Suppose that the coupon rate for a TIPS is $2\%.$ The CPI at issue date is $120.$ Suppose further that an investor purchases $$10,000$ of par value of this issue at issue date. TIPS pay semiannual coupons.

a$.$ At the end of the first six months, the CPI becomes $140.$ What is the amount of coupon interest $($in dollars$)$ that will be paid to this investor at the end of the first six months? $(4$ points$)$

b$.$ At the maturity, the CPI drops to $110,$ what would be the final payment $($including the last coupon payment and the principal$)$ paid to the bondholder?