APR vs APY: Why They Differ

APR and APY both describe an annual interest rate, yet the same 6% can be reported as either 6.00% or 6.17% depending on which label is attached. The difference is compounding — and knowing which side of the quote you are on explains why lenders and banks pick the one they do.

Nominal vs effective rates

An APR (annual percentage rate) is a nominal rate: the yearly rate stated without accounting for compounding that happens within the year. An APY (annual percentage yield) is an effective rate: what you actually earn or pay over a full year once intra-year compounding is included. If interest is applied only once per year, the two are identical. Any more frequent compounding drives the effective figure above the nominal one.

The gap is not rounding noise. It is real money that compounds on itself: interest credited mid-year starts earning its own interest for the remainder of the year.

The bridge formula

Converting a nominal annual rate r compounded n times per year into the effective annual rate is one line:

APY = (1 + r/n)ⁿ − 1

Each period earns r/n, that growth applies n times, and subtracting 1 strips out the original principal. For a 6% nominal rate:

• Compounded annually (n = 1): (1.06)¹ − 1 = 6.00%
• Compounded monthly (n = 12): (1.005)¹² − 1 = 6.17%
• Compounded daily (n = 365): (1 + 0.06/365)³⁶⁵ − 1 ≈ 6.18%

Going the other direction, solve for r: APR = n × ((1 + APY)^(1/n) − 1). As n grows without bound the effective rate approaches the continuous-compounding limit e^r − 1 — for 6% that is about 6.184%. Notice how most of the drift happens in the first few steps: monthly captures nearly all of it, daily barely moves the needle (the same diminishing returns covered in how compound interest works).

Why lenders quote APR and savings quote APY

The split is part regulation, part psychology. US regulation requires APR on loans (Truth in Lending) and APY on deposit accounts (Truth in Savings), and each side quotes the figure that flatters its product. On a loan, a nominal APR looks smaller than the effective rate you effectively bear when interest compounds monthly. On a savings account, an APY looks bigger than the nominal rate the bank is advertising. Same math, opposite incentives: borrowers see the smaller number, savers see the larger one.

This also means the two labels are not symmetric. An APY is always a complete, comparable annual figure. An APR usually is not — it is the starting point from which the effective rate is built.

When APR is not purely nominal

Two wrinkles keep APR from being simply "the nominal rate." First, on US mortgages the disclosed APR folds certain lender fees into the rate, so a loan's APR is typically higher than its advertised interest rate — that spread is the fee burden expressed as a rate, useful for comparing offers. Second, credit card APRs are nominal rates with interest compounded monthly, so carrying a balance costs slightly more than the APR suggests: a 24% APR costs about 26.8% a year effectively. In both cases the fix is the same — convert everything to an effective annual figure before comparing.

Comparing offers safely

Any comparison between two financial products should use one consistent unit:

• Comparing savings accounts at different compounding frequencies? Compare APYs directly — that is the whole point of the number.
• Comparing loans with different fee structures? Compare APRs (for mortgages, which include fees) or nominal rates plus a fees tally.
• Comparing anything across the loan/savings divide? Convert both to effective annual rate with the bridge formula first.

The underlying compounding machinery behind both conversions is the (1 + r/n)^(nt) growth curve; how to put scenarios side by side is covered in compound interest comparison.

Try it yourself

The Compound Frequency Calculator applies the bridge formula across annual, monthly, daily, and continuous compounding so you can watch the effective rate converge. The Compound Interest Calculator turns any nominal rate and frequency into an actual balance over time, and the Compound Interest Comparison Calculator puts competing scenarios on one line each — the fastest way to see an APY difference in dollars.