Question

Consider two bonds, a 3-year bond paying an annual coupon of 7%, and a 20-year bond, also with an annual coupon of 7%. Both bonds currently sell at par value. Now suppose that interest rates rise and the yield to maturity of the two bonds increases to 10%.

a. What is the new price of the 3-year bond? (Round your answer to 2 decimal places.)

b. What is the new price of the 20-year bond? (Round your answer to 2 decimal places.)

c. Do longer or shorter maturity bonds appear to be more sensitive to changes in interest rates?

Answer 1

Solution :

a) Calculation of price of the 3-year bond :

Here, we have,

Face value ( F ) = $1,000

Coupon rate ( C ) = 7%

Rate ( R ) = 10%

Number of coupon payments till maturity ( N ) = 3

Now,

Price of Bond = ( C * F * [ ( 1 - ( (1+R )^-N) ) / R ]  + ( F / (1+R)^N )

= ( 7% * 1000 * [ ( 1 - ( (1+10%)^-3 ) ) / 10% ] + ( 1000 / (1+10%)^3 ) )

Price of the 3-year bond = $ 925.39

b) Calculation of price of the 20-year bond :

Here, we have,

Face value ( F ) = $1,000

Coupon rate ( C ) = 7%

Rate ( R ) = 10%

Number of coupon payments till maturity ( N ) = 20

Now,

Price of Bond = ( C * F * [ ( 1 - ( (1+R )^-N) ) / R ]  + ( F / (1+R)^N )

= ( 7% * 1000 * [ ( 1 - ( (1+10%)^-20) ) / 10% ] + ( 1000 / (1+10%)^20 ) )

Price of the 20-year bond = $ 744.59

c) Longer

Long term bonds are more sensitive to short term bonds .This is so because longer the duration ,higher is the risk . So, when interest rate changes ,longer duration prices will fall more than by short term bonds.