You took out a $$200,000$ mortgage for $30$ years. The contract rate is tied to the one$-$year U$.$S$.$ treasury rate $($index rate$).$ The fixed risk premium for your mortgage is $9\%.$ Your interest rate will be adjusted every year.

For the first year, the index rate is $1\mathrm{.}5\%.$ What is the outstanding principal at the end of year $1?$

$$95,758$

$$198,999$

$$197,769$

$$96,726$