It is May 5, 2013. The quoted price of a government bond with a 12% coupon that matures on July 27, 2024, is 110-24. What is the cash price?

It is July 30, 2015. The cheapest-to-deliver bond in a September 2015 Treasury bond futures contract is a 13% coupon bond, and delivery is expected to be made on September 30, 2015. Coupon payments on the bond are made on February 4 and August 4 each year. The term structure is flat, and the rate of interest with semiannual compounding is 12% per annum. The conversion factor for the bond is 1.5. The current quoted bond price is $110. Calculate the quoted futures price for the contract.

Portfolio A consists of a one-year zero-coupon bond with a face value of $2,000 and a 10-year zero-coupon bond with a face value of $6,000. Portfolio B consists of a 5.95-year zero-coupon bond with a face value of $5,000. The current yield on all bonds is 10% per annum.

Show that both portfolios have the same duration.

Show that the percentage changes in the values of the two portfolios for a 0.1% per annum increase in yields are the same.

What are the percentage changes in the values of the two portfolios for a 5% per annum increase in yields?