# Equivalent Rate Calculator (AER)

URL: https://speedycalculator.com/calculators/finance/equivalent-rate/
Last updated: 2026-10-25

> The equivalent rate calculator converts a nominal interest rate with one compounding frequency into the equivalent rate with another – for example monthly into quarterly – and gives the annual equivalent rate (AER).

## Inputs

- Nominal interest rate (%)
- Compounding frequency
- New compounding frequency

## Results

- Annual equivalent rate (AER)
- Equivalent nominal rate
- Equivalent rate per new period

## Formula

```
AER = (1 + r₁ ÷ n₁)^n₁ − 1
Equivalent rate r₂ = n₂ × [(1 + AER)^(1 ÷ n₂) − 1]
```

## Explanation

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

FieldWhat to enterNominal interest rateIn %Compounding frequencyChoose one: Yearly, Semi-annually, Quarterly, Monthly …New compounding frequencyChoose 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 (%)2.52.50523.753.761755.02096.256.28267.57.5471010.0836

## 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 %.

## FAQ

**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.