Question

A bond pays annual interest. Its coupon rate is 7.00%. Its value at maturity is $1,000.00. It matures in 4.00 years. Its yield to maturity is currently 4.00%. The duration of this bond is _______ years.

Answer 1

Period	Cash flow	Discounting factor Df = 1/(1+Yield)^Period	PV of the cash flows = Cash flow x Df	Weighted cash flow = Period x Cash flow	Present value of weighted cash flow = Weighted Cash flow x Df
1	70	0.961538462	67.31	70	67.31
2	70	0.924556213	64.72	140	129.44
3	70	0.888996359	62.23	210	186.69
4	1070	0.854804191	914.64	4280	3658.56
		Total	1108.90	Total	4042.00
		Price of the Bond	1108.90	Weighted Price	4042.00

Duration = Weighted price of the bond / Price of the bond = 4042 / 1108.90

Duration = ~ 3.645 Years

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If you want to calculate modified duration then:

Modified Duration = Duration / (1+Yield)

Modified Duration = 3.645/1.04

Modified Duration = ~ 3.50 Years