You buy a call option with a strike price of $$80$ for $$22\mathrm{.}50,$ sell two call options with a strike price

of $$100$ for $$9\mathrm{.}00$ each, and buy a call option with a strike price of $$120$ for $$2\mathrm{.}50.$ All the options

are European and expire in $1$ year. The one$-$year interest rate is $2\%.$ Draw the payoff diagram on

the expiration date for the three options and the portfolio. Why would you embark on this strategy? Please do draw the payoff diagram.