Question

If a zero-coupon bond has face value of $1000. The bond has 8 years to mature. The current bond price is $510. The yield to maturity (YTM) of the bond is ____%?

Answer 1

The yield to maturity (YTM) of a zero-coupon bond with a face value of $1000, current price of $510, and 8 years to maturity is approximately 11.54%.

Step-by-step explanation:

To calculate the yield to maturity (YTM) of a zero-coupon bond, which does not make periodic interest payments, we use the formula that relates the current price of the bond, its face value (also known as par value), and the time to maturity. The formula for YTM in terms of these variables is:

YTM = [(Face Value / Present Value)^(1/n)] - 1

Where the face value is the amount the bond will be worth at maturity, the present value is the current price of the bond, and n is the number of years until the bond matures.

Using the provided information: Face Value = $1,000, Present Value = $510, and n = 8 years, we can substitute these values into the formula to find the YTM:

YTM = [($1,000 / $510)^(1/8)] - 1

Calculating this gives us:

YTM = [(1.9608)^(0.125)] - 1 ≈ 0.1154 or 11.54%

Therefore, the yield to maturity of the bond is approximately 11.54%.

Answer 2

The yield to maturity of a zero-coupon bond with a face value of $1000, current price of $510, and 8 years to maturity is approximately 11.45%. This is the annualized return an investor would get if they bought the bond at the current price and held it until maturity.

Step-by-step explanation:

Calculating Yield to Maturity (YTM) on a Zero-Coupon Bond

To calculate the yield to maturity (YTM) of a zero-coupon bond with a face value of $1000, a current price of $510, and 8 years to maturity, we can use the formula for YTM on a zero-coupon bond. The formula is as follows:

YTM = (Face Value / Present Value)^(1/n) - 1

Where Face Value is the bond's payoff at maturity, Present Value is the current price of the bond, and n is the number of years until maturity. Plugging in the given numbers:

YTM = (1000 / 510)^(1/8) - 1

Calculating this gives us:

YTM = (1.96078431372)^(0.125) - 1

YTM ≈ 0.1145 or 11.45%

The yield to maturity of the bond is approximately 11.45%. This represents the annualized return the investor would get if they purchased the bond at $510 and held it until its maturity in 8 years, under the assumption that the bond will pay its full face value at maturity with no risk of default.