4) A perpetuity (consol) has a yield to maturity of 60% when it is bought by an investor and pays an annual coupon of$1800L In answering the question, show your work, including formulas. (30 points) a) What is its current price? [Call this case (21), interest rate stays at 60%] b) Suppose the going market interest rate rises to 90%. What happens to the price of the consol (if it changes, calculate the new price}? c) In case (b), suppose the investor sells the consul after holding it for one- year. What is the investor's one-year rate of return? How much does it differ from the one-year rate of return if the interest rate did not change? d} Suppose instead that just after buying the bond when interest rates are 60%, the going market interest rate falls to 30% from the original 60%. What happens to the price of the consol (if it changes, calculate the new price)? e) In case (d), suppose the investor sells the consol after holding it for one- year. What is the investor's one-year rate of return? How much does it differ from the oneyear rate of return if the interest rate did not change? f) List the rate of capital gain, the initial current yield. and rate of return in cases (a), (b). and (d)