An investment earns 4.5% compounded quarterly. What is the APY?
To calculate the Annual Percentage Yield (APY), we first need to determine the effective annual rate (EAR) using the formula:
EAR = (1 + (nominal rate / periods per year)) ^ periods per year - 1
In this case, the nominal rate is 4.5% and it is compounded quarterly (4 times per year). Plugging these values into the formula:
EAR = (1 + (0.045 / 4)) ^ 4 - 1
EAR = (1 + 0.01125) ^ 4 - 1
EAR = (1.01125) ^ 4 - 1
EAR ≈ 1.0469 or 4.69%
Therefore, the Annual Percentage Yield (APY) for an investment that earns 4.5% compounded quarterly is approximately 4.69%.