Question

An Apple annual coupon bond has a coupon rate of 5.1%, face value of $1,000, and 4 years to maturity. If its yield to maturity is 5.1%, 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	51.00	1.05	48.53	48.53
2	51.00	1.10	46.17	92.34
3	51.00	1.16	43.93	131.79
4	1,051.00	1.22	861.37	3,445.50
			Total	3,718.15

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

=3718.15/(1000*1)

=3.718153

Modified duration = Macaulay duration/(1+YTM)

=3.72/(1+0.051)

=3.538