Derive the formulas to calculate modified duration and convexity measure for a perpetuity. Know that the present value, or price, of a perpetuity is C$/$y$,$ where C is the

cash flow per year and y is the yield per year. How would the answer be different if the payment frequency is semiannually versus annually?

$($Hint: you may want to calculate the derivatives of price with respect to yield.$)$