Question

Find the duration of a bond with settlement date June 15, 2018, and maturity date December 23, 2027. The coupon rate of the bond is 9%, and the bond pays coupons semiannually. The bond is selling at a yield to maturity of 10%. (Do not round intermediate calculations. Round your answers to 4 decimal places.)

Macaulay duration:
Modified duration:

Answer 1

Macaulay Duration = (PV₁ / PV) * T₁ + (PV₂ / PV) * T₂ +.....+ (PV_n / PV) * T_n

Where PV₁, PV₂ and PV_n refer to the present value of cash flows that occur T₁, T₂ and T_n years in future and PV is the price of the bond i.e. the sum of present value of all the bond cash flows at time 0.

Macaulay Duration is 6.5022

Modified duration = Macaulay Duration / (1 + (YTM / m)), where m is the number of coupon payments per year

Modified duration = 6.5022 / (1 + (10% / 2)) = 6.1925