1. A bond has just been issued. The bond has an annual coupon rate of 9% and coupons are paid annually. The bond has a face value of $1,000 and will mature in 10 years. The bonds yield to maturity is 12%.
   1. Calculate the price of the bond at the yield to maturity of 12%.
   2. Calculate a new price for the bond if the yield to maturity decreases to 10.5%.
   3. Calculate the actual change in the bonds price as the yield to maturity changes from 12% to 10.5%.
   4. Calculate the bonds duration at a yield to maturity of 12%.
   5. Calculate the bonds duration at a yield to maturity of 10.5%.
   6. Use the bonds duration to calculate the approximate bond price change as the yield to maturity changes from 12% to 10.5%.
   7. Use the bonds modified duration to calculate the approximate bond price change as the yield to maturity changes from 12% to 10.5%.