What does YTM equal when given a semi-annual yield?

The yield to maturity (YTM) on a bond with semi-annual compounding is calculated by converting the semi-annual yield into an effective annual yield. When given a semi-annual yield, it is important to understand that this yield is applied twice within a year due to the semi-annual compounding frequency.

To convert the semi-annual yield to its effective annual yield, the formula used is (1 + semi)^2. In this context, "semi" represents the semi-annual yield expressed as a decimal. By squaring (1 + semi), you account for the compounding effect of receiving interest payments twice throughout the year: the first semi-annual yield is earned at the end of the first six months, and the second semi-annual yield is earned on both the original investment and the first interest payment at the end of the second six-month period.

This formula correctly accounts for the compound interest effect that occurs with semi-annual yields and provides the effective annual rate that investors should use when comparing bonds with different compounding periods. The other choices do not appropriately reflect the nature of compounding or how yields are converted, as they either understate or misrepresent the calculation necessary for effective annual yield.