APY vs interest rate
Banks publish two rate numbers and they mean different things. Getting them mixed up is the single most common error in savings maths, and it is the one that makes projections too optimistic.
The two numbers
The interest rate is the nominal annual rate the bank applies to your balance. It says nothing about how often it gets applied. The annual percentage yield is what you end up with after a year once the compounding has happened.
If a bank quotes 4.00% and compounds daily, it takes 0.04, divides by 365, and applies that tiny amount to your balance every day. Because each day's interest joins the balance, the next day earns slightly more. Over a full year that process turns 4.00% into 4.0808%. On $10,000 you receive $408.08 rather than $400.00.
The formula
APY = (1 + r/n)n minus 1, where r is the nominal annual rate as a decimal and n is the number of compounding periods per year.
For the daily case: 0.04 divided by 365 gives 0.00010959. Add one to get 1.00010959, raise it to the power of 365 to get 1.040808, and subtract one. That is 4.0808%.
The APY calculator runs this both ways, so you can also start from an advertised APY and recover the nominal rate behind it.
How much the compounding schedule is worth
| Compounding | APY | Year one interest |
|---|---|---|
| Annually | 4.0000% | $400.00 |
| Quarterly | 4.0604% | $406.04 |
| Monthly | 4.0742% | $407.42 |
| Daily | 4.0808% | $408.08 |
Eight dollars separates the two extremes. Banks advertise daily compounding as though it were a feature worth switching for, and on realistic balances it is worth a cup of coffee a year. The rate itself is where the money is.
Why the law made APY mandatory
Before standard disclosure, banks could quote whatever rate flattered them, and comparing two accounts meant reverse-engineering each one's compounding schedule. The Truth in Savings Act and Regulation DD ended that by requiring a single figure, calculated one agreed way, on deposit account disclosures.
It is one of the few genuinely useful pieces of consumer finance regulation. If both banks are quoting APY, the higher number pays more. There is nothing else to check.
APY is not APR
APR describes borrowing. It bundles the interest rate with certain fees to give a comparable cost of credit, and it generally does not compound. APY describes deposits and does compound.
A 6% APR on a loan and a 6% APY on a savings account are not mirror images of each other, and the difference goes in the direction that costs you money in both cases. Seeing APR on a savings product is unusual enough to be worth a second read of the disclosure.
The mistake this guide exists to stop
Once you have an APY, do not compound it again. This sounds obvious and it is the most common error in savings calculators on the web.
Take a 4.00% APY and a calculator that divides it by twelve, then compounds monthly. It reports $10,407.42 on a $10,000 balance after a year. The correct answer is $10,400.00, because 4.00% APY means 4.00% after a year by definition. The error is $7.42 in year one. Run the same mistake for thirty years and it inflates the balance by $701.01.
The correct way to advance a balance by one month using an APY is to multiply by (1 + APY)1/12. That inverts the compounding rather than reapplying it. Our methodology page shows the working, and the savings calculator uses it.
Questions about APY and interest rates
Which number should I compare accounts on?
APY, every time. It is the only figure that already accounts for how often the bank compounds, so two APYs are directly comparable. Federal rules require deposit accounts to disclose it for exactly this reason.
Is APY always higher than the interest rate?
It is higher whenever interest compounds more than once a year, and equal when it compounds annually. A 4.00% rate becomes 4.0808% APY with daily compounding and stays 4.0000% with annual compounding. APY is never lower.
What is the difference between APY and APR?
APY is what you earn on deposits and includes compounding. APR is what you pay on borrowing and includes fees but generally excludes compounding. They answer different questions for different products, so a direct comparison between the two is not meaningful.
Why does my bank show both a rate and an APY?
Because Regulation DD requires the APY on deposit disclosures, while the interest rate is what the bank actually applies to your balance each period. Both are legitimate figures. Only one of them is safe to compare across banks.
If I already know the APY, do I need the interest rate?
No. Once you have the APY, the compounding schedule and the nominal rate are both redundant for working out what you will earn. Feeding an APY back through a compounding formula is the most common way people overstate their returns.
Sources
- Consumer Financial Protection Bureau, Regulation DD (Truth in Savings) . Sets the standard APY calculation and disclosure requirements
- FDIC, National Rates and Rate Caps