## Annual Percentage Yield and Compound Interest

Sunday, March 30, 2008 | | 0 comments »

On January 1st 2007, I had $100 in my Presidents Choice Financial Savings Account. At 4% interest believed that I would by December 31, 2007, I would have$104.07. This is because interest is calculated daily and paid monthly. I would then receive interest for my interest. This is the power of compound interest. This is what makes your money to grow.

However at the end of the year my $100 had grown to$103.99. This was a difference of \$0.08. What happened? Well what PC Financial does (so do most major financial institutions) is state the Annual Percentage Yield or the Effective Interest Rate.

This means that when PC Financial states that they pay 4% interest APY, they have already factored in the compound interest that you will earn for the year at their compounding schedule.

The mathematics behind this calculation (yes, I comprehend the formula and can explain High School Finite) is:

$APY = \left(1 + \frac {i_{nom}} {N} \right)^N -1$

where

inom is the nominal interest rate and
N is the number of compounding periods per year.

For large N we have, approximately,

$APY \approx e^{i_{nom}} - 1,$