Equivalent Rate Calculator - AER
Enter a nominal interest rate and its compounding frequency, then choose a new frequency. The calculator converts the rate so it earns exactly the same return, and shows the Annual Equivalent Rate (AER) - the true yearly yield regardless of how often interest compounds. Used by savers, investors, and finance professionals to compare accounts on a level playing field.
What is the Annual Equivalent Rate (AER)?
The Annual Equivalent Rate (AER) is the true annual yield on a savings account or investment after compounding is taken into account. Banks and building societies are required by law to quote AER on savings products so customers can compare them fairly. If one account pays interest monthly and another pays it annually, their headline rates look similar but they are not: the monthly account benefits from interest being added more often, which itself earns interest. AER eliminates that ambiguity by converting every rate to the same annual basis. It is sometimes called the Effective Annual Rate (EAR) or Effective Annual Interest Rate (EAIR).
How the equivalent rate formula works
The AER formula is: AER = (1 + r/m)^m - 1, where r is the nominal annual rate as a decimal and m is the number of compounding periods per year. For continuous compounding (the mathematical limit as m approaches infinity) the formula simplifies to AER = e^r - 1. To convert back: if you know the AER and want the equivalent nominal rate at a new frequency q, invert the formula to get: nominal rate = q x [(1 + AER)^(1/q) - 1]. This calculator applies both directions automatically. A 5% nominal rate compounded monthly gives an AER of about 5.116%, meaning you would need a 5.116% annually-compounded rate to match it. Compounded quarterly, the equivalent nominal rate is roughly 5.021%.
Nominal rate vs AER: which should you use?
Always use the AER when comparing savings accounts or fixed deposits. The nominal rate tells you the headline figure the bank advertises; the AER tells you what you will actually earn in a year. The gap widens with higher rates and more frequent compounding: at 10% nominal, monthly compounding produces an AER of 10.47%, a meaningful difference. Gross rate (the nominal rate without tax deductions) is useful for pre-tax comparisons, but still does not capture compounding. Summarised: nominal rate is the starting label, gross rate strips out tax, and AER is the real-world annual yield after compounding. This calculator converts between any pair of compounding frequencies so you can see what a monthly account actually offers compared to a quarterly one, or find the daily rate that matches a given monthly one.
When to use the equivalent rate conversion
The equivalent rate conversion is useful whenever two financial products state their rates at different compounding frequencies. Common scenarios include: comparing a UK savings account (often quoted as AER with monthly crediting) against a European account (may quote annually); modelling a bond with semi-annual coupon payments against a deposit paying quarterly; converting a bank-quoted monthly rate into the annual equivalent for reporting or budgeting; or checking that a remortgage offer at a monthly rate matches the annual figure quoted by a comparison site. The periodic rate - the rate applied in each individual period - is the figure used in most spreadsheet functions such as PMT, FV and PV, so use the "periodic rate" output when building your own models.
AER vs nominal rate by compounding frequency
| Compounding | Periods/year | Nominal rate | AER |
|---|---|---|---|
| Annually | 1 | 5.0000% | 5.0000% |
| Semi-annually | 2 | 5.0000% | 5.0625% |
| Quarterly | 4 | 5.0000% | 5.0945% |
| Monthly | 12 | 5.0000% | 5.1162% |
| Weekly | 52 | 5.0000% | 5.1246% |
| Daily | 365 | 5.0000% | 5.1267% |
| Continuous | infinite | 5.0000% | 5.1271% |
Effective Annual Rate (AER) for a 5% nominal rate at common compounding schedules. More frequent compounding always produces a higher AER.
Frequently asked questions
What is the difference between AER and APR?
AER (Annual Equivalent Rate) is used for savings and investments - it shows the true annual return after compounding. APR (Annual Percentage Rate) is used for loans and credit - it includes fees and charges as well as interest, expressed as an annual rate. Both aim to give you a single comparable figure, but they apply to opposite sides of a financial product: AER is what you earn, APR is what you pay.
Does more frequent compounding always increase my return?
Yes, for savings and investment products, more frequent compounding always increases the AER relative to the nominal rate. However, the gains diminish rapidly: the jump from annual to monthly compounding is significant, but the jump from monthly to daily is tiny. At very high frequencies the AER approaches the continuously-compounded limit of e^r - 1, which for a 5% nominal rate is about 5.127% - only 0.011 percentage points above daily compounding.
Why does the equivalent rate change when I change the target frequency?
The equivalent rate is the nominal rate that, when compounded at your chosen new frequency, delivers the same AER as the original rate. Because AER stays fixed, you need to adjust the nominal figure to compensate for how often compounding happens. If you switch from monthly to quarterly, interest compounds fewer times per year, so the nominal rate must be slightly higher to maintain the same total return. The AER is the constant anchor; the nominal rate is what changes.
How do I compare a monthly interest account with a quarterly one?
Enter the monthly account nominal rate with "monthly" as the compounding frequency, then choose "quarterly" as the new frequency. The calculator gives you the quarterly equivalent nominal rate and - more importantly - the AER for both. Two accounts with the same AER will deliver identical returns over a full year, regardless of when interest is credited to your account.
What is continuous compounding and when does it apply?
Continuous compounding is the mathematical limit of compound interest as the compounding frequency approaches infinity. In practice, no retail bank compounds continuously - it is mainly used in theoretical finance, options pricing models, and some interbank lending rates. The formula is AER = e^r - 1, where e is Euler's number (approximately 2.71828). This calculator supports continuous compounding so you can use it in academic or modelling contexts.
Is AER the same as the effective annual rate (EAR)?
Yes. AER and EAR are the same calculation expressed under different names. "AER" is the UK regulatory term used for savings products; "EAR" is more common in the United States and in academic finance. Some sources also call it EAIR (Effective Annual Interest Rate). All three use the formula (1 + r/m)^m - 1.