A perpetuity is an annuity that pays a fixed cash amount c indefinitely. (a) Show that the price (present value) of a perpetuity paying an annual coupon c is P = cy where y> 0 is the relevant market interest rate or yield. (b) Consider a perpetuity that pays a $1 coupon every year and trades at $80. Calculate its yield y. (c) Suppose you bought 1,000 perpetuities at $80 each, and then that the yield calculated in (b) goes up 25 basis points (i.e. +0.25%). Calculate your profit or loss (P&L).