Question

James has a loan of 10,000, which is to be repaid with 10 level annual payments at an annual effective interest rate of 14.5%.

Calculate the Macaulay duration of the loan using the 14.5% interest rate.

Answer 1

James has a loan of 10,000, which is to be repaid with 10 level annual payments at an annual effective interest rate of 14.5%.

First calculating annual payment using formula

PMT = PV*r/(1 - (1+r)^(-t)) = 10000*0.145/(1 - 1.145^-10) = $1954.69

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

Total PV = sum of PV of all PMT = $10000

Weight = PV of PMT/ toal PV

duration = weight*year

Macaulay duration of the bond = sum of all PMT's duration = 4.42 years

Year	PMT	PV of PMT PMT/(1+rate)^t	weight = PV of PMT/total PV	duration
1	$ 1,954.69	$           1,707.15	0.1707	0.1707
2	$ 1,954.69	$           1,490.96	0.1491	0.2982
3	$ 1,954.69	$           1,302.15	0.1302	0.3906
4	$ 1,954.69	$           1,137.25	0.1137	0.4549
5	$ 1,954.69	$               993.23	0.0993	0.4966
6	$ 1,954.69	$               867.45	0.0867	0.5205
7	$ 1,954.69	$               757.60	0.0758	0.5303
8	$ 1,954.69	$               661.66	0.0662	0.5293
9	$ 1,954.69	$               577.87	0.0578	0.5201
10	$ 1,954.69	$               504.69	0.0505	0.5047
	Total PV	$         10,000.00		4.4159