A project yields an annual benefit of ($ 25) a year, starting next year and continuing forever.

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A project yields an annual benefit of \(\$ 25\) a year, starting next year and continuing forever. What is the present value of the benefits if the interest rate is 10 percent? [Hint: The infinite sum \(x+x^{2}+x^{3}+\cdots\) is equal to \(x /(1-x)\), where \(x\) is a number less than 1.] Generalize your answer to show that if the perpetual annual benefit is \(B\) and the interest rate is \(r\), then the present value is \(B / r\).

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Public Finance

ISBN: 9780073511283

8th Edition

Authors: Harvey Rosen, Ted Gayer

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