Question

Compute the duration of a bond that pays $100 in year 1 and $5 in year 2. The term-structure of interest rates is flat at 10%. It means r1 = r2 = 10%

Answer 1

Given about a bond,

bond pays, $100 in year 1 and $5 in year 2

YTM = 10%

duration is calculated in below table:

here PV of PMT = PMT/(1+YTM)^year

Price = sum of all PVs = $95.04

Weight = PV of pmt/total PV

duration of PMT = weight*year

Duration of bond = sum of duartion of all coupons = 1.04 years

Year	PMT	PV of PMT PMT/(1+rate/2)^period	weight = PV of PMT/total PV	Duration = weight*year
1	$       100.00	$                 90.91	0.9565	0.9565
2	$            5.00	$                   4.13	0.0435	0.0870
	Price	$                 95.04	Duration	1.04