Convert between APR and APY at any compounding frequency.
APR (nominal)
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APY (effective)
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Same loan, two different numbers, and that is on purpose
APR and APY both describe an interest rate, but they answer different questions, and the gap between them is the entire reason compounding builds wealth and debt. APR is the nominal rate: the stated annual rate before you account for interest earning interest within the year. APY is the effective rate: what you actually earn or pay once that intra-year compounding is folded in. A bank advertising your savings will quote APY, because compounding makes it the larger, more flattering number. A lender quoting a loan often leads with APR, because it is the smaller one. Reading a rate without knowing which type it is can quietly mislead you.
This converter moves between the two at any compounding frequency. Going from APR to APY it compounds the nominal rate over the periods you choose. Going the other way it strips compounding back out to recover the nominal rate. The frequency is the lever, more frequent compounding widens the gap.
What 5% becomes when it compounds daily
Take the default: a 5% APR converted to APY with daily compounding over 365 periods. The math raises 1 plus the daily rate to the 365th power and subtracts 1.
| Compounding frequency | APY from a 5% APR |
|---|
The same 5% nominal rate becomes a 5.127% effective yield once it compounds every day. The 0.127 point of extra yield looks tiny, and on a small balance it is. On a $100,000 balance it is $127 a year you would miss if you compared a daily-compounding account against an annually-compounding one purely on their APR. Notice how the gains shrink as you go down the table: most of the benefit of compounding is captured by the time you reach monthly, and the jump from monthly to daily is small. There is no such thing as compounding so frequent it changes the picture dramatically.
Where the APR you are quoted is not the whole story
On the lending side, the APR a US lender discloses under the Truth in Lending Act is meant to bundle in certain fees, like points and some origination costs, so it is broader than a raw interest rate. But it still does not reflect monthly compounding the way APY would, so the APR on a mortgage understates the true annualized cost of carrying the loan. On credit cards the gap is more dramatic, because most cards compound interest daily on the balance. A card quoting a 24% APR carries an effective rate north of 27% once daily compounding runs for a year, which is why a balance that never gets paid down grows faster than the headline rate suggests. When you are comparing two products, the only fair comparison is APY against APY, never one product's APY against another's APR.
Which rate should I use to compare savings accounts?
Always APY. It is the standardized figure US banks must disclose precisely so consumers can compare accounts on an apples-to-apples basis, and it already bakes in each bank's compounding schedule. If one account quotes an APY and another quotes only a nominal rate, convert the nominal one to APY here at its stated compounding frequency before you decide.
Why would anyone quote APR instead of APY?
Because APR is the smaller number, and on borrowing it is the legally required disclosure. A lender is not hiding anything by quoting APR, it is the standard for loans, but it does mean the figure you see is not the effective annual cost. Run the loan's APR through this tool at its compounding frequency to see what you are really paying, then judge the loan on that effective rate.