#APY #compoundinginterest #investment #nominalinterestrate #financialmathematics Annual Percentage Yield is the real rate of return earned on investment, taking into account the effect of compounding interest. It is defined by the formula: $ APY = (1 + \frac{i_{nom}}{N})^{N}- 1 $ $i_{nom}$ is the nominal interest rate and $N$ is the number of compounding periods per year. If you deposited $100 for one year at 5% interest and your deposit was compounded quarterly, at the end of the year you would have $105.09. If you had been paid with simple interest, you would have had $105. The APY would be: $ (1 + \frac{.05}{4})^4 - 1 = .05095 = 5.095\%. $