Annuity Due Vs. Ordinary Annuity. The term "annuity" refers to a series of fixed payments that are either received or paid out by an individual. Annuity payments are typically fixed both in terms of the dollar amount of funds paid and the length of time the funds are paid, although there may be exceptions to this pattern in certain annuity contracts. Both the ordinary annuity and annuity due are common annuity types.