An insurance company issued a $109 million one-year, zero-coupon note at 9 percent add-on annual interest (paying one coupon at the end of the year) and used the proceeds plus $29 million in equity to fund a $138 million face value, two-year commercial loan at 8 percent annual interest. Immediately after these transactions were (simultaneously) undertaken, all interest rates went up 1.6 percent.

a. What is the market value of the insurance company’s loan investment after the changes in interest rates? (Do not round intermediate calculations. Enter your answer in millions rounded to 3 decimal places. (e.g., 32.16))

  Market value of the loan investment     $  million

b. What is the duration of the loan investment when it was first issued? (Do not round intermediate calculations. Round your answer to 3 decimal places. (e.g., 32.161))

  Duration of the loan investment     years

c. Using duration, what is the new expected value of the loan if interest rates are predicted to increase to 9.6 percent from the initial 8 percent? (Do not round intermediate calculations. Enter your answer in millions rounded to 3 decimal places. (e.g., 32.16))

  New expected value        $  million

d. What is the market value of the insurance company’s $109 million liability when interest rates rise by 1.6 percent? (Do not round intermediate calculations. Enter your answer in millions rounded to 3 decimal places. (e.g., 32.161))

  Market value of the liability       $  million

e. What is the duration of the insurance company’s liability when it is first issued?

  Duration of the liability        year(s)