Question

A fixed coupon bond with 4 years until maturity has a coupon rate of 5% paid annually and is currently trading at a yield of 4% p.a. Compute the following:

Calculate the Price of the bond.

Answer this :Calculate the Duration and Modified Duration of the Bond

Answer 1

Price of bond is present value of coupon payment plus present value of face value
Duration	Sum of (present value of Cash flow*Year)/Price of bond
Modified duration	Duration/(1+YTM/n)
YTM	Yield to maturity
n	number of coupon payment per year
Assuming face value of bond is $1000
Calculation of price of bond and duration
Year	Cash flow	Discount factor @ 4%		Present value	Present value*year
1	50	0.961538462	1/(1.04^1)	$48.08	$48.08
2	50	0.924556213	1/(1.04^2)	$46.23	$92.46
3	50	0.888996359	1/(1.04^3)	$44.45	$133.35
4	1050	0.854804191	1/(1.04^4)	$897.54	$3,590.18
				$1,036.30	$3,864.06
Coupon amount	1000*5%
Duration	3864.06/1036.30
Duration	3.73
Thus, price of bond is $1,036.30
Duration is 3.73
Modified duration	3.73/(1+(0.04/1))
Modified duration	3.73/1.04
Modified duration	3.59