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: 10


investment is worthwhile.

Work Step by Step

We have a $5$ year investment at $6\%$ of $\$500,000$. Thus, we have: $$ r=0.06,\ \ \ \ t=5,\ \ \ P=500000$$ Then $PV$ after $5$ years is: \begin{align*} PV&= 500000\left( e^{-0.06(1)}+ e^{-0.06(2)}+ e^{-0.06(3)}+ e^{-0.06(4)}+ e^{-0.06(5)} \right)\\ & \approx 2,095,700.63 \end{align*} We see that $PV$ is larger than the initial investment of $2$ million, so the investment is worthwhile.
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