We derive the present value and accumulated value formulas for zeta annuities-immediate, due, and continuously payable for all real values of s, thus generalizing annuity formulas like an and (Ia)n to the case where a payment of j-s is made at time j. Taking the limit n = 8, the annuities become perpetuities, and the present value formula for a zeta perpetuity-immediate coincides with the polylogarithm.