According to the MoneyChimp calculator, the answer is $173,479.22. How important is it to understand what you are doing? Calculate this one for yourself, and you should get $187,357.56. Which one is right? You are, of course! What's going on is that MoneyChimp assumes (but does tell you) that the annuity is in the form of an annuity due, not an ordinary annuity. Recall that, with an annuity due, the payments occur at the beginning of the period rather than the end of the period. The moral of this story is clear: caveat calculator.

Ross et al.: Fundamentals III. Valuation of Future 6. Discounted Cash Flow © The McGraw-Hill of Corporate Finance, Sixth Cash Flows Valuation Companies, 2002

Edition, Alternate Edition

176 PART THREE Valuation of Future Cash Flows

I. Symbols:

PV = Present value, what future cash flows are worth today FVt = Future value, what cash flows are worth in the future r = Interest rate, rate of return, or discount rate per period—typically, but not always, one year t = Number of periods—typically, but not always, the number of years C = Cash amount

II. Future value of C per period for t periods at r percent per period:

A series of identical cash flows is called an annuity, and the term [(1 + r)' - 1]/r is called the annuity future value factor.

III. Present value of C per period for t periods at r percent per period:

The term {1 - [1/(1 + r)t]}/r is called the annuity present value factor.

IV. Present value of a perpetuity of C per period:

A perpetuity has the same cash flow every year forever.

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