APY is the number you are quoted on a deposit, and it includes the effect of compounding. APR is the number you are quoted on credit, and it does not show intra-year compounding but does include certain fees. They are defined by two different federal regulations for two different purposes, which is why comparing one to the other directly is a mistake rather than a shortcut.

What exactly does APY mean?

Annual percentage yield is defined in Regulation DD, which implements the Truth in Savings Act. The definition is a percentage rate reflecting the total amount of interest paid on an account, based on the interest rate and the frequency of compounding for a 365-day period.

The point of the definition is comparability. Two banks can advertise the same 5.00 per cent interest rate and pay different amounts, because one compounds monthly and the other daily. APY folds that difference into a single number, so two APYs can be compared directly even when the underlying mechanics differ.

The arithmetic is not large but it is real:

• 5.00 per cent compounded once a year is an APY of 5.0000 per cent
• compounded quarterly, 5.0945 per cent
• compounded monthly, 5.1162 per cent
• compounded daily, 5.1267 per cent

APY equals the nominal rate only when interest compounds exactly once a year. Every other frequency makes APY higher.

And what does APR mean?

Annual percentage rate is a credit disclosure, defined under Regulation Z, which implements the Truth in Lending Act and covers mortgages, car loans and credit cards.

It does two things APY does not. It annualises a periodic rate without showing the effect of compounding within the year. And it takes certain finance charges into account, so the figure is a cost of credit rather than a pure interest rate.

That second feature is why a mortgage disclosure shows two numbers. The note rate is the interest rate used to calculate your payment. The APR is higher, because it folds in points and certain closing costs spread across the life of the loan. If you see a rate of 6.25 per cent and an APR of 6.47 per cent on the same offer, the gap is the fees.

So APR excludes compounding. Does that make it understate the cost?

On a credit card, yes, and this is the part that costs people real money.

An issuer converts the APR into a daily periodic rate by dividing by 365, then applies it to the balance each day. If you carry a balance, yesterday's interest is part of today's balance, so the interest compounds daily even though the quoted APR does not reflect that.

Take a 24.99 per cent APR. The daily periodic rate is about 0.0685 per cent. Compounded over a full year on a carried balance, the effective cost is roughly 28.4 per cent, about three and a half percentage points above the quoted figure.

The practical consequence: on a card, the quoted APR is the floor of what carrying a balance costs, not the total. On a loan with fixed instalments and no revolving balance, the APR is a fair representation.

Why does compounding frequency matter so little at these rates, and so much elsewhere?

Because the gap between a nominal rate and its APY grows with the rate, not just with the frequency.

At 5 per cent, daily compounding adds about 0.13 percentage points over annual compounding. At 24.99 per cent, the same daily compounding adds roughly 3.4 points. The arithmetic is the same; the stakes are not.

That asymmetry is exactly why the two disclosures ended up on opposite sides of the balance sheet. On deposits, where rates are low, compounding is a small effect and the regulation still insists on showing it. On revolving credit, where rates are high, compounding is a large effect and the quoted figure does not show it at all.

Nothing about that is hidden. It is a consequence of two statutes written at different times for different purposes, and it means the one place where reading the quoted number literally will cost you money is the place where the number is largest.

Does any of this change if the rate is variable?

Both figures are snapshots, and a variable rate makes them snapshots of something that will move.

A savings APY on a variable-rate account is calculated from today's rate, and the bank can change the rate at any time with notice. Nothing in the disclosure promises that the APY will still be available next month, which is why a chart of a bank's historical rate is more informative than its current headline.

A variable APR on a card is usually tied to the prime rate with a fixed margin on top, so it moves when the policy rate moves. A card quoted at prime plus 18 points reprices automatically, and the quoted APR on your statement will not be the one you were approved at.

Fixed-rate instalment loans are the clean case. The APR is set at origination and holds for the life of the loan, which is the only situation in this article where a single quoted number describes the whole arrangement.

Which number should I compare?

Like for like, and never across the two.

On deposits, compare APY to APY. A savings account, a certificate of deposit and a money market account can all be compared on APY, which is exactly what the disclosure exists for.

On credit, compare APR to APR, because it is the only quoted figure that includes fees. Two mortgages with the same note rate and different APRs are not the same offer.

Comparing a 5.1 per cent savings APY to a 5.1 per cent loan APR tells you almost nothing, because the first includes compounding and no fees and the second includes fees and no compounding.

Why do banks quote different things in different places?

Because the regulations require it, and the incentives line up with it.

On a deposit, the bank must advertise APY, which is the higher of the two possible figures and the flattering one. On a loan, it must disclose APR, which includes fees and is therefore higher than the note rate, and is the less flattering one. In both cases the regulated disclosure is the one that is harder to game.

Where it gets slippery is the unregulated space around them. A promotional headline rate for three months, a bonus paid only if you keep a balance, or a tiered structure where the advertised APY applies only to the first few thousand dollars, are all ways to publish a correct APY that very few customers will actually earn. The figure is accurate and the implication is not.

The same spread between what a bank pays depositors and what it charges borrowers is the core of how banks make money.

Does APY apply to investments?

Not properly, and the confusion is worth clearing up.

APY is a deposit disclosure for an account paying a contractual rate of interest. A stock, a fund or a bond does not pay an APY. What they produce is a return, which is not promised and can be negative, and the correct comparison measure for those is total return or yield to maturity rather than APY.

When a crypto or fintech product advertises an APY, read it carefully. The term is being borrowed from a regime designed for insured deposits paying contractual interest, and it is being applied to something that is usually neither insured nor contractual. Whether deposit insurance applies is a separate question, and how FDIC insurance works covers the US position.

What about APY on a CD with a term under a year?

This is where the 365-day convention shows.

APY annualises, so a six-month certificate quoting 5.00 per cent APY does not pay you 5 per cent over the six months. It pays the amount that, if the rate continued for a full year with the same compounding, would total 5 per cent. Over six months you receive roughly half of it.

The same logic applies in reverse to introductory offers. A 7 per cent APY for the first three months is worth about one and three quarter per cent in actual interest, after which the rate reverts. The APY figure is correctly calculated and the headline is doing work the arithmetic does not support.

The short version

APY answers what will I earn, including compounding, with no fees in it. APR answers what will I pay, including certain fees, with no compounding shown.

On a deposit, read the APY and then check how long the quoted rate lasts and whether it applies to your whole balance. On credit, read the APR and then check whether it is a revolving balance, in which case daily compounding makes the true cost higher than the number quoted.

This article explains two disclosure standards and is not financial advice.