Calculate the Yield-to-Maturity of a Zero Coupon Bond

What is the yield-to-maturity of a zero coupon bond that is trading at $974.00, matures in exactly 5 months, and has a face value of $1,000?

The yield-to-maturity of the zero coupon bond is approximately 3.12%. This is calculated by dividing the discount by the face value and adjusting for the time to maturity.

Calculating Yield-to-Maturity of a Zero Coupon Bond

A zero coupon bond is a type of bond that does not pay periodic interest. Instead, it is issued at a discount to its face value and redeemed at face value upon maturity. The yield-to-maturity of a zero coupon bond represents the annualized rate of return an investor can expect if the bond is held until maturity.

Steps to Calculate Yield-to-Maturity:

1. Determine the discount or premium:

Calculate the difference between the bond's current price and its face value.

Discount/Premium = Face Value - Current Price

Discount/Premium = $1,000 - $974.00

Discount/Premium = $26.00 (discount)

2. Calculate the annualized yield:

Divide the discount or premium by the face value and adjust for the time to maturity.

Annualized Yield = (Discount/Premium / Face Value) * (12 / Time to Maturity in months)

Annualized Yield = ($26.00 / $1,000) * (12 / 5)

Annualized Yield = 0.0312 or 3.12%

3. Round the annualized yield to the nearest second digit after the decimal point.

Yield-to-Maturity (YTM) = 3.12% (rounded to the nearest second decimal place)

Therefore, the yield-to-maturity of the zero coupon bond is 3.12%.

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