**Equivalent Rate (AER)Calculator**

The **annual equivalent rate (AER)**, or effective rate, is the **interest rate** on a loan or is financial product . AER is q = 1 in the equivalent interest rate . Equivalent Rate equal to desired compounding frequency multiple number of value 1 equivalent interest rate divided to initial compounding frequency multiple initial compounding frequency divided to desired compounding frequency less than number of value 1.

**Formula us, **

i = q * [(1 + r/m)m/q – 1]

*let us consider*,

- Nominal interest rate: the nominal annual interest rate;

- Compounding frequency: the number of times compounding occurs annually. It is the frequency you would like to transform into another frequency;
- New compounding frequency;
- Equivalent interest rate; and
- Effective rate (annual equivalent rate – AER).

**Calculate the Equivalent Rate**

- i- nominal annual interest rate;(5%)
- m- initial compounding frequency;(150)
- q- desired compounding frequency; and(200)
- r- equivalent interest rate.(4.99979%)

**AER Formula us,**

r = (1 + i/m)m – 1

**For example,**

nominal interest rate of 2% compounded monthly is equivalent to 5.116%. 4% compounded monthly has a periodic rate .

**Calculate the AER**

r = (1 + i/m)m – 1

4/12 ≈ 0.3333%.After one year, the initial capital is increased by a factor of

(1 + 0.003333)12 ≈ 1.039996

AER = 3.999%.