Why can a 4% annual interest rate produce an APY above 4%?

Name the rate before calculating

The CFPB explains compound interest as earning interest on both saved principal and previously earned interest. Its U.S. Regulation DD appendix separately sets out annual percentage yield calculations for deposit disclosures. Those legal calculations depend on the account terms and actual term length.

This exercise uses a nominal annual deposit interest rate, not a legally defined borrowing APR. Loan APR can include specified borrowing charges and follows different rules. A label saying only “annual rate” is insufficient: record compounding frequency, term, rate changes and whether credited interest remains in the account.

An original four-period deposit ledger

Stipulate a fictional opening deposit of 1,000, a constant nominal annual rate of 4%, four equal modeled quarterly compounding periods and no deposits or withdrawals. Divide 0.04 by 4 to obtain a 1% periodic rate. Ignore fees, taxes and intermediate rounding; the example is not an available account offer.

The balances after each period are 1,010;1,020.10;1,030.301; and 1,040.60401. The interest amounts are 10;10.10;10.201; and 10.30301. Adding the four interest amounts gives 40.60401, exactly the ending balance minus the starting 1,000.

Reconcile dollars and the annual percentage

The full-year effective yield is 40.60401/1,000=0.04060401, or 4.060401%. Equivalently, (1+0.04/4)^4−1 gives the same result. This exceeds 4% because interest credited before the end of the year earns additional interest in later modeled periods.

For this unchanged-principal, full-year example, the ending-balance ratio and interest-to-principal ratio reconcile. Do not substitute an ending balance containing new deposits into that simple return calculation: contributions change the balance without being interest. Actual U.S. APY disclosures also specify calculation and rounding conventions.

Hold the effective yield constant as a control

Now stipulate a second fictional account that compounds once at year end at 4.060401%. The same 1,000 becomes 1,040.60401. More frequent compounding did not make the first account better when the two effective annual yields were equal; the nominal rates were different.

Conversely, annual compounding at exactly 4% would end at 1,040. The 40.60401−40=0.60401 difference belongs to this particular principal, rate and interval model. It is not an extra universal bonus to add on top of an already stated APY.

Check the boundaries that a percentage omits

A variable rate, an early withdrawal, a balance tier, a fee or a different interest-crediting rule can change actual dollars received. A promotional APY does not itself prove that funds remain accessible on a needed date or that a balance is protected against loss.

Use a comparison record containing the opening principal, term, rate schedule, compounding rule, withdrawals and charges. Recompute ending dollars under the actual contract. A slightly higher displayed percentage is not enough to establish which account serves a particular person’s needs.

Method, sources, and limits

The ledger and equal-yield control are original hypothetical teaching inputs, calculated on 27 October 2026. Four modeled quarters simplify the compounding mechanism; this page is not an account advertisement, a statutory APY compliance calculation or a recommendation to move money. AI-assisted drafting is not qualified human financial review.