Question

Consider two bonds, a 3-year bond paying an annual coupon of 6.50% and a 10-year bond also with an annual coupon of 6.50%. Both currently sell at a face value of $1,000. Now suppose interest rates rise to 9%. a. What is the new price of the 3-year bonds? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What is the new price of the 10-year bonds? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

New price of 3 year bond

Price of the bond could be calculated using below formula.

P = C* [{1 - (1 + YTM) ^ -n}/ (YTM)] + [F/ (1 + YTM) ^ -n]

Where,

                Face value = $1000

                Coupon rate = 6.5%

                YTM or Required rate = 9%

                Time to maturity (n) = 3 years

                Annual coupon C = $65

Let's put all the values in the formula to find the bond current value

P = 65* [{1 - (1 + 0.09) ^ -3}/ (0.09)] + [1000/ (1 + 0.09) ^3]

P = 65* [{1 - (1.09) ^ -3}/ (0.09)] + [1000/ (1.09) ^3]

P = 65* [{1 - 0.77218}/ 0.09] + [1000/ 1.29503]

P = 65* [0.22782/ 0.09] + [772.18288]

P = 65* 2.53133 + 772.18288

P = 164.53645 + 772.18288

P = 936.71933

So price of the bond is $936.72

New price of 10 year bond

                Face value = $1000

                Coupon rate = 6.5%

                YTM or Required rate = 9%

                Time to maturity (n) = 10 years

                Annual coupon C = $65

Let's put all the values in the formula to find the bond current value

P = 65* [{1 - (1 + 0.09) ^ -10}/ (0.09)] + [1000/ (1 + 0.09) ^10]

P = 65* [{1 - (1.09) ^ -10}/ (0.09)] + [1000/ (1.09) ^10]

P = 65* [{1 - 0.42241}/ 0.09] + [1000/ 2.36736]

P = 65* [0.57759/ 0.09] + [422.41146]

P = 65* 6.41767 + 422.41146

P = 417.14855 + 422.41146

P = 839.56001

So price of the bond is $839.56

--------------------------------------------------------------------------------------------------------------------------

Feel free to comment if you need further assistance J

Pls rate this answer if you found it useful.