An immediate annuity does not have an initial phase (accumulation phase) of "gradual, regular paymens by the annuity holder" - instead an immediate annuity uses a lump sum payment from the annuity holder which is then deposited with a life insurer who, using actuarial calculations based on life expectancy and project rates of interest, will convert it into a series of periodic payments, typically for the life of the annuitant. The life insurer assumes the risk that the annuitant could live beyond his life expectancy which would extend the obligation. If the annuitant lives for 10 years beyond his life expectancy, they stand to earn a substantial sum over their original investment and projected return.
Annuities can also be setup to pay out for a specific period of time, for instance a 10 year period.
Once the payments begin, 30 days after the deposit, the annuity becomes irrevocable; meaning that lump sum of money is no longer available to the annuitant except through the periodic payments. The payment amount and schedule is also locked in. The income from the periodic payments consists of both return of principal and interest earned. Only the interest portion is includable as taxable income.