Question

A $1,000 par value bond has a 9% annual coupon and matures in 5.50 years. If the current market interest rate on bonds of this type is 7% p.a., calculate this bond’s invoice price, accrued interest, and clean price.

Answer 1

Calculation of Invoice price
Coupon Interest rate =					9.00%
Par value of bond =					$1,000.00
Interest per coupon		(1000*9%) =			$90.00
YTM rate					7.00%
No. of years to Maturity					5.50
Calculation of price of bond @ 7% YTM
Annual Interest received =				90.00
Cumulative P.V.F. @ 7 % for 5.50 Years =
(1- ((1/(1.07)^5.5)))/0.07				4.439003
Present value of interest received					$399.51
Maturity amount received =				1000
P.V.F. @ 7% for 5.50 th year =
(1/(1+0.07)^5.5)				0.68927
Present value of Maturity amount					$689.27
Price of bond					$1,088.78
So, Clean price of bond is $1088.78.
Calculation of Accrued Interest
Interest accrured since last coupon date is					$    45.00
1000 *9% * 0.50 years =
Calculation of Invoice price or dirty price
Invoice price = Clean price + accrued Interest
	$1,088.78	+ $45
	$1,133.78
So, Invoice price of bond is $1,133.78.