College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.7 - Financial Models - 6.7 Assess Your Understanding - Page 475: 30


Better deal: $ 7.9\%$ compounded daily.

Work Step by Step

Apply the Effective Rate of Interest Theorem: The effective rate of interest $r_{e}$ of an investment earning an annual interest rate $r$ is given by Compounding $n$ times per year: $\displaystyle \quad r_{e}=\left(1+\frac{r}{n}\right)^{n}-1$ Continuous compounding: $\quad \quad r_{e}=e^{r}-1$ --- We compare the effective rates. The larger $r_{e}$ represents the better deal. $ 8\%$ compounded semiannually $r_{e}=\displaystyle \left(1+\frac{0.08}{2}\right)^{2}-1=0.0816$ $ 7.9\%$ compounded daily: $r_{e}=\displaystyle \left(1+\frac{0.079}{365}\right)^{365}-1\approx 0.082195071$ Better deal: $ 7.9\%$ compounded daily.
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