Question

A $1,000 par value bond has 7.5% semiannual coupons and matures on July 1, 2017 at $1050. Find the actual feeling price of this bond on November 15, 2013 and the price that would be quoted in a financial newspaper on the same date, based on a nominal annual yield rate of 5.8% compounded semiannually. Use the actual number of days to compare the accrued interest.

Answer 1

The actual selling price on Nov 15,2013 will be the
clean price on Jul 1,2013 plus the accrued interest
till Nov 15.
The newspaper will quote the clean Price as on Jul1,2013
Annual yield =5.8% compounded semiannually
EAR =(1+5.8%/2)^2-1=5.88% pa=2.94% semiannually
Par value of bond	$                 1,000
Semiannual coupon payment @7.5%	$                 37.50
Maturity value	$                 1,050
The clean price of bond on Jul 1 ,2013 will be the PV
of all coupons and maturity value discounted @2.94% semi annually

Period	Interest	Maturity amt	Total amt	PV Factor @2.94% per period	PV of cash flows
Jul 1 2013	37.5		37.5	1	37.50
Dec 31 2013	37.5		37.5	0.9714	36.43
Jul 1 2014	37.5		37.5	0.9437	35.39
Dec 31 2014	37.5		37.5	0.9167	34.38
Jul 1 2015	37.5		37.5	0.8906	33.40
Dec 31 2015	37.5		37.5	0.8651	32.44
Jul 1 2016	37.5		37.5	0.8404	31.52
Dec 31 2016	37.5		37.5	0.8164	30.62
Jul 1 2017	37.5		37.5	0.7931	29.74
Jul 1 2017		1050	1050	0.7931	832.76
				Total	1,134.16

So the clean Price of the Bons as on Jul 1,2013 would be	$            1,134.16
So the price quoted in financial newspaper as on Nov 15,2013 would be the clean price on Jul 1,2013=	$            1,134.16
Now the accrued interest @7.5% on par value for Jul 1- Nov 15 will be =interest for 137 days=1000*7.5%*137/365=$28.15
So the selling Price ason Nov 15,2013 will be =$1134.16+$28.15=		$          1,162.31