Suppose that you purchase a three-year coupon bond with annual coupons of 2%, paid semi-annually and a face value of $100. Suppose that the term structure is flat at 2% APR compounded semi-annually.

(a) Compute the present value of the bond. 

(b) Compute the duration and modified duration of the bond.

(c) Suppose that interest rates go up 10 basis points (0.10%). Approximately, what is the change in value of the bond? Be sure to state whether the value goes up or down. 

(d) Suppose that you have a portfolio and put 50% of your money in this three-year coupon bond and 50% of your money in a bond with a five-year zero coupon bond. What would the duration of the portfolio be?