APR to APY Calculator

Frequently Asked Questions

What is the difference between APR and APY?

APR is the simple nominal rate without compounding. APY (also called EAR) includes the effect of compounding within the year, so for the same APR a higher compounding frequency gives a higher APY.

How is APY calculated?

APY = (1 + APR/n)ⁿ − 1, where n is the number of compounding periods per year. Going the other way, APR = n·((1 + APY)^(1/n) − 1).

Why does this matter when comparing accounts?

Two savings accounts can quote different things - one APR, one APY. Converting both to APY puts them on equal footing so you compare true earnings.

What about continuous compounding?

As n → ∞, APY approaches e^APR − 1. The gain over daily compounding is tiny, but the formula is the theoretical limit.

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This calculator provides estimates for informational purposes only. Actual financial outcomes depend on market conditions, personal circumstances, and decisions. Not financial advice. Consult a certified financial planner before making financial decisions affecting your future.

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How This Calculator Works

APR (annual percentage rate) is the nominal rate quoted on a loan or deposit before compounding is applied. APY (annual percentage yield), also called the effective annual rate, is what you actually earn or pay once interest is added back to the balance and itself starts earning interest. Because of that snowball effect, APY is always ≥ APR whenever compounding happens more than once a year, and the two are only equal when interest compounds exactly once annually. This tool converts in both directions: enter an APR and a compounding frequency to get the true APY, or enter an APY to recover the nominal APR a bank would have to advertise to deliver that yield. The wider the gap between the two numbers, the more aggressively the product compounds - a useful tell when comparing offers that quote different conventions. Regulators in many markets require the effective figure to be disclosed precisely so consumers are not misled by a flattering nominal headline, but the two conventions still coexist in everyday marketing, which is why a converter that works both ways is more practical than one that only goes in a single direction.

Formula / Method

Converting nominal to effective: APY = (1 + APR ÷ n)ⁿ − 1, where n is the number of compounding periods per year (12 for monthly, 4 for quarterly, 365 for daily). Going the other way, the nominal APR that produces a given APY is APR = n × ((1 + APY)^1÷n − 1). As n grows toward infinity the APY approaches the continuous-compounding limit e^APR − 1, which is why daily and continuous compounding differ by only a sliver while monthly versus annual differs noticeably. The calculator guards against a zero or negative period count and treats a blank field as "not entered" rather than silently using zero. It also reports the dollar interest on a $10,000 reference balance under both conventions so the abstract percentage gap is translated into a concrete amount you can feel, which is often more persuasive than the rate spread alone when deciding between two accounts.

Worked Example

Take a 6% APR compounded monthly, so n = 12. Each month the rate applied is 6% ÷ 12 = 0.5%. Over a year that is (1 + 0.005)¹² − 1 ≈ 0.061678, an APY of about 6.1678%. On a $10,000 balance the nominal figure suggests $600 of interest, but the compounded reality is roughly $616.78 - an extra $16.78 purely from interest-on-interest. Reverse it: if a savings account advertises a 6.1678% APY and compounds monthly, the underlying nominal APR is 12 × ((1.061678)^1÷12 − 1) ≈ 6.00%, confirming the round trip.

Common Mistakes

Comparing one bank's APR against another bank's APY directly - always convert both to the same convention first.

Assuming "APR" on a credit card already includes compounding; card issuers quote nominal APR but charge interest daily, so your effective cost is higher.

Using n = 1 for a product that actually compounds daily, which understates yield by the full APR-to-APY spread.

Forgetting that lender APR (Truth-in-Lending) also bundles fees, a different concept from the pure compounding conversion shown here.

Treating the spread as fixed: it widens sharply as the base rate rises, so the convention matters more on a 20% card than on a 1% account.

Tips & FAQ

Which number should I focus on? For what you truly earn or pay, APY is the honest figure; APR is mostly a quoting convention. Why do banks advertise APY on deposits but APR on loans? Marketing - the higher APY looks better on savings, while the lower APR looks better on borrowing, even though the customer experiences the effective rate either way. Does more frequent compounding always help me? Only on money you are owed; on debt, more frequent compounding works against you. As a rule of thumb, the difference between monthly and daily compounding is tiny, but the difference between annual and monthly is the one worth checking before you sign anything.

APR to APY Calculator

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