Banks quote one number when they want to pay you and a different one when they want to charge you, and the difference is not an accident. APY, the annual percentage yield, includes the effect of compounding, so it shows what you truly earn on a deposit. APR, the annual percentage rate, is a nominal figure that leaves compounding out. Knowing which is which keeps you from comparing two rates that are not measuring the same thing.
What APR measures
APR is a simple annualized rate: take a periodic rate and multiply it by the number of periods in a year. It does not account for interest earning interest during the year, so it understates the real yield when compounding happens more than once annually. On the lending side, regulators require an APR that also folds in certain loan fees, which is why it is the standard cost measure for borrowing. As a deposit rate, though, APR is just the stated nominal rate before compounding.
What APY measures
APY captures the full effect of compounding, so it is always equal to or higher than the nominal rate. The formula is APY equals (1 plus r divided by n) raised to the power n, minus 1, where r is the nominal annual rate and n is the number of compounding periods per year. The more frequently interest compounds, the more the APY pulls ahead of the nominal rate. Because APY reflects what you actually keep, it is the honest number for comparing savings accounts and CDs.
Why the law splits them
United States rules deliberately assign each term to a side of the ledger. The Truth in Savings Act and Regulation DD require banks to advertise deposit rates as APY so savers can compare on equal footing. The Truth in Lending Act and Regulation Z require lenders to disclose borrowing costs as APR. This is why your savings statement shows APY and your loan paperwork shows APR.
Comparing rates the right way
When shopping for a place to park cash, compare APY to APY and ignore any nominal rate a bank leads with. When shopping for a loan, compare APR to APR so fees are included. Mixing the two makes a deposit look worse or a loan look cheaper than it is. If a bank quotes only a nominal rate, you can convert it to APY yourself with the compounding formula.
A savings account advertises a 5 percent nominal rate compounded monthly. Using the APY formula, (1 plus 0.05 divided by 12) to the 12th power minus 1 works out to about 5.12 percent APY. So a bank quoting 5 percent nominal is really paying 5.12 percent once monthly compounding is counted.
Key takeaways
- APR is a nominal annual rate that ignores compounding within the year.
- APY includes compounding and is always equal to or higher than the nominal rate.
- Banks quote APY on deposits and APR on loans by regulation.
- Always compare APY to APY and APR to APR, never one against the other.
Common mistakes
- Comparing one bank's nominal rate against another's APY.
- Assuming APY and APR are just two names for the same number.
- Ignoring how compounding frequency changes the effective yield.
FAQ
Is a higher APY always better for savings?
For a pure deposit, yes, a higher APY means more interest, though you should still check for fees or balance requirements that could offset it.
Why is the APR on my loan higher than the interest rate?
Loan APR includes certain fees and costs on top of the nominal interest rate, so it reflects the fuller cost of borrowing.