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: 11


(a) investment is worthwhile (b) $\$2708.50$

Work Step by Step

We are given: $$ r=0.08,\ \ \ \ t=5,\ \ \ P=7000$$ (a) Then $PV$ after $5$ years is \begin{align*} PV&= 7000\left( e^{-0.08(1)}+ e^{-0.08(2)}+ e^{-0.08(3)}+ e^{-0.08(4)}+ e^{-0.08(5)} \right)\\ & \approx 27708.50 \end{align*} The reduced labor cost is bigger than the cost of the computer system. Hence, the investment is worthwhile. (b) The amount of money the company will actually save is $$ 27708.50- 25000=\$2708.50$$
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