An interest rate describes the stated annual rate paid on a deposit. Annual percentage yield, usually shortened to APY, also reflects compounding under the account's assumptions. The difference appears when interest starts earning further interest.
Both figures need their labels. A calculator receiving a nominal annual interest rate should not treat an APY as the same input and then compound it again. That would count the compounding effect twice.
Start with a fictional deposit
Suppose a fictional account contains $10,000 and pays a 4% annual interest rate. There are no fees, additional deposits or withdrawals in this example. The rate stays unchanged for the full year.
With annual compounding, the year's interest is $400. The ending balance is $10,400. Because no interest earns further interest within that year, the annual yield is also 4%.
Now change only the compounding frequency to monthly. The monthly periodic rate is 0.04 divided by 12. After each period, interest joins the amount used for the next period's calculation.
The first month's unrounded interest is about $33.33. The next calculation starts from a slightly larger balance. The later interest amounts therefore grow even though the annual rate has not changed.
Calculate the annual yield
For equal monthly periods and a fixed nominal annual rate, the example's growth factor is (1 + 0.04 / 12) raised to the power of 12. It is approximately 1.04074154.
The $10,000 ending balance is about $10,407.42, with $407.42 of interest before tax. The APY is about 4.0742%, commonly displayed with fewer decimal places. The extra $7.42 comes from interest earning interest within the year.
This calculation assumes equal periods and leaves rounding until the end. Actual deposit disclosures can use daily balance methods, actual dates, tiered rates or other rules. CFPB's APY regulation describes the prescribed annualisation calculations, which are more detailed than a general monthly example.
An APY is already annualised
Suppose another fictional account quotes a 4% APY. For $10,000 left in that account for a full year under the quote's assumptions, the annual interest is $400. Applying monthly compounding to 4% again would produce the wrong comparison.
The nominal interest rate associated with that APY depends on the compounding frequency. The account disclosure, rather than the abbreviated marketing number, contains those details.
An annualised figure also does not mean a six-month account earns the whole year's percentage. Under the first example's 4% nominal rate with monthly compounding, six periods produce a balance of approximately $10,201.67. The interest is $201.67 before tax, not $400 or $407.42.
Fees, changes and withdrawn interest
A rate calculation describes interest. A service fee reduces the account's balance through a separate charge. The interest result and the amount left after charges are therefore different records.
A variable rate can change during the year. A projection that repeats today's rate across twelve months assumes it stays unchanged. The calculation does not establish that the account will actually pay that rate for the full period.
Withdrawing interest also changes what remains to earn further interest. A displayed APY can assume interest stays on deposit. A monthly cash payout is a different cashflow arrangement from retaining every credit in the account.
Reading a calculator result
FinTarget's compound interest calculator illustrates growth from stated inputs. The input's meaning and the compounding setting need to match the calculation being demonstrated.
A reproducible example records the principal, whether the percentage is a nominal rate or APY, the term, the compounding frequency and the treatment of interest payments. Those labels explain a difference of a few dollars without turning the example into an account recommendation.