APR, APY, EAR, and AER: Nominal Versus Compounded Rates

Summary

The document explains why annual rate labels can refer to different treatments of compounding. In the US usage it describes, nominal APR is generally a simple annualized rate, while effective APR or APY accounts for compounding; EAR is more commonly used than APY to compare rates with different compounding frequencies. It also notes that legal rules may require APR to be advertised instead of APY.

For the UK, the answer says the terminology is similar but distinguishes rates by whether they apply to interest owed or balances earned: EAR accounts for compounding on interest owed, while AER accounts for compounding on savings balances. The discussion is a brief terminology clarification rather than a detailed regulatory survey. It does not provide formulas, examples, or jurisdiction-specific legal citations, so users should verify how a rate is defined in the relevant product and market.

Key ideas

• Nominal APR generally expresses a rate without compounding in the US context described.
• Effective APR and APY incorporate the effect of compounding.
• EAR is commonly used in the US to compare rates with different compounding frequencies.
• The document distinguishes UK EAR on interest owed from AER on balances earned.

Tags

# Annual Percentage Rate and Yield


# Annual Percentage Rate and Yield












I found references relative to US where the Nominal Annual Percentage Rate or simply APR is defined as the simple interest rate (i.e. proportional to time and without compounding).

Instead the effective APR or Annual Percentage Yield (APY) takes into account the effect of interest compounding. Also in US there are some legal provisions requiring that APR (and not the APY) to be advertised.

But how is the situation on the UK side? Are the meanings the same? APR=simple, APY=compound too?

## Answer by Matt Wolf (score 1, accepted)

https://quant.stackexchange.com/a/7492

First off, APR can be both, compounded or not compounded, depending on whether you talk about nominal APR or effective APR. Though, generally in the US when people talk APR it is referring to the nominal APR. Also, APY is not a generally used term in the US, usually EAR is used which is taking into account compounding in order to make rates comparable across different compounding frequencies.

In the UK the situation is very similar with the following exception:

- EAR is the rate, taking into account compounding, on interest owed

- AER is the rate, taking into account compounding, on balances earned

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.