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##### Find the future value of $2,000 invested for five years at 8% if the interest is compounded:

**Description**

solution

**Question**

1. Find the future value of $2,000 invested for five years at 8% if the interest is compounded;a. annually;b. semi-annually;c. continuously;2. In January, you sell short 400 shares of XYZ stock at a price of $90. In February, the stock pays a dividend of $4 per share. You close your position in March when the stock price is $80.;a. What specific action is required to close your position in March?;b. Find your total profit or loss.;3. Find the price of a six-month forward on a stock trading for $20 that pays no dividends, when the risk-free rate is 6%. For this problem and the rest of this assignment, you may assume that all interest rates are given as continuously compounded annual rates.;4. A stock trading at $60 is expected to pay one dividend of $3 six months from now. The risk-free rate is 4%.;a. Find the present value of the $3 dividend to be received six months from now.;b. Find the price of a one-year forward on this stock.;5. A stock index with a dividend yield of 2% is currently valued at 1,550, The risk-free rate is 5%. Find the price of a nine-month forward on this stock index.;6. Suppose that the current exchange rate is $1.2709 = ?1, the risk free rate in the U.S. is 1.25%, and the risk free rate in Europe is 4.75%. Find the price of a six-month forward for ?1.;7. Storing gold costs $4 per ounce at the beginning of each year. The spot price of gold is $1,360 and the risk-free rate is 3%. Find the price of a one-year futures contract for gold.;8. Suppose that a stock index with no dividends and a current price of $1,000 is expected to gain 10% over the next year, while the risk-free rate is 3%. A one-year forward will be priced at $1,030, while we expect the index to be at $1,100 in one year.;a. Explain how we know that the one-year forward will be priced at $1,030.;b. Explain why something expected to be worth $1,100 is priced at $1,030. In other words, what does the difference represent?

Paper#28333 | Written in 18-Jul-2015

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