Assume annually compounded rates for all maturities are r%, where r is positive. Let the current time be n = 0. Now consider an exotic annuity that pays $n at year n, n = 1, 2, . . . ,N.

(i) Find a formula for the present value of the annuity as a function of r and N.

(ii) What is the present value of the annuity when it becomes a perpetuity as N towards infinity?