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:
$r = 0.1411764706(100)\%
\\r = 14.11764706\%
\\r \approx 14.1\%$
