# What is Effective Annual Rate?

## The interest rate that baffled me.

## Compound Interest Terminologies

When thinking about compounding interests of your investment, you need to take into account **compounding periods m,**

**nominal rate**as well as the

*r***compounding frequency**

*t.***Nominal rate***r***Compounding periods***m***Compounding frequency***t*there are in a year x 10)*m*

## Example

Consider this scenario: An investment over one year at an annual interest rate of 10%, compounded semiannually. Typically the quoted rate is the nominal rate *r*, and “compounded semiannually” means the amount of money we invested will be compounded every half-yearly, so there are two compounding periods over our investment term of one year. Therefore:

- nominal rate
*r* - compounding periods
*m* - compounding frequency
= 2*t*

So for every $1 we invested, we will get back:

$1 x (1 + r/m)^t = $1 x (1 + 10%/2)² = $1 x (1.05)² =

$1.1025

And the interest we earned on this investment of $1 is $0.1025, which translates to **10.25%**. Notice how the quoted rate, or nominal rate ** r = 10% **but we are effectively earning

*10.25%!*This interest rate that we are effectively earning on our investment is called the ** Effective Interest Rate**, which in this case is the 10.25%. The 10% nominal rate is actually the interest rate we would earn in one year if we do not have the nasty compounding frequencies

**and periods**

*t***In that case:**

*m.*- nominal rate
*r* - compounding periods
*m* - compounding frequency
= 1*t*

So for every $1 we invested we will get back:

$1 x (1 + r/m)^t = $1 x (1 + 10%/

1)¹= $1 x (1.1)¹ =$1.10

## In short

We are actually using the same formula to calculate — ** effective interest rate r’ **but substituting different

**The effective interest rate**

*m and t.***will satisfy this equation:**

*r’*1 +

r’= (1 + r/m)^t