Present Value of an Infinite Life Annuity (Perpetuities)

An annuity that goes on for ever is called a perpetuity. The present value of a perpetuity of Rs C amount is given by the formula:


This is because as the length of time for which the annuity is received increases. the annuity discount factor also increases but if the length goes on extending, this increase in the annuity factor slows down. In fact. as annuity life becomes infinitely long, the annuity discount approaches an upper limit. Such a limit is Iii. In other words, the appropriate factor is found merely dividing 1 by the discount rate. The validity of this method can be seen by looking at the facts in Table A-4 for discount rates of 8, 12, 16 and .20 percent for a period of 10 years. As the number of years approaches 50, the value of these factors approaches, 12.23, 8.31, 6.25 and 5.00 respectively. Substituting 0.08, 0.12~0.16 and 0.20 into our upper discount limit formula of 1/i, we find the factors tor finding the present value of perpetuities at these rates as 12.5, 8.33: 6.25 and 5.00.

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