Consider an investor who purchases a Treasury inflation$-$indexed note with an original principal amount of $$100,000,$ a $3\mathrm{.}125$ percent annual coupon rate $($coupon is paid semiannually$),$ and $10$ years to maturity. The semiannual inflation rate during the $6$ months ending $3$ months before the first coupon payment $($the $3-$month lag is necessary to allow for the release of the official CPI figures$)$ is $3\mathrm{.}41$ percent. Over the next $6-$month period inflation is $1\mathrm{.}25$ percent. Calculate the adjusted principal amount for the second coupon payment.