PROBLEM SET $7$: BINOMIAL TREES

$(25$ Points$)$ Assume a non$-$dividend paying stock's price can go up by $20\%$ or down by $15\%$ over the next year. The continuously compounded risk$-$free interest rate is $11\mathrm{.}25\%.$

A $1-$year European put option with a strike of $$78$ has a one$-$period binomial price of $$2\mathrm{.}96.$

Given the price of the stock is greater than $$70,$ compute the current stock price $(S_0).$