A four-year bond has a 7% coupon rate and a face value of $1,000. If the current price of the bond is $904.90, calculate the yield to maturity of the bond (assuming annual interest payments).Group of answer choices10%7%9%5%
Question
A four-year bond has a 7% coupon rate and a face value of 904.90, calculate the yield to maturity of the bond (assuming annual interest payments).Group of answer choices10%7%9%5%
Solution
To calculate the yield to maturity (YTM) of the bond, we can use the formula for YTM which is:
YTM = [C + (F - P)/n] / [(F + P)/2]
Where: C = Annual coupon payment (7% of the face value, 1,000) P = Purchase price of the bond ($904.90) n = Years until maturity (4 years)
Step 1: Calculate the annual coupon payment C = 7/100 * 1,000 = $70
Step 2: Calculate the difference between the face value and the purchase price divided by the years until maturity (F - P)/n = (1,000 - 904.90) / 4 = $23.775
Step 3: Calculate the average of the face value and the purchase price (F + P)/2 = (1,000 + 904.90) / 2 = $952.45
Step 4: Substitute the values into the YTM formula YTM = [70 + 23.775] / 952.45 = 0.098 or 9.8%
So, the yield to maturity of the bond is approximately 9.8%, which is closest to 10% among the given options. Therefore, the answer is 10%.
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