You are provided the following information about a bond that was issued 7 years ago. The bond has a par value of $1000, has 8 years until maturity, and carries a 10% coupon with interest being paid semi-annually. What is the effective yield to maturity if we assume the bond is currently priced at $896.64? Question 1 Select one: a. 6.02% b. 10% c. 12.04% d. 12.41%
Question
You are provided the following information about a bond that was issued 7 years ago. The bond has a par value of 896.64?
Question 1 Select one:
a. 6.02%
b. 10%
c. 12.04%
d. 12.41%
Solution
To solve this problem, we need to use the Yield to Maturity (YTM) formula for a bond. The YTM is the total anticipated return on a bond if the bond is held until it matures.
The formula for YTM when interest is paid semi-annually is:
YTM = [C + (F - P)/n] / [(F + P)/2]
Where: C = Annual coupon payment (10% of the face value of 100) F = Face value of the bond (896.64) n = Number of years until maturity (8 years)
However, since the bond pays interest semi-annually, we need to adjust the values in the formula. The coupon payment is divided by 2, and the number of periods is multiplied by 2:
C = 50 n = 8 * 2 = 16
Substituting these values into the formula gives:
YTM = [1000 - 1000 + $896.64)/2]
Solving this equation will give the semi-annual YTM. To get the annual YTM, multiply the semi-annual YTM by 2.
After calculating, you will find that the YTM is approximately 6.02%. Therefore, the correct answer is:
a. 6.02%
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