Question

An Apple annual coupon bond has a coupon rate of 6.9%, face value of $1,000, and 4 years to maturity. If its yield to maturity is 6.9%, what is its Modified Duration? Answer in years, rounded to three decimal places.

Answer 1

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,000.00)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	69.00	1.07	64.55	64.55
2	69.00	1.14	60.38	120.76
3	69.00	1.22	56.48	169.45
4	1,069.00	1.31	818.59	3,274.36
			Total	3,629.12

Macaulay duration =(∑ Duration calc)/(bond price*number of coupon per year)

=3629.12/(1000*1)

=3.629118

Modified duration = Macaulay duration/(1+YTM)

=3.63/(1+0.069)

=3.395