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SREEDEVI SUNILKUMAR has given a very brief and to the point answer.
annuity has a limit because it is for a specific period but perpetuity is not limited in time
Annuities are payments (or cash flows) of equal amount every period for a limited number of periods. Examples of annuities are loan payments for your car and periodic payments from a lottery win. Perpetuities on the other hand are payments (or cash flows) also of equal amounts that are made every period for an unlimited number of periods. Examples of perpetuities are property tax payments and preferred stocks.
The "Term Annuity" and "Perpetuity" may be treated as 'Synonym' except for the difference in No. of Annual/ instalment prepayments. In "perpetuity" the annual payment instalments tends to INFINITY... that is the main difference. All other characteristics are more or less same. One more difference is that in case of "perpetuity" sometimes there may be exemption for payment of 'consideration' to get perpetuity awards on behalf of the beneficiary AS A BENEFIT ON ACCOUNT OF LOYALTY CONSIDERATION.
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