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: 20

Answer

$r \approx 14.1\%$

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 and the given values in the problem to obtain: $A= P(1+rt) \\\$1820 = \$1700(1+r \cdot \frac{6}{12}) \\\$1820 = \$1700(1+r \cdot \frac{1}{2}) \\\$1820 = \$1700(1+ \frac{r}{2}) $ Divide $\$1700$ to both sides of the equation to obtain: $\dfrac{\$1820}{\$1700} = 1 + \frac{r}{2} \\1.070588235 = 1+\frac{r}{2}$ Subtract 1 to both sides of the equation to obtain: $1.070588235 - 1 = \frac{r}{2} \\0.070588235 = \frac{r}{2}$ Multiply 2 on both sides of the equation to obtain: $0.1411764706 = r$ Convert to percent by multiplying by 100 to obtain: $r = 0.1411764706(100)\% \\r = 14.11764706\% \\r \approx 14.1\%$
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