Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 8 - Personal Finance - 8.3 Simple Interest - Exercise Set 8.3 - Page 512: 19


$r \approx 31.3\%$

Work Step by Step

RECALL: The formula for the future value $A$ is: $A=P(1+rt)$ where P= principal amount borrowed r = interest rate per year t = time in years Use the formula above, with $A=\$2840$, $P=\$2300$, and $t=\frac{9}{12}$, to obtain: $\$2840 = \$2300(1+r \cdot \frac{9}{12}) \\\$2840 = \$2300(1+r \cdot 0.75) \\\$2840=\$2300(1+0.75r)$ Divide $\$2300$ on both sides of the equation to obtain: $\frac{2840}{2300} = 1+0.75r$ Subtract $1$ on both sides of the equation to obtain: $\frac{2840}{2300}-1 = 0.75r \\0.2347826087=0.75r \\\frac{0.2347826087}{0.75}=r \\0.3130434783=r$ Convert to percent to obtain: $31.30434783\% = r \\r \approx 31.3\%$
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