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Finance Suppose you have bought a put option to sell with an exercise price of $50 per share for 100 shares over next 4 month trading at $3. a. draw the put and profit digram? +art b. what the break-even? c. what is the exercise value if the stock price fell to $45? A one-year European put option on a non-dividend-paying stock with strike at $50 currently trades at $5.55. The current stock price is $45. The stock exhibits an annual volatility of 30%The annual risk-free interest rate is 5% compounded continuously. Determine the price of a European call option on the same stock with the same parameters as those of this put option. Loops and fields Exercise 27. Find all ideals of the following rings: 1) (Z1s +15115) 2) (Z36, +36136) 3) (Ms(Z20), +..), H. Exercise 28. Give an example of a noncommutative ring contains 6 ideals only with proof. 212 How Exercise 29. Let R be a ring with identity 1 and let / = { ab ER} Prove that I is a right ideal of the ring M2x2(R), but it is not a left ideal. H. Exercise 30. Determine the simple and not simple rings of the following with proof? (1) (27, +7,-7) (2) (2.40, +40-40) (3) (M.(R), +..) (4) (M. (Z), +,.). Corollary 2.16. Let R be a ring with identity 1 and let / be a proper left (resp. right) ideal of a ring R. Prove that has no invertible element. Proof. Exercise. Exercise 26. Find all ideals of the following rings.1 (218, +18-18) How 2) (Z19, +19.-19). Exercise 9. Prove that the intersection of any family of subrings of a ring R is a subring of R. Exercise 10. Show that whether the union of any two subrings of a ring Ris a subring of R or not and why? Exercise 11. Let R=M2x2(Z) be the ring of all 2 x 2 matrices over a ring Z. ab Z}. Show that whether (S. +..) is a subring of Ror not and why?. Let S =