Consider two bonds, a 3-year bond paying an annual coupon of 10%, and a 20-year bond, also with an annual coupon of 10%. Both bonds currently sell at par value. Now suppose that interest rates rise and the yield to maturity of the two bonds increases to 14%. 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? Longer Shorter

Question

Business

Jaylen Bauer

4 May, 20:13

Consider two bonds, a 3-year bond paying an annual coupon of 10%, and a 20-year bond, also with an annual coupon of 10%. Both bonds currently sell at par value. Now suppose that interest rates rise and the yield to maturity of the two bonds increases to 14%. 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? Longer Shorter

+3

Answers (1)

Know the Answer?

Kaitlyn Walters · Answer 1

Assume face value of both bond be $ 1,000

A) price of a 3 year bond = (PVAF10%,3 * interest) + (PVF10%,3 * Face value)

= (2.48685 * 50) + (.75131 * 1000)

= 124.34 + 751.31

= $ 875.65

B) Price of a 10 year bond = (PVAF10%,10 * interest) + (PVF10%,10 * Face value)

= (6.14457 * 50) + (.38554 * 1000)

= 307.23 + 385.54

= $ 692.77

c) 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.