Mary buys a perpetuity-due with level annual payments of $25. Jane buys a

geometric annuity-immediate with 13 annual payments. Janes 1st payment is $52 and each

subsequent payment is r% larger than the previous one. The present values of Marys perpetuity

is equal to the present value of Janes annuity, under an effffective annual interest rate of i% =

r%. Find the value of r (equivalently i) for which this holds, where r < 1.