We need to calculate the yield to maturity (YTM) of a bond given its current price, coupon rate, par value, and time to maturity. The bond has a current price of $908, a coupon rate of 11%, a par value of $1000, and 8 years to maturity. We need to find the YTM to the nearest percent.
2025/7/8
1. Problem Description
We need to calculate the yield to maturity (YTM) of a bond given its current price, coupon rate, par value, and time to maturity. The bond has a current price of 1000, and 8 years to maturity. We need to find the YTM to the nearest percent.
2. Solution Steps
The approximate formula for Yield to Maturity (YTM) is:
Where:
= Annual coupon payment
= Face Value (Par Value)
= Current Value (Current Price)
= Number of years to maturity
First, calculate the annual coupon payment:
C = \text{Coupon Rate} \times \text{Face Value} = 0.11 \times \1000 = \
Next, plug the values into the YTM formula:
YTM = (\110 + (\1000 - \908)/8) / ((\1000 + \908)/2)$
YTM = (\110 + \92/8) / (\1908/2)$
YTM = (\110 + \11.5) / \954$
YTM = \121.5 / \
Convert the YTM to a percentage and round to the nearest percent:
3. Final Answer
The yield to maturity is approximately 13 percent.
So, the answer is d. 13 percent.