Example $6-6$ Consider an investor who, on January $1,2022,$ purchases a TIPS bond with an original principal of $$100,000,$ a $4$ percent coupon rate, and $10$ years to maturity. The inflation$-$adjusted principal at the end of the first six months, on June $30,2022,$ is found by multiplying the original par value $($$$100,000)$ by the semiannual inflation rate. Ifthesemiannualinflationrateduringthefirstsixmonthsis$0\mathrm{.}5$percent, the principal amount used to determine the first coupon payment is$?$ How about the coupon payment? Supposethatthesemiannualinflationrateforthesecondsix$-$month period is $1$ percent. Then the inflation$-$adjusted principal at the end of the second six months is$?$ How about the second coupon payment?