised to the power (1/12), minus 1. At 4.00% APY that is 0.3274% a month — note it is slightly less than 4.00% divided by 12 (0.3333%), because dividing by 12 would double-count the compounding and overstate the year. The loop then credits that monthly rate twelve times. On $10,000 the first month credits $32.74, the credits creep upward as each one joins the balance, and the year closes at exactly $10,400.00 — the check that the conversion is right. A daily APY calculator does the same job with a 365th root: the daily rate from a 4.00% APY is about 0.0107% a day, credited 365 times to the same $10,400.00 endpoint. If a calculator you use lands anywhere else after a full year on a single deposit, its conversion is wrong, whichever root it claims to use.

APY vs APR vs interest rate: three different numbers

Three terms get mixed up constantly, and the mix-up costs money when it happens on a loan. The interest rate (nominal rate) is the stated rate before compounding — the raw ingredient. APY is that rate after compounding, for money you deposit: the yield you actually receive. APR is the mirror image for money you borrow: the yearly cost of a loan, including most fees, expressed as a rate. APR belongs to borrowing, APY belongs to saving, and the nominal rate belongs to neither until a compounding schedule is attached to it. The full three-way comparison, with worked loan-side examples, is in our article on APR vs APY vs interest rate — and the practical consequence is simple: compare deposit accounts on APY, compare loans on APR, and never compare one against the other.

Sources: FDIC National Rates and Rate Caps, October 2026 (national average savings rate 0.38% as cited on the HYSA hub); Consumer Financial Protection Bureau, consumer guides defining APY as the effective annual yield on a deposit account. All APY figures in this article are illustrative worked examples, not current offers from any bank. This article is general information, not financial advice.