An insurance company issued a $108 million one-year, zero-coupon note at 8 percent add-on annual interest (paying one coupon at the end of the year) and used the proceeds plus $28 million in equity to fund a $136 million face value, two-year commercial loan at 6 percent annual interest.

Immediately after these transactions were (simultaneously) undertaken, all interest rates went up 1.5 percent.

a. What is the market value of the insurance company's loan investment after the changes in interest rates?

b. What is the duration of the loan investment when it was first issued?

c. Using duration, what is the new expected value of the loan if interest rates are predicted to increase to 7.5 percent from the initial 6 percent?

d. What is the market value of the insurance company's $108 million liability when interest rates rise by 1.5 percent?