APR vs APY: why the difference matters

APR is the annualized interest rate on a loan or deposit before compounding, and APY is the same rate after compounding within the year is included. The two numbers describe the same underlying loan, and they almost never agree. APY is always equal to or higher than APR, and the gap widens with how often interest gets added to the principal.

Lenders quote APR. Savers see APY. Credit card statements quote APR but charge you APY. The mismatch is legal and standardized, written into different parts of the same regulatory regime, but it's the single most common reason a retail investor or a junior analyst misreads a financial product on first pass.

How it works

Start with a 12% APR. If interest pays once a year, that's it. You earn (or owe) 12% over twelve months, and the APY is also 12%. No compounding, no gap.

Now compound monthly. Each month accrues 1% (12% / 12). After January you sit on $101 against a $100 deposit. February's 1% applies to $101, not $100, so it pays $1.01 instead of $1.00. Repeat for the full year and the effective return is (1.01)^12 − 1, which equals 12.68%. That 0.68% gap is the compounding. The mechanics rest on principal and interest from What is a loan.

The same formula, written once and substituted three ways:

APY = (1 + APR/n)^n − 1

12% APR, monthly:    (1 + 0.12/12)^12   − 1 = 12.68%
12% APR, daily:      (1 + 0.12/365)^365 − 1 = 12.747%
12% APR, continuous: e^0.12             − 1 = 12.750%

Compound daily and the gap widens further. Compound continuously, the theoretical limit used in derivatives pricing, and you hit the third line above. The marginal gain shrinks fast. Going from annual to monthly buys you 68 basis points. Going from daily to continuous buys you less than half a basis point.

The math runs both directions. Credit cards advertise APR for the same regulatory reason savings products advertise APY: the lower-sounding number markets better. A 24% credit card APR with daily compounding works out to 27.12% APY, and if you carry a balance for the full year, that 3.12 percentage point gap is what the card actually charges you above the headline rate.

Why it matters

Compare two products quoted on different conventions and you'll get the wrong answer. A "5% APR" CD and a "5% APY" money market fund don't pay the same. The CD pays more if it compounds more than once a year, and the money market fund pays exactly what it says. Without normalizing, you're stacking apples on oranges.

Regulators picked which side has to quote what. In the US, Truth in Lending requires APR for loans and Regulation DD requires APY for deposit accounts. The intent is consumer protection: borrowers see the higher number on what they pay, savers see the higher number on what they earn. Both make their respective products look slightly worse on paper, which is the point.

For institutional capital, the convention matters less than the math. A pension fund modeling expected returns over a 10-year holding period can't take a brokerage's APR quote at face value: they convert it to APY, or to a continuously compounded rate, before the number gets plugged into a portfolio model that rolls cashflows forward across hundreds of periods. Mixing conventions inside a model is a small error per year that compounds (literally) over the holding period.

Where this shows up in institutional crypto-backed lending

Onchain lending protocols expose both numbers. Borrowing rates are usually quoted as APR (per-block accrual, no compounding assumption baked in), while supplier earnings often display as APY because interest re-deposits into the supplier's principal continuously. The same protocol can show one rate to a borrower and a higher rate to a supplier on the same market, and the spread between them looks tighter than it really is.

For Rekord and similar institutional RWA platforms, the distinction matters operationally. Returns paid out of an underlying portfolio of real-world loans run on a different cashflow rhythm than the on-chain numbers suggest. See The capital cycle: how stablecoin deposits become real-world returns and Cashflow timing and reward sustainability for what changes when the displayed rate and the actual cash arrival diverge.