Convert an interest rate quoted at one compounding frequency into its equivalent rate at another — the same true cost or return, expressed a different way.
A 6% rate compounded monthly doesn't grow money at exactly 6% a year — it grows slightly faster, because each month's interest starts earning its own interest right away instead of waiting for the year to end. Converting between compounding frequencies answers a simple but important question: what annual rate would produce the exact same growth, regardless of how often it compounds along the way?
APR (annual percentage rate) is the simple, nominal rate — what you'd get by just multiplying the periodic rate by the number of periods in a year, ignoring compounding. APY (annual percentage yield) is the real, effective rate after accounting for compounding. APY is always equal to or higher than APR for the same underlying rate, and the gap widens as compounding gets more frequent.
It's the mathematical limit of compounding infinitely often — used in some theoretical finance and a handful of real financial products. It produces the highest possible effective rate for a given nominal rate.
APY, whenever it's available, since it already accounts for compounding and reflects what you'd actually earn or pay over a year. Comparing raw APRs with different compounding frequencies can be misleading.
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