Question

Trena has agreed to pay Jayme the following payments:

1. 30,000 at the end of 2 years;
2. 50,000 at the end of 5 years; and
3. 10,000 at the end of 8 years.

You are given that v=0.9.

Calculate the Modified duration of Trena's liability.

Answer 1

Trena has agreed to pay Jayme the following payments:

1. 30,000 at the end of 2 years;
2. 50,000 at the end of 5 years; and
3. 10,000 at the end of 8 years.

You are given that v=0.9.

here PV of PMT = PMT*v^t

Total PV = sum of PV of all PMT = $58129.17

Weight = PV of PMT/ toal PV

duration = weight*year

Macaulay duration of the bond = sum of all PMT's duration = 3.9681 years

Modified duration = Macaulayduration*v = 3.9681*0.9 = 3.57 years

Year	PMT	PV of PMT PMT/(1+rate)^t	weight = PV of PMT/total PV	duration
2	$ 30,000.00	$         24,300.00	0.4180	0.8361
5	$ 50,000.00	$         29,524.50	0.5079	2.5396
8	$ 10,000.00	$           4,304.67	0.0741	0.5924
	Total PV	$         58,129.17	Duration	3.9681