Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 4 - Exponential and Logarithmic Functions - Section 4.7 Financial Models - 4.7 Assess Your Understanding - Page 346: 33


$24.573 \%$

Work Step by Step

Recall: $A = P \left(1+\dfrac{r}{n} \right)^{n t}$ where $P:$ The principal amount $r:$ Annual interest rate $n:$ Number of compoundings per year $t:$ Number of years $A:$ Amount after $t$ years Here we have: $t= 5$ $\text{Compounded annually } \to n = 1$ Since the investment is to be tripled $ \hspace{20pt} \therefore A = 3P$ $3P = P\left(1+\dfrac{r}{1} \right)^{1 \times 5}$ $3P = P (1+r)^5$ Divide both sides by $P$: $3 = (1+r)^5$ $(1+r) = \sqrt[5]{3}$ $r = \sqrt[5]{3}-1$ $r \approx 0.24573$ $r = \boxed{24.573 \%}$
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