Rachel is considering an investment in Yonan Communications, whose stock currently sells for $$55.$ A put option on Yonan's stock, with an exercise price of $$50,$ has a market value of $$2\mathrm{.}87.$ Meanwhile, a call on the stock with the same exercise price and time until expiration has a market value of $$9\mathrm{.}29.$ The market believes that at the expiration of the options, the stock price will be $$40$ or $$65$ with equal probability. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the questions below.

Open spreadsheet

a$.$ What is the premium associated with the put option? The call option? Do not round intermediate calculations. Round your answers to the nearest cent.

The premium associated with the put option: $ $$

The premium associated with the call option: $ $$

b$.$ If Yonan's stock price increases to $$65,$ what would be the return to an investor who bought a share of the stock? If the investor bought a call option on the stock? If the investor bought a put option on the stock? Do not round intermediate calculations. Round your answers to two decimal places.

Investment

Returns

Own stock $\%$

Buy call option $\%$

Buy put option $\%$