Question

A $3500 bond paying interest at j1 = 10% matures on June 1, 2030. On July 22, 2004, it was purchased for $3551 plus bond interest. On April 3, 2009, it was sold for $3443 plus bond interest. Estimate the yield j1 by the method of averages.

Answer 1

To calculate the yield method of averages we have figures mentioned below, to calculate the average return yield we should have the interest gain for the bond holding years and the value of the bond sold in specific year.

Bond paying interest = 10%

Rate of bond purchased = $ 3551

Rate of bond sold $ 3443

Below table is the calculation for simple bond yield of j1 of the years bond holded.

A	B	C	D	E
Total period Year	Bond Value	Interest rate	No. of Days/Months/Year for the bond paid	Interest earned for the year	Calcualtion for the "E" Column
22-Jul-2004 to 31-Dec-2004	3500	10%	162 Days	158.2191781	=3500*10%*162/365
2005	3500	10%	1 Year	350	=3500*10%
2006	3500	10%	1 Year	350	=3500*10%
2007	3500	10%	1 Year	350	=3500*10%
2008	3500	10%	1 Year	350	=3500*10%
1-Jan-2009 to 3-Apr-2009	3500	10%	92 Days	88.21917808	=3500*10%*162/365
			Total	1646.438356

So here toal interest gain of j1 is $1646.44.

So our net gain being puchased price minus sales price plus interest received i.e. mentioned below;

= $3551 - $3443 = -$108 (being a loss we are marking it has minus)

= -$108 + $1646.44

= $1538 for a approximate period of 5 years, which is $307.6 per year.

So, $307.6 yield per year shows 8.78% returs per annum which is moderate yield of j1 and lesser than regular 10% per annum yield