An insurance company is obligated to pay $200,000 at the end of year 4 and $500,000 at the end of year 7. The company wants to immunize its position. The current interest rate is 10 percent per year.

(a.) What is the duration of its obligation?

(b.) If the plan uses a zero-coupon bond with maturity of 5 years, and a 30-year annuity currently yielding 10 percent to construct the immunized position, how much money ought to be placed in each asset?

(c.) Suppose the market interest rate remains unchanged. Is the position still immunized after one year? Why?