Annuity factor

The ordinary-annuity factor for n periods at rate r is [1 − (1 + r)^−n]/r. Multiplying the factor by the equal payment gives the present value one period before the first payment. Tables contain factors for selected whole-number rates and periods, usually rounded. They save repeated single-period calculations but do not change cash-flow timing. When payments start later, first value the annuity at the appropriate earlier date and then discount that value to time zero. Unequal payments need individual discounting or separate equal-payment groups.