Suppose a five-year, $1 000 bond with annual coupons has a price of $897.83 and a yield to maturity of 6.3%. What is the bond's coupon rate?
Question
Suppose a five-year, 897.83 and a yield to maturity of 6.3%. What is the bond's coupon rate?
Solution
To find the bond's coupon rate, we need to use the formula for the price of a bond, which is:
P = C * (1 - (1 + r)^-n) / r + FV / (1 + r)^n
where: P = price of the bond = 1,000
We can rearrange the formula to solve for C:
C = (P - FV / (1 + r)^n) * r / (1 - (1 + r)^-n)
Substituting the given values:
C = (1,000 / (1 + 0.063)^5) * 0.063 / (1 - (1 + 0.063)^-5)
After calculating the above expression, we get the annual coupon payment. To find the coupon rate, we divide the annual coupon payment by the face value of the bond and multiply by 100% to express it as a percentage.
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