Problem $1.$ In class, we have learned that the value of a forward contract is the

same as the value of the stock$-$and$-$bond portfolio that replicates the contract. The

value of the $(x,y)$ portfolio, with $x$ share of stock and $y$ units of cash bond, is

$V=S_1(\frac{f(3)-f(2)}{S_3-S_2})+e^{-r*t}(f(3)-(\frac{f(3)-f(2)}{S_3-S_2})*S_3)$

This is a complicated expression. Let us define a variable,

$q=\frac{S_1{e}^{r*t}-S_2}{S_3-S_2}$

Show that the value $V$ can be written as

$V=e^{-r*t}[(1-q)f(2)+qf(3)]$