APR vs APY: the 2% difference that matters

APR is the rate banks quote on what you borrow. APY is the rate they quote on what you deposit. They differ because of compounding — and the asymmetry is no accident.

The short version

APR (Annual Percentage Rate) is the nominal annual interest rate, ignoring compounding. APY (Annual Percentage Yield) is the effective rate after compounding is included.

If you have an account paying 6% APR compounded monthly, you don't actually earn 6% per year — you earn about 6.17%. That 0.17% is the compounding effect: each month's interest gets added to your balance, and the next month's interest is calculated on the new, slightly larger balance.

APY = (1 + APR / n)ⁿ − 1

where n is the number of compounding periods per year. Monthly compounding → n = 12. Daily → n = 365. Continuous → APY = e^APR − 1.

Why banks advertise different ones

By US federal law (the Truth in Lending Act for loans, and Regulation DD for deposits), banks must disclose:

APR on loans. The number that looks lower than the true cost.
APY on deposits. The number that looks higher than the nominal rate.

This is not a coincidence. Both choices flatter the bank. On a loan, the APR they advertise (say 6%) is less than what you actually pay (6.17% APY with monthly compounding). On a savings account, the APY they advertise (say 5%) is more than the nominal APR (4.89%).

The asymmetry to remember: if a credit card says "24% APR," your effective annual rate is closer to 26.8%. If a high-yield savings account says "5% APY," the nominal rate they're earning interest at is closer to 4.88%. Banks pick the side of the comparison that makes their offer look best.

The numbers, in practice

Here's how APR translates to APY at common compounding frequencies, for a 6% APR:

Annually (n=1): APY = 6.00%
Quarterly (n=4): APY = 6.14%
Monthly (n=12): APY = 6.17%
Daily (n=365): APY = 6.18%
Continuously: APY = 6.18%

Two patterns: (1) more frequent compounding always increases APY, but (2) the marginal benefit drops off fast. Going from yearly to monthly compounding adds 0.17%; going from monthly to daily adds 0.01%. Past daily, there's almost nothing left.

When APR-vs-APY actually matters

For most people, most of the time, the difference is small — 0.1% to 0.5%. But there are scenarios where it's significant:

Comparing loan offers with different compounding frequencies. A 6% APR mortgage with monthly compounding is cheaper than a 6% APR car loan with daily compounding. Convert both to APY to compare apples to apples.
Credit cards. The "24% APR" on a credit card is almost always daily compounding, putting effective APY around 27%. This is part of why credit-card debt spirals — the headline number understates the bleed.
High-yield savings comparisons. If one bank advertises "4.9% APR" and another "5.0% APY," they may be paying the same. Always compare APY to APY.
Long horizons. Even small APY differences compound dramatically over decades. 0.5% extra over 30 years on $100,000 is about $20,000 more.

See it in dollars

The compound interest calculator lets you toggle compounding frequency and watch the gap between APR and APY widen over time.

Open calculator →

The "true cost" version: APR with fees

There's a third number that confuses things further: the APR required by mortgage disclosure rules, which includes loan origination fees. This APR is higher than the nominal interest rate, because it amortizes the fees over the loan's life as additional interest.

Example: a $300,000 mortgage at 6.0% nominal with $3,000 in fees has a disclosed APR of about 6.10%. The fees act like prepaid interest. This is the only common case where the APR shown is bigger than the nominal rate — and it exists to help borrowers compare loans whose fees differ.

Quick conversion rules of thumb

Monthly compounding: APY ≈ APR + (APR² ÷ 24). For 6% APR → APY ≈ 6.15% (actual: 6.17%).
Daily compounding: APY ≈ APR + (APR² ÷ 24) + a hair. Practically the same as monthly.
Continuous compounding: APY = e^APR − 1. For 6% APR → APY ≈ 6.184%.

For practical purposes, anything beyond monthly compounding gives you the "continuous compounding" answer to two decimal places.

The bottom line

APR and APY are not different products — they're different ways of measuring the same product. APY is the honest number (what you actually earn or pay over a year, with compounding); APR is the convenient number (easier to compute, easier to advertise). When you see a financial product quoted in one, always ask what it would be in the other. The gap tells you about the compounding frequency and, indirectly, about which side of the transaction the institution is on.