Consider two bonds, a 3-year bond paying an annual coupon of 6.90% and a 10-year bond also with an annual coupon of 6.90%. Both currently sell at a face value of $1,000. Now suppose interest rates rise to 12%. Required:
a. What is the new price of the 3-year bonds?
b. What is the new price of the 10-year bonds?

a.

$877.51

b.

$711.84

Explanation:

Price of the bond is the present value of all cash flows of the bond. These cash flows include the coupon payment and the maturity payment of the bond. Both of these cash flows discounted and added to calculate the value of the bond.

According to given data

Face value of the bond is $1,000

Coupon payment = C = $1,000 x 6.9% = $69 annually

Market Rate = 12% annually

Price of the bond is calculated by following formula:

Price of the Bond = C x [ ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]

a.

Numbers of period = 3

Placing values in the formula

Price of the Bond = $69 x [ ( 1 - ( 1 + 12% )^-3 ) / 12% ] + [ $1,000 / ( 1 + 12% )^3 ]

Price of the Bond = $165.73 + $711.78

Price of the Bond = $877.51

b.

Numbers of period = 10

Placing values in the formula

Price of the Bond = $69 x [ ( 1 - ( 1 + 12% )^-10 ) / 12% ] + [ $1,000 / ( 1 + 12% )^10 ]

Price of the Bond = $389.87 + 321.97

Price of the Bond = $711.84