Suppose that a $3-$month American call option that has an exercise price of $$30$ is selling at $$5$ and its underlying stock price is $$20.$

a$.$ Explain why investors are willing to buy this call option that has a negative exercise value.

b$.$ If this call option has a positive exercise value, investors may have a change to make arbitrage profits by exercising the option immediately after buying it$.$ However, this is not likely to happen. Explain how the positive exercise value affects the option's price $($premium$)?$