Question

Consider the following.

a. What is the duration of a four-year Treasury bond with a 11 percent semiannual coupon selling at par?

b. What is the duration of a three-year Treasury bond with a 11 percent semiannual coupon selling at par?

c. What is the duration of a two-year Treasury bond with a 11 percent semiannual coupon selling at par?

Please show work using Duration Equation, not excel.

Answer 1

1
=1/2*(1*5.5%*1000/1.055+2*5.5%*1000/1.055^2+3*5.5%*1000/1.055^3+4*5.5%*1000/1.055^4+5*5.5%*1000/1.055^5+6*5.5%*1000/1.055^6+7*5.5%*1000/1.055^7+8*5.5%*1000/1.055^8+8*1000/1.055^8)/1000=3.34148355859891

2
=1/2*(1*5.5%*1000/1.055+2*5.5%*1000/1.055^2+3*5.5%*1000/1.055^3+4*5.5%*1000/1.055^4+5*5.5%*1000/1.055^5+6*5.5%*1000/1.055^6+6*1000/1.055^6)/1000=2.63514223780955

3
=1/2*(1*5.5%*1000/1.055+2*5.5%*1000/1.055^2+3*5.5%*1000/1.055^3+4*5.5%*1000/1.055^4+4*1000/1.055^4)/1000=1.84896668923798