please give answers to each questions with clear steps. and please writing or typing the answers clearly, it is better to type the answers, many thanks!

3. Take an asset in fixed supply that will pay either 12 (with 50% prob.) or 6 (with 50% prob.) in a year's time. Assume the expected dividend in a year is zero. a. If the discount rate is 10% what is the fundamental price of the asset? (10 marks.) b. What if the asset is purchased with a loan? Assume there is limited liability and that in case the bad outcome happens the borrower can default on the loan (obtaining a payoff of zero). (10 marks.) c. How do your answers to 3.a and 3.b change if the discount rate is 2%? (5 marks.) d. How do your answers to 3.a and 3.b change if the asset pays either 15 (with 50% prob.) or 3 (with 50% prob.)? (5 marks.)