Calculus (3rd Edition)

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

Chapter 8 - Techniques of Integration - 8.7 Improper Integrals - Exercises - Page 442: 79


$\approx \$ 3571.4~$

Work Step by Step

The present value of the income stream after $T$ years can be computed as: $\int_0^T 250e^{-0.07t} dt=[\dfrac{250e^{-0.07t}}{-0.07}]_0^T\\=\dfrac{250}{0.07}(1-e^{-0.07T}) $ Now, the present value of the entire income stream will be: $\int_0^{\infty} 250e^{-0.07t} dt=\lim\limits_{T \to \infty}\int_0^T 250e^{-0.07t} \ dt \\=\dfrac{250}{0.07}(1-0) \\ \approx\$ 3571.4~$
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