Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.2 - The Natural Exponential Function - 4.2 Exercises - Page 343: 36

Answer

(a) When $rate=2\%$ $A\approx\$10169.99$ (b) When $rate=3\%$ $A\approx\$11466.63$ (c) When $rate=4.5\%$ $A\approx\$13728.05$ (d) When $rate=7\%$ $A\approx\$18530.93$

Work Step by Step

*A quick review* For Continuously Compound Interest we have the following formula (Also explained in previous chapters): $A = Pe^{rt}$ $t$ - number of years $r$ - interest rate per year (In decimal form) $P$ - principal $A$ - amount of money after $t$ years --- In this case we know $P=8000$, $t=12$; so we will use: $A(r)=8000e^{12r}$ (a) When $r=2\%=0.02$ $A(r)=8000e^{12\times0.02}=8000e^{0.24}\approx\$10169.99$ (b) When $r=3\%=0.03$ $A(r)=8000e^{12\times0.03}=8000e^{0.36}\approx\$11466.63$ (c) When $r=4.5\%=0.045$ $A(r)=8000e^{12\times0.045}=8000e^{0.54}\approx\$13728.05$ (d) When $r=7\%=0.07$ $A(r)=8000e^{12\times0.07}=8000e^{0.84}\approx\$18530.93$
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