Problem $4[15$ points$]$:

You are working on the structuring desk in the fixed income division of an investment bank.

A salesperson stops by and asks you to help one of her institutional clients. The client will receive

a cash inflow of USD $100$ million one year from now and would like to invest it for one year there$-$

after $($The client will invest the funds at the end of year $1$ and the strategy will return the funds

at the end of year $2).$ However the client would like to lock into today's rates. Below is a table of

prices for zero$-$coupon bonds of various maturities.

a$)$ What one$-$year forward rate of return can the client lock in one year from now?

b$)$ Construct a trade that allows the bank to offer the client this rate of return. The strategy

that you devise should not require the bank to commit any of its own capital. You will need

to indicate the quantity of each security that you purchase or sell.