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Investopedia explains 'Ad Infinitum'
Payments received ad infinitum do indeed go on a very long time. But it's important to realize that, because of the time value of money, the present value (i.e, the value today) of those payments very far off in the future (say, 50 years from now) is negligible. Thus the present value of an ordinary annuity (i.e., one with a fixed end) of 50 years is not very much less than that of a perpetuity whose payments go on ad infinitum.
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