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This assignment requires the following knowledge: For K different events, if the probability that each of them happens is p (0< p < 1) and all events happen independently, the probability that all events happen together is . Five firms, namely A, B, C, D and E, issue discounted bonds with face value $1,000 and maturity 5 years in the market. All firms are pretty risky and each of them has a change of 0.5 of collapse during the five years (thus bankrupted and cannot pay back the bond accordingly). The bonds are all sold at an interest rate of 50% (the value is not surprising due to the extremely high risk of default). What is the present value of the bond given the interest rate, the face value and the maturity? Hint: we temporarily do not consider the issue of default.   Say now you buy one bond from each of the five firms, what is the total amount you lent out today? Eventually only one firm does not fail and pays back the bond, what is the money you collect back 5 years later? You gain or loss in this case? If more than one firm pays back the bond, will you get more money back?   What is the chance (probability) that you get nothing back assuming that firms fail independently? Together with the answer in (2), is it good deal to buy one bond from each of the five firms?   Repeat (2) and (3) with the only difference that now you buy 5 bonds from a single firm.   Now we assume that the five firms all have similar businesses in Greece (and those are their only businesses), therefore, all firm fail together if the economy in Greece fails. Will you answer in (3) change?                         A travelling salesman enters the barter market of a small town finding the following prices:   1 bottle of milk can change of 3 apples or 2 bananas or 18 berries 1 apple can change for 1/3 bottle of milk or ½ bananas or 6 berries 1 banana can change for ½ bottle of milk or 2 apples or 9 berries 1 berry cam change for 1/18 bottle of milk or 1/6 apples or 1/9 bananas   Now suppose besides the barter market, people can also directly sell goods to the trading association for coins, which can be used anywhere in the whole country. The prices are:   1 bottle of milk for 36 pence 1 apple for 12 pence 1 banana for 18 pence 1 berry for 2 pence   Goods purchased by the association will go back to the market for exchange.   Say the salesman arrives at the town with 50 apples. What is the total amount the trading association needs to pay for the goods?       What will happen to the barter rate of the small town? Hint: You answer in (1) in inspiring.

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