A 20-year maturity bond with face value of $1,000 makes semiannual coupon paymen
ID: 2712899 • Letter: A
Question
A 20-year maturity bond with face value of $1,000 makes semiannual coupon payments and has a coupon rate of 6%.
a. What is the bond’s yield to maturity if the bond is selling for $1,080? Enter annual yield to maturity as your answer. (Do not round intermediate calculations. Round your answer to 3 decimal places.)
b. What is the bond’s yield to maturity if the bond is selling for $1,000? Enter annual yield to maturity as your answer. (Do not round intermediate calculations.)
c. What is the bond’s yield to maturity if the bond is selling for $1,280? Enter annual yield to maturity as your answer. (Do not round intermediate calculations. Round your answer to 3 decimal places.)
Explanation / Answer
Yield to maturity = Coupon + Pro-rated discount / (Redemption price + Purchase price) /2
a. YTM= 30* + 2** / 1040***
Yield to maturity = 32 /1040 = 3.077 % ( It is semi-anually)
Annual yield to maturity = 3.077 * 2 = 6.154 %
* Coupon = 1000 * (6/2) = 1000 * 3% = 30
** Pro-rated discount = (1080 - 1000 ) / 40 = 2 [ 40 = 2 *20]
*** 1040 = (1000 + 1080) / 2
b. YTM= 30* + 0** / 1000***
Yield to maturity = 30 /1000 = 3 % ( It is semi-anually)
Annual yield to maturity = 3 * 2 = 6 %
* Coupon = 1000 * (6/2) = 1000 * 3% = 30
** Pro-rated discount = (1000 - 1000 ) / 40 = 0 [ 40 = 2 *20]
*** 1000 = (1000 + 1000) / 2
c. YTM= 30* + 7** / 1140***
Yield to maturity = 37 /1140 = 3.245 % ( It is semi-anually)
Annual yield to maturity = 3.245 * 2 = 6.49 %
* Coupon = 1000 * (6/2) = 1000 * 3% = 30
** Pro-rated discount = (1280 - 1000 ) / 40 = 7 [ 40 = 2 *20]
*** 1140 = (1000 + 1280) / 2
Conclusion:- Annual yield to maturity
a. 6.154 % b. 6% c. 6.49%Related Questions
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