The stock price is currently $$100.$ It is known that at the end of $3$ months, it will be either $$110$ or $$85.$ The risk$-$free interest rate is $5\%$ per annum with continuous compounding. Suppose S is the stock price at the end of $3$ months. What is the current value of the derivative that pays $$natural logarithm of S$$ at maturity? Use a binomial tree model, and round the result to three decimal places.

$1.$ $$4\mathrm{.}442$

$2.$ $$4\mathrm{.}553$

$3.$ $$4\mathrm{.}700$

$4.$ None of the above

$5.$ $$4\mathrm{.}861$