Question

Li Life Insurance Company is paying Cora an annuity due of 234 per year for the next 10 years.

Calculate the Modified duration of Cora's annuity at an annual effective interest rate of 8.5%

Answer 1

Given that, Li Life Insurance Company is paying Cora an annuity due of 234 per year for the next 10 years. interest rate = 8.5% per year

Since this is an annuity due, 1st payment is made now or in year 0, and last payment is made at the start of year 10 or at the end of year 9.

here PV of PMT = PMT/(1+rate)^t

Total PV = sum of PV of all PMT = $1665.86

Weight = PV of PMT/ toal PV

duration = weight*year

Macaulay duration of the bond = sum of all PMT's duration = 3.8344 years

Modified duration = Macaulayduration/(1+rate) = 3.8344/1.085 = 3.53 years

Year	PMT	PV of PMT PMT/(1+rate)^t	weight = PV of PMT/total PV	duration
0	$     234.00	$               234.00	0.1405	0.0000
1	$     234.00	$               215.67	0.1295	0.1295
2	$     234.00	$               198.77	0.1193	0.2386
3	$     234.00	$               183.20	0.1100	0.3299
4	$     234.00	$               168.85	0.1014	0.4054
5	$     234.00	$               155.62	0.0934	0.4671
6	$     234.00	$               143.43	0.0861	0.5166
7	$     234.00	$               132.19	0.0794	0.5555
8	$     234.00	$               121.84	0.0731	0.5851
9	$     234.00	$               112.29	0.0674	0.6067
	Total PV	$           1,665.86		3.8344