Answers/disc... Financial Engineering and Risk Management Part I week 2

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1. A major lottery advertises that it pays the winner $10 million. However this prize money is paid at the rate of $500,000 each year (with the first payment being immediate) for a total of 20 payments. What is the present value of this prize at 10% interest compounded annually? 

Report your answer in $millions, rounded to two decimal places. So, for example, if you compute the answer to be 5.7124 million dollars then you should submit an answer of 5.71.


2. A young couple has made a deposit of the first month's rent (equal to $1,000) on a 6-month apartment lease. The deposit is refundable at the end of six months if they stay until the end of the lease. The next day they find a different apartment that they like just as well, but its monthly rent is only $900. And they would again have to put a deposit of $900 refundable at the end of 6 months. They plan to be in the apartment only 6 months. Should they switch to the new apartment? Assume an (admittedly unrealistic!) interest rate of 12% per month compounded monthly.


3. Suppose the spot rates for 1 and 2 years are

�1=6.3% and �2=6.9% with annual compounding. Recall that in this course, interest rates are always quoted on an annual basis unless otherwise specified. What is the discount rate �(0,2)?

Please submit your answer rounded to three decimal places. For example, if your answer is 0.4567 then you should submit an answer of 0.457.


4. Suppose the spot rates for 1 and 2 years are �1=6.3% and �2=6.9% with annual compounding. Recall that in this course, interest rates are always quoted on an annual basis unless otherwise specified. What is the forward rate, �1,2 assuming annual compounding?

Please submit your answer as a percentage rounded to one decimal place. For example, if your answer is 8.789% then you should submit an answer of 8.8.


5. The current price of a stock is $400 per share and it pays no dividend. Assuming a constant interest rate of 8% per year compounded quarterly, what is the stock's theoretical forward price for delivery in 9 months?

Please submit your answer rounded to two decimal places. For example, if your answer is 567.1234 then you should submit an answer of 567.12


6. Suppose the borrowing rate

��=10% compounded annually. However, the lending rate (or equivalently, the interest rate on deposits) is only 8% compounded annually.

Compute the difference between the upper and lower bounds on the price of a perpetuity that pays A=10,000$ per year.

Please submit your answer rounded to the nearest dollar. If your answer is 23,456.789 then you should submit an answer of 23457.


7. Suppose we hold a forward contract on a stock with expiration

6 months from now. We entered into this contract 6 months ago, so when we entered into the contract the expiration was �=1 year. The stock price 6 months ago was �0=100, the current stock price is 125 and the current interest rate is �=10% compounded semi-annually (This is the same rate that prevailed 6 months ago). What is the current value of our forward contract?

Please submit your answer in dollars rounded to the nearest dollar. If your answer is 42.678 then you should submit an answer of 43.

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