## The Annuity Formula

An Annuity pays the The second type of cash flow stream that lends itself to a quick formula is an annuity, which is same amount for T years.

a stream of cash flows for a given number of periods. Unlike a perpetuity, payments stop after T periods. For example, if the interest rate is 10% per period, what is the value of an annuity that pays $5 per period for 3 periods?

Let us first do this the slow way. You can hand-compute the net present value to be

What is the shortcut to compute the net present value of an annuity? It is the annuity formula, which is

Is this really a short-cut? Maybe not for 3 periods, but try a 360-period annuity, and let me know which method you prefer. Either works.

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