# What is the effective interest rate?

Jul 4, 2015

The rate of interest at which a sum actually grows if compounding occurs more than once a year.

#### Explanation:

You deposit a sum of money in a bank that pays 8% interest a year, compounded yearly. (Those were the good-old days for depositors).

I deposit my money in another bank that pays 8% a year, but it is compounded every 3 months - quarterly. So, at the end of every 3 months the bank gives me interest. At the end of the year, who will have the most money in their account?

I will because at the end of the first 3 months I receive interest and then at the end of the next 3 months I will receive interest on my original deposit plus interest on the interest I have already earned...and so on for the year.

We can use a simple formula to calculate the actual or effective interest rate that I received.

$\left(1 + {\left(\frac{m}{n}\right)}^{n}\right) - 1$

Where
M = the yearly or nominal rate - 8% in this case.
N = the number of times a year compounding occurs.

My effective rate is

(1 + (.08)/4)^4 - 1)

8.24% and yours was 8% (we could prove this using the formula).