Quantitative Problem:

Madeline Manufacturing Inc.$\text{'}$s current stock price is $$40$ per share. Call options for this stock exist that permit the holder to purchase one share at an exerise $$30.$

These options will expire at the end of $1$ year, at which time Madeline's stock will be selling at one of two prices $$20$ or $$45.$ The risk$-$free rate is $7\%.$ Using the binomial

option pricing model, create a riskless hedged investment and answer the following question:

After the payoffs have been equalized and the riskless hedged investment is created, what is the value of the portfolio in one year? Round your answer to the nearest cent.

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