Calculating Yield to Maturity for a Zero-Coupon Bond

Understanding Yield to Maturity

Yield to maturity (YTM) is an important concept in bond investing as it represents the annual return an investor can expect to receive if a bond is held until maturity. It takes into account the bond's current market price, face value, and time to maturity. YTM is a crucial metric for investors to assess the potential return on their investment in bonds.

Calculating YTM for a Zero-Coupon Bond

A zero-coupon bond is a bond that does not pay periodic interest payments, but instead is issued at a discount to its face value and pays the face value at maturity. To calculate the YTM for a zero-coupon bond, you can use the following formula:

YTM = [(FV/PV)^(1/n)] - 1

Where:

• FV = Face value of the bond ($5,000 in this case)
• PV = Current market price of the bond ($4,360 in this case)
• n = Number of periods until maturity (15 years in this case)

Plugging in the values from the data provided:

YTM = [(5000/4360)^(1/15)] - 1 = approximately 0.017533 or 1.7533%

Answer: None of the Provided Options are Correct

The correct yield to maturity for the zero-coupon bond with a face value of $5,000, currently trading at $4,360, and 15 years to maturity is approximately 1.7533%. None of the provided answer choices (0.459%, 0.917%, 87.2%, 56.4%) are correct.

Explanation

The YTM of a bond is the interest rate that equates the present value of the bond's future cash flows to its current market price. For zero-coupon bonds, the only cash flow is the payment of the face value at maturity. By applying the YTM formula, we calculated the annual YTM to be approximately 1.7533%.