An insurance company has liabilities of $200 million with duration of 15 years. Assume the yields on all risk-free bonds are 5%.

a. What position in 10-year and 20-year zero coupon bonds will fully immunize the liabilities of this insurance company?

b. If yields on all bonds fall immediately to 4%, what will be the actual change in the total value of the liabilities and the total value of the assets (the portfolio of 10-year and 20-year zero coupon bonds) determined in part a above?