## Annuities

Consider a series of T payments, each of amount 1 at times 1 ,...,T. Such a stream of payments is called annuity immediate (with payments at the end of the period). The present value of this cash flow for i > 0 is

and often it is also called the Present Value Interest Factor of an Annuity abbreviated as PVIFAi-T■ For i = 0 we have = T. Sometimes the interest rate is attached to symbol a: a^ii or o>Y\.i%-

Consider again a series of T payments, cach of amount 1 but now at times 0,... ,T — 1. Such a stream of payments is called annuity due (with payments at the beginning of the period). The present value of this cash flow for i > 0 is

(12) = (1 + i)o>T]> a^ = 1 + O<T^T\ f°r T >2.

For an infinite stream of constant payments of amount 1, the annuity is called perpetuity and if it is immediate or due, its present value is

b t respectively.

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