## Thinking Mathematically (6th Edition)

$r \approx 14.1\%$
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\%\$