Effective Yield refers to the return on an investment, typically a bond, that takes into account the effects of compounding interest over a period. It represents the actual annual yield earned on an investment, rather than the nominal or stated interest rate, by considering how often the interest is compounded.

Key Aspects of Effective Yield:

1. Compounding:
   • The effective yield includes the impact of interest being compounded over time. This means that interest is calculated on both the initial principal and the accumulated interest from previous periods.
2. Formula:
   • The formula to calculate the effective yield is:

   $$ \text{Effective Yield} = \left(1 + \frac{i}{n}\right)^n – 1 $$

   • Where $i$ is the nominal (stated) interest rate, and $n$ is the number of compounding periods per year.
3. Comparison with Nominal Yield:
   • The nominal yield (or coupon rate) does not account for compounding, whereas the effective yield does. Therefore, the effective yield is usually higher than the nominal yield if interest is compounded more than once per year.
4. Importance in Investments:
   • The effective yield provides a more accurate measure of the return on an investment, particularly for bonds with interest that compounds more frequently than annually.
   • Investors use effective yield to compare the true profitability of different bonds or fixed-income investments.

Example:

• Suppose a bond has a nominal annual interest rate of 5%, and interest is compounded semi-annually. To calculate the effective yield:

$$ \text{Effective Yield} = \left(1 + \frac{0.05}{2}\right)^2 – 1 = 5.0625\% $$

• In this case, the effective yield would be 5.0625%, slightly higher than the nominal rate of 5% due to the effect of compounding.