Question $4.$ Assume the binomial model. A non$-$dividend paying stock has

a current price of $50$$$.$ Current date is $t=0.u=1\mathrm{.}1,d=0\mathrm{.}8,$ annual

compound interest rate is $0\mathrm{.}05.$ A derivative pays $\sqrt[\phantom{2}]{S_1}$ at year $1,$ and $\sqrt[\phantom{2}]{S_2}$

at year $t=2.$ Compute the price of this derivative at time $t=0.$ Hint :

decompose this derivative into two simpler ones. PLEASE SOLVE BY HAND ON PAPER WITH CLEAR STEPS.