APR and APY describe the same interest rate from two angles. APR is the nominal rate — the headline number — while APY is the effective rate that includes the effect of compounding within the year. Because interest earns interest, APY is always at least as high as APR, and the more often it compounds the wider the gap. That's why APY is the figure to compare: two accounts both advertising "12% APR" aren't equal if one compounds daily and the other annually.
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: the standard effective-annual-rate formula, recomputed in code. Not financial advice.
The conversion formulas
Here n is the number of compounding periods per year — 12 for monthly, 4 for quarterly, 365 for daily. The first formula grows the periodic rate across all n periods to find the true annual yield; the second undoes it. Annual compounding (n = 1) leaves APY equal to APR. As n rises, APY climbs toward the continuous-compounding limit of eAPR − 1.
Worked example — 12% APR compounded monthly
Scenario: a 12% nominal APR with monthly compounding (n = 12).
The effective yield is 12.6825% — compounding adds about 0.68 points over the nominal 12%. Frequency is everything: the same 12% APR is just 12.0000% APY compounded annually, 12.5509% quarterly, and 12.7475% daily. Run in reverse, a 12.6825% APY compounded monthly converts straight back to a 12.0000% APR — handy when a bank advertises APY but you want the nominal rate to compare against an APR-quoted product.
Frequently Asked Questions
APR is nominal; APY includes compounding. APY ≥ APR. 12% APR monthly = 12.6825% APY.
APY = (1 + APR ÷ n)ⁿ − 1. For 12% monthly: (1.01)¹² − 1 = 12.6825%.
APR = n × ((1 + APY)^(1/n) − 1). 12.6825% APY monthly → 12.0000% APR.
APY to APY — it accounts for compounding frequency, so it's the fair comparison.
This tool treats APR as pure interest. A regulatory loan APR may bundle some fees.