Consider two bonds, a 3-year bond paying an annual coupon of 5%, and a 20-year bond, also with an annual coupon of 5%. Both bonds currently sell at par value. Now suppose that interest rates rise and the yield to maturity of the two bonds increases to 8%. a. What is the new price of the 3-year bond?

$922.69  

Explanation:

The price of the 3-year bond can be computed using the below bond price formula:

Price=face value/(1+r)^n+coupon*(1-(1+r)^-n)/r

face value is $1000

r is the new interest rate of 8%

n is the number of annual coupons the bond would pay which is 3

coupon=face value*coupon rate=$1000*5%=$50

price=1000/(1+8%)^3+50*(1-(1+8%)^-3)/8%

price of 3-year bond=$922.69  

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