Consider a simple financial model with three times, $t=0,1,2.$

The model includes a single stock, $S,$ which pays no dividends. The initial price per share of the stock is $S_0=$$$40.$

There is also a bank that allows investments at a one period interest rate $r=\mathrm{.}08.$ This means an amount A invested at $t=0$ will grow to $(1+r)A$ at $t=1.$ An amount $B$ invested at time $t=1$ will grow to $(1+r)B$ at $t=2.$ Combining these, an amount $C$ invested at $t=0$ can grow to $(1+r{)}^{2}C$ at $t=2.$

Note that this model simply extends the model in the previous problem by one period.

Consider a contract that requires it's owner to receive one share of stock at time $t=1$ and one more share of stock at time $t=2.$ In exchange, the owner of the contract makes two payments of $K$ dollars, one at time $t=1$ and the second at time $t=2.$

What is the value of this contract $($in terms of $K)$ at $t=0?$