Bond B 20 years; 7% annual coupon , YTM=10%

(a) If the interest rate rises, will the actual price of Bond B be higher or lower than the estimated price based on duration approximation?

Answer - If the interest rate rises, the actual price of Bond B will be lower than the estimated price based on duration approximation.

Reason- There is an inverse relationship between the interest rates and price of the bond. When the interest rate rises, the bond price falls and vice-versa.

Solution -

Given -

Years - 20

YTM = 10%

Annual Coupon Rate = 7%

Assume Face value of Bond B = 1000

Calcualtion of Bond Pricing at Interest Rate = 10%

10 % = {(1000*7%) + [(1000-Bond Price)/20] / (1000+Bond Price)/2}

On solving this, we get

Bond Price = 750 (approx.)

Now let us assume that the interest rate increases by 2%, then

Years - 20

YTM = 12%

Annual Coupon Rate = 7%

Assume Face value of Bond B = 1000

Calcualtion of Bond Pricing at Interest Rate = 12%

12 % = {(1000*7%) + [(1000-Bond Price)/20] / (1000+Bond Price)/2}

On solving this, we get

Bond Price = 626 (approx.)

Conclusion - So, we see that when YTM increases from 10 to 12 %, the Bond Pricing falls.