A TIPS bond is $1\mathrm{.}5$ years away from maturity. This bond has a $3\mathrm{.}5\%$ yield, $4\mathrm{.}8\%$ coupon rate, and makes semiannual payments. The CPI is currently at $200.$ You expect the CPI to increase to $220$ after $6$ months, to $231$ after $12$ months, and to $240\mathrm{.}24$ after $18$ months.$$ Calculate the price of this bond.