#### Answer

$r \approx 31.3\%$

#### 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:
$31.30434783\% = r
\\r \approx 31.3\%$