The Treasury department issued a 10-year bond on January 1, 2015. The par value is $1,000 and the annual coupon rate is 10%. The bond pays two coupons every year, one at the end of June and one at the end of December. The required annual yield is 8%. An investor bought the bond on March 31, 2015. What is the price that he should pay for the bond

$1,135.90

Explanation:

The bond price formula is given below, the formula implies that the price of the bond is the present value of future cash flows which are the semiannual coupons and the face value

Bond price=face value/(1+r)^n+semiannual coupon*(1-(1+r)^-n/r

face value=$1,000

r= semiannual yield to maturity=8%*6/12=4%

n=number of semiannual coupons in 10 years=10*2=20

semiannual coupon=face value*coupon rate*6/12=$1,000*10%*6/12=$50

bond price=$1,000/(1+4%)^20+$50*(1-(1+4%)^-20/4%

bond price=$1000/(1.04)^20+$50*(1-(1.04)^-20/0.04

bond price=$1000/2.191123143 +$50*(1-0.456386946 )/0.04

bond price=$1000/2.191123143 +$50*0.543613054/0.04

bond price= $456.38  +$679.52  

= $1,135.90  

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