Suppose a portfolio manager purchases \(\$ 1\) million of par value of a Treasury inflation protection security. The real rate (determined at the auction) is \(3.2 \%\).

a. Assume that at the end of the first six months the CPI-U is \(3.6 \%\) (annual rate). Compute

(1) the inflation adjustment to principal at the end of the first six months, 

(2) the inflation-adjusted principal at the end of the first six months, and

(3) the coupon payment made to the investor at the end of the first six months.

b. Assume that at the end of the second six months the CPI-U is \(4.0 \%\) (annual rate). Compute 

(1) the inflation adjustment to principal at the end of the second six months, 

(2) the inflation-adjusted principal at the end of the second six months, 

(3) the coupon payment made to the investor at the end of the second six months.