Problem 2: Consider a 10-year bond that pays a 5 percent coupon semi-annually wi

Question

Problem 2: Consider a 10-year bond that pays a 5 percent coupon semi-annually with a face value of $1000.

a.       What is the price of this bond if the annualized yield to maturity of 4 percent (i.e., the stated rate is .04 compounded semi-annually)?  

b.      What is the price of this bond if the annualized yield to maturity of 5 percent (i.e., the stated rate is .05 compounded semi-annually)?  

c.       What is the price of this bond if the annualized yield to maturity of 6 percent (i.e., the stated rate is .06 compounded semi-annually)?  

d.      What is the price of this bond if the annualized effective rate is 5 percent?

Problem 3: Consider the bond described in Problem 2 above but let the coupon be paid annually. Answer questions a through c in Problem 2 above for this annual coupon paying bond.  

Explanation / Answer

Problem 2

semi annual payment = 5%*1000/2= 25

a.price of this bond if the annualized yield to maturity of 4 percent = 25/(1+2%) +25/(1+2%)^2 +25/(1+2%)^3 .......1025/(1+2%)^20 =$1,081.76

b.price of this bond if the annualized yield to maturity of 5 percent =25/(1+2.5%) +25/(1+2.5%)^2 +25/(1+2.5%)^3 .......1025/(1+2.5%)^20 =$1000

c.price of this bond if the annualized yield to maturity of 6 percent =25/(1+3%) +25/(1+3%)^2 +25/(1+3%)^3 .......1025/(1+3%)^20 =$925.61

d. semiannual rate = (1+5%)^(1/2)-1 =2.470%

price of this bond if the annualizedeffectiverate is 5 percent =25/(1+ 2.470%) +25/(1+ 2.470%)^2 +25/(1+ 2.470%)^3 .......1025/(1+ 2.470%)^20 =$1,004.69

Problem 3

annual payment = 5%*1000 = 50

a.price of this bond if the annualized yield to maturity of 4 percent = 50/(1+4%) +50/(1+4%)^2 +50/(1+4%)^3 .......1050/(1+4%)^10 =$1,081.11

b.price of this bond if the annualized yield to maturity of 5 percent =50/(1+5%) +50/(1+5%)^2 +50/(1+5%)^3 .......1050/(1+5%)^10 =$1000

c.price of this bond if the annualized yield to maturity of 6 percent=50/(1+6%) +50/(1+6%)^2 +50/(1+6%)^3 .......1050/(1+6%)^10 =$926.40

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.