Question

You find a bond with 5 years until maturity that has a coupon rate of 7.6 percent and a yield to maturity of 5.9 percent. What is the Macaulay duration? Solve by hand.

Answer 1

Let the face value be 1000 .Interest = 1000*.076 = 76

period	cash flow	period *cash flow	PVF @ 5.9%	present value of cash flow   [cash flow * PVF]	present value of period *cash flow   [ period *cash flow *PVF]
1	76	1*76=76	.94429	71.7660	76*.94429=71.7660
2	76	2*76 = 152	.89168	67.7677	152*.89168= 135.5354
3	76	228	.84200	63.992	191.976
4	76	304	.79509	60.4268	241.7074
5	1000+76=1076	5380	.75079	807.8500	4039.2502
		6140		1071.8025	4680.235

Macaulay duration = 4680.235/1071.8025

             = 4.37 years