Consider a derivative whose payoff at expiration is $S_T^2+1$ if $S_T<mn\; id="EditorElement\_3192876">1</mn><mn\; id="EditorElement\_3192877">0</mn><mn\; id="EditorElement\_3192878">0</mn>$ and $S_T^2+S_T-100$ if $S_{T}100.$ Assuming the volatility is $,$ the risk$-$free rate $r,$ and the spot price $S_0,$ compute the price of this derivative today.

Hint: Write the derivative as $3$ derivatives $($a power option, an option and a digital option$)$ and price each separately.