Question

3. Assume an original issue bond with 30 years remaining to maturity which is sold at par or $1000. It has a coupon rate of

3.5 % which is the same as the going rate of interest in the market and its duration is 20.

What would its new price be if the interest rates rise by 25 basis points. Show all calculations.

b. What would be the new price if the interest rate in the market falls to 3.25%.? Show all calculations

Answer 1

3 a. Duration =20
Original Price =1000
YTM is same as coupon rate =3.5%
Actual new Price =PV of Par Value+PV of Coupons =1000/(1+3.25%)^30+35*((1-(1+3.25%)^-30)/3.25%)=1047.45
New Price if interest rates rise by 0.25% using duration=-Duration*Change in YTM*Price =-20*-0.25%*1000=50
New Price with duration =1000+50 =1050

b. Actual new Price =PV of Par Value+PV of Coupons =1000/(1+3.75%)^30+35*((1-(1+3.75%)^-30)/3.75%)=955.43
New Price if interest rates falls by 0.25% using duration=-Duration*Change in YTM*Price =-20*0.25%*1000=-50
New Price with duration =1000-50 =950