A $1000 bond with semi-annual coupons at j₂ = 7% maturing at par on June 1,2015 was purchased on June 1,2003 at 97 and sold on June 1,2010 at 105.Find the yield rate,j₂,earned using the method of averages.

Question

Quizplus · Accepted Answer

To calculate the yield rate earned using the method of averages, we need to use the formula:

(Annual coupon payment + (Bond price at maturity - Bond price at purchase) / years held) / ((Bond price at maturity + Bond price at purchase) / 2)

First, we need to calculate the annual coupon payment. Since the bond has semi-annual coupons, we need to divide the coupon rate by 2 and multiply by the par value:

(7%/2) x $1000 = $35

Next, we can calculate the bond price at maturity using the par value:

$1000

The bond price at purchase is given as 97, so we can use this to calculate the gain:

105 - 97 = $8

The number of years held is:

2010 - 2003 = 7

Now, we can plug all of these values into the formula:

($35 + ($8/7)) / (($1000 + 97) / 2) = 0.0851 or 8.51%

Therefore, the answer is C) 8.51%.

A $1000 Bond with Semi-Annual Coupons at J2 = 7

A $1000 Bond with Semi-Annual Coupons at J₂ = 7