📐 APY Calculator: APR to APY (and APY to APR)

Compare savings and loan rates on the same basis.

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Formula at a glance

APR ↔ APY Calculator: APY — (1 + APR ÷ n)ⁿ − 1. Example: 5% APR compounded monthly → APY (effective annual rate): 5.1162%
How the APR ↔ APY Calculator works: APY — (1 + APR ÷ n)ⁿ − 1

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📘 About the APY Calculator

APR is the yearly rate before compounding; APY (also called AER or effective annual rate) is what you actually earn or pay once interest is added to the balance during the year.

The more often interest compounds, the bigger the gap: 5% APR compounded monthly is 5.116% APY.

🧮 Formula

APY
(1 + APR ÷ n)ⁿ − 1
APR
n × ((1 + APY)^(1/n) − 1)

✏️ Worked examples

5% APR compounded monthly

You enter
Rate5%
ConvertAPR → APY
CompoundingMonthly
You get
APY (effective annual rate)5.1162%
Compoundingmonthly
Difference0.1162 percentage points

5.1162%.

4.5% APY to APR (daily)

You enter
Rate4.5%
ConvertAPY → APR
CompoundingDaily
You get
APR (nominal annual rate)4.402%
Compoundingdaily
Difference0.098 percentage points

4.402%.

🧭 How to use this calculator

What you enter

  • Rate (%)
  • Convert
  • Compounding

What you get

  • APY (effective annual rate)
  • Compounding
  • Difference

❓ Frequently asked questions

What is the difference between APR and APY?

APY includes compounding; APR does not. For savings look at APY, for loans APR (plus fees).

Is APY the same as AER?

Yes — AER (UK) and EAR are the same idea as APY.

How does daily compounding affect APY?

5% APR becomes 5.127% APY with daily compounding, versus 5.116% monthly.

Why do credit cards show APR?

Lenders are required to show APR; the effective rate with monthly compounding is higher.