Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 4 - Exponential Functions - 4.4 Applications to Compound Interest - Exercises and Problems for Section 4.4 - Exercises and Problems - Page 167: 12

Answer

(a) $100 \%$ (b) $144.141 \%$ (c) $171.457 \%$

Work Step by Step

(a) The effective annual rate for an account paying $100 \%$ compounded annually is $100 \%$ (b) The interest rate per quarter is $100 / 4$. Therefore, the effective interest rate is $$i= \left(1+\frac{100}{4}\right)^{4}-1= 144.141\%$$ (c) The interest rate per day is $100/ 365$. Therefore, the effective interest rate is $$i= \left(1+\frac{100}{365}\right)^{365}-1= 171.457 \%$$
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