Question

An 8% semiannual coupon bond matures in 5 years. The bond has a face value of $1,000 and a current yield of 8.2761%.

What is the bond's price? Do not round intermediate calculations. Round your answer to the nearest cent.

$   

Answer 1

Price of bond is equal to present value of coupon payments plus present value of par value.
We have the following information
Semi annual coupon rate	4%	8%/2
Semi annual coupon amount	40	1000*4%
Face value	1000
Semi annual current yield	4.13805%	8.2761%/2
Number of payments	10	5*2
Price of bond = 40*PVAD(i=4.13805%,n=10)+1000*PV(i=4.13805%,n=10)
Price of bond = 40*PVIFA(i=4.13805%,n=10)+1000*(1/(1.0413805^10))
Price of bond = 40*8.05544+1000*0.6666618
Price of bond	$988.88
Calculation of PVAD
PVAD = (1-(1+r^-N)/r
PVAD = (1-(1.0413805^-10))/0.0413805
PVAD	8.05544
Therefore the price of bond is $988.88, it is below the par value since coupon rate is below the yield to maturity.