Suppose ABC Corporation has an obligation to pay $10,000 and $40,000 at the end of 5 years and 7 years respectively. In order to meet this obligation, it plans to invest money by selecting from the following three bonds:

All bonds have the same face value $1000. Assume that the annual rate of interest to be used in all calculations is 6%. Consider semi-annual compounding. (Keep your answers to 2 decimal places, e.g. xxx.12.)

(a) Find the present value and duration of the obligation.

(b) Suppose the Corporation decides to use bonds 2 and 3. Denote by V 2 and V 3 to be the amounts of money to be invested in the two bonds, respectively. To get an immunized portfolio, write down appropriate equations in V 2 and V 3 first, and solve for V 2 and V 3.

Coupon Rate Maturity (years) Yield Bond 1 4% Bond 2 5% Bond 3 7% 3 6 10 6% 6% 6%