Answer
$4.9\%$
Work Step by Step
Given $$ P= 4000;\ \ A= 4400;\ \ t= 2;\ \ r= ?$$ Set in the given values into the equation and solve for the interest rate, $ r$. $$\begin{aligned}
P(1+r)^t&= A\\
4000(1+r)^2&=4400\\
(1+r)^2&= \frac{4400}{4000}\\
(1+r)^2&=1.1\\
1+r&= \pm\sqrt{1.1}\\
r&=\sqrt{1.1}-1\\
r& = 0.049= 4.9\%
\end{aligned}$$ We took only the positive value since $r$ must be positive for the money to grow.
The required interest rate is about $4.9\%$.
