Question

Consider two bonds, a 3-year bond paying an annual coupon of 7.00% and a 10-year bond also with an annual coupon of 7.00%. Both currently sell at a face value of $1,000. Now suppose interest rates rise to 12%.

a. What is the new price of the 3-year bonds? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. What is the new price of the 10-year bonds? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

c. Which bonds are more sensitive to a change in interest rates?

Long-term bonds

Short-term bonds

Answer 1

a)       For 3 years Bond:

F = Face value =	$1,000.00
C = Coupon rate =	7.00%
Rate = Yield =	12.00%
Number of coupon payments till maturity = N =	3
PV or Price of Bond = (C x F x ((1-((1+R)^-N)) / R) + (F/(1+R)^N)
Price of the bond = (7%*1000*((1-((1+12%)^-3))/12%)+(1000/(1+12%)^3))
Price of the bond =	$879.91

b)      For 10 years Bond:

F = Face value =	$1,000.00
C = Coupon rate =	7.00%
Rate = Yield =	12.00%
Number of coupon payments till maturity = N =	10
PV or Price of Bond = (C x F x ((1-((1+R)^-N)) / R) + (F/(1+R)^N)
Price of the bond = (7%*1000*((1-((1+12%)^-10))/12%)+(1000/(1+12%)^10))
Price of the bond =	$717.49

c)       Long-term bonds are more sensitive to change in interest rate as the discounting term for cash flow increases hence it shows more sensitivity towards the price.