Consider a bond with the following terms: • 10 years to maturity • $1,000 face value • Coupons are paid 2 times per year • Annual coupon rate is 5% For problems 1- 5, assume a constant discount rate across maturities of 6%. Also, assume that the bond will make its next coupon payment in exactly 1/2 years.

 
1.) Compute the exact modified duration of the bond

2.) Approximate the modified duration of the bond    

3.) Compute the exact convexity of the bond (not the approximation)

4.) Approximate the convexity of the bond

5.) Suppose now that the discount rate increased to 10%
Find the exact price of the bond under the new discount rate.