# The duration of a bond with 8%

The duration of a bond with 8% annual coupon rate when the yieldto maturity is 10% and two years left to maturity is:

Question 10 options:

 1) 1.75 years
 2) 1.80 years
 3) 1.92 years
 4) 2.96 years

Suppose the Face value of the bond = \$1000

Annual coupon rate = 8%

Annual coupon payment = Annual coupon rate*Face value = 8%*1000= 80

Yield to maturity = YTM = 10%

The cashflow for this bond is: C1 = 80, C2 = 1080

Present value of C1 = PV(C1) = C1/(1+YTM)1 = 80/(1+10%)1 =

Present value of C2 = PV(C2) = C2/(1+YTM)2 = 1080/(1+10%)2 =

 Period Cashflow PV of cashflow 1 80 72.72727273 2 1080 892.5619835

Price of the bond is the sum of the present value of all thecash flows

Price of the bond = P = PV(C1) + PV(C2) = 72.7272727272727 +892.561983471074 = 965.289256198347

Bond’s Price = P = 965.289256198347

Now, Duration is calculated using the formula:

Duration =[(1*72.7272727272727)+(2*892.561983471074)]/965.289256198347 =(72.7272727272727+1785.12396694215)/965.289256198347 =1857.85123966942/965.289256198347 = 1.92465753424658 ~ 1.92years(Rounded to two decimals)

Duration = 1.92 years

Answer -> 1.92 years (option 3)

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