Question

Calculate the duration of a 3 year from maturity bond that has a 5.00% annual pay coupon rate and a 2.50% yield. (Use 4 decimal point precision.)

Answer 1

Annual coupon rate = 5%

YTM = 2.5%

Face value of the bond = 1000

Time to maturity = 3 years

Following are the cash flows for this bond:

C₁ = 50, C₂ = 50, C₃ = 50+1000 = 1050

Present Value of these cash flows are:

Present value of C₁ = PV(C₁) = C₁/(1+r)¹ = 50/(1+2.5%)¹ = 48.780487804878

Present value of C₂ = PV(C₂) = C₂/(1+r)² = 50/(1+2.5%)² = 47.5907198096371

Present value of C₃ = PV(C₃) = C₃/(1+r)³ = 1050/(1+2.5%)³ = 975.029381465736

Present value of the bond is the sum of present value of aall future cash flows

Present value of bond = PV_Bond = PV(C₁) + PV(C₂) + PV(C₃) = 48.780487804878+47.5907198096371+975.029381465736 = 1071.40058908025

Duration of the bond is given by the below formula:

Duration = [(1*48.780487804878)+(2*47.5907198096371)+(3*975.029381465736)]/1071.40058908025 = 3069.05007182136/1071.40058908025 = 2.86452154600363

Answer -> Duration = 2.8645 years