Two rates are equivalent if they produce the same growth in a year. The AER (annual equivalent rate), used in the UK for savings, puts every account on the same footing regardless of how often interest is paid.
How to use the Equivalent Rate Calculator
- Nominal interest rate
- Compounding frequency
- New compounding frequency
Results update as you type, and every field accepts the units shown in its menu.
How it works
Enter the nominal rate and its compounding frequency, and choose the new compounding frequency.
Tips
- Use the nominal annual rate and pick the compounding frequency your bank or broker states.
- Small differences in return or fees compound into large differences over decades.
- Run the calculation with a cautious, a central and an optimistic return to see the range of outcomes.
- Past returns do not guarantee future returns – nothing here is investment advice.
Common mistakes to avoid
- Comparing an APR with an APY or effective rate.
- Ignoring inflation, taxes and fees when judging a real return.
- Entering a percentage as a decimal (5 instead of 0.05 is correct here).
Inputs explained
| Field | What to enter |
|---|---|
| Nominal interest rate | In % |
| Compounding frequency | Choose one: Yearly, Semi-annually, Quarterly, Monthly … |
| New compounding frequency | Choose one: Yearly, Semi-annually, Quarterly, Monthly … |
What each result means
- Annual equivalent rate (AER) = effr([Nominal interest rate]÷100, [Compounding frequency])×100
- Equivalent nominal rate = nomr([Annual equivalent rate (AER)]÷100, [New compounding frequency])×100
Example values
How the main result changes when Nominal interest rate changes and everything else stays at the example values above:
| Nominal interest rate (%) | Equivalent nominal rate (%) |
|---|---|
| 2.5 | 2.5052 |
| 3.75 | 3.7617 |
| 5 | 5.0209 |
| 6.25 | 6.2826 |
| 7.5 | 7.547 |
| 10 | 10.0836 |
Formula
AER = (1 + r₁ ÷ n₁)^n₁ − 1Equivalent rate r₂ = n₂ × [(1 + AER)^(1 ÷ n₂) − 1]Worked example
Inputs — Nominal interest rate: 5 %; Compounding frequency: Monthly; New compounding frequency: Quarterly.
Results — Annual equivalent rate (AER) = 5.1162 %; Equivalent nominal rate = 5.0209 %; Equivalent rate per new period = 1.2552 %.
Frequently asked questions
What is AER?
The annual equivalent rate – the yearly rate including compounding, used for UK savings.
How do I convert a monthly rate to quarterly?
Find the AER, then convert it to the quarterly nominal rate.
Why do equivalent rates differ?
Less frequent compounding needs a higher nominal rate to give the same yearly growth.
What formula does the Equivalent Rate Calculator use?
AER = (1 + r₁ ÷ n₁)^n₁ − 1.