An insurance company needs to make payments to a consumer of $10 million in 1 year (t=1) and $4 million in year 5 (t=5). The yield curve is considered to be flat at 10%.

a. If it wants to fully fund and immunize its obligation to this customer with a single issue of a zero-coupon bond, what maturity bond must it purchase? Note: your answer must be ONE zero-coupon bond.

b. What must be the face value (i.e., the principal amount) and market value (at t=0) of that zero-coupon bond?

c. Suppose yields next year at t=1 are 9%. What is the value of the zero that the organization bought in part (a)?