A perpetuity (consol) has a yield to maturity of 50% when it's bought by an investor and pays an annual coupon of $100. Show your work, including formulas.

1. a) What is its current price? [ call this case a, interest rate stays at 50%]

2. b) Suppose the going market interest rate falls to 20%. What happens to the

   price of the consol (if it changes, calculate the new price)?

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c) In case (b), suppose the investor sells the consol after holding it for one- year. What is the investors one-year rate of return? How much does it differ from the one-year rate of return if the interest rate did not change?

4. d) Suppose the going market interest rate rises to 75% from the original 50% at which the investor bought the consol. What happens to the price of the consol (if it changes, calculate the new price)?

5. e) In case (d), suppose the investor sells the consol after holding it for one year. What is the investors one-year rate of return? How much does it differ from the one-year rate of return if the interest rate did not change?

6. f) List the rate of capital gain, the initial current yield, and rate of return in cases (a), (b), and (d).