On a financial market risk free debt is available at a yearly interest rate of $5\%.$

A stock is traded at a price of $90.$ The stock pays no dividends and has a

volatility of $17\%,$ measured as the yearly standard deviation. European call and put

options on the stock are also traded. Options with exercise prices of $75$ and $95$ are

available; they mature $6$ months from now. An investor buys a call option with an

exercise price of $75$ and sells a call option with an exercise price of $95.$

$($a$)$ What are the maximal profit and the maximal loss the investor can obtain

from this position when the options mature? Use calculations to support your answer and

make additional assumptions if necessary.