Question

A bond has a $1,000 par value, 8 years to maturity, and a 7% annual coupon and sells for $980. a. What is its yield to maturity (YTM)? Round your answer to two decimal places. %

Answer 1

To calculate the yield to maturity (YTM) of a bond, use the formula: YTM = ((Annual Interest Payment + (Face Value - Market Price) / Number of Years) / ((Face Value + Market Price) / 2)) * 100. Plugging in the values for this bond, the YTM is 7.57%.

Step-by-step explanation:

To calculate the yield to maturity (YTM) of a bond, we need to consider the bond's current market price, its par value, the number of years to maturity, and its annual coupon rate.

In this case, the bond has a par value of $1,000, 8 years to maturity, a 7% annual coupon rate, and is currently selling for $980.

To calculate the yield to maturity, we can use the formula:

YTM = ((Annual Interest Payment + (Face Value - Market Price) / Number of Years) / ((Face Value + Market Price) / 2)) * 100

Plugging in the values for this bond, we get:

1. Annual Interest Payment = Par Value * Coupon Rate = $1,000 * 7% = $70
2. (Face Value - Market Price) / Number of Years = ($1,000 - $980) / 8 = $20 / 8 = $2.50
3. (Face Value + Market Price) / 2 = ($1,000 + $980) / 2 = $1,980 / 2 = $990

Substituting these values into the formula:

YTM = (($70 + $2.50) / $990) * 100 = 7.57%