Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.5 Compound Interest and Present Value - Exercises - Page 355: 18



Work Step by Step

Since we have for $ R(t) =R$ $$ P V = \frac{R}{r}\left(1-e^{-r T}\right) $$ Then for large $T$ \begin{align*} PV&=\lim_{T\to \infty }\frac{R}{r}\left(1-e^{-r T}\right)\\ &=\frac{R}{r} \end{align*}
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