ANSWER:
4th option: 9.33 percent
STEP-BY-STEP EXPLANATION:
We have that the compound interest formula is the following:
[tex]I=A\left(1+\frac{r}{100}\right)^t[/tex]Where I is the interest payment, A is the initial invested value, r is the rate and t is the time in this case in years.
Therefore, we substitute and calculate the annual rate, like this:
[tex]\begin{gathered} 20000=14000\left(1+\frac{r}{100}\right)^4 \\ \\ 14000\left(1+\frac{r}{100}\right)^4=20000 \\ \\ \left(1+\frac{r}{100}\right)^4=\frac{20000}{14000} \\ \\ \left(1+\frac{r}{100}\right)^4=\frac{10}{7} \\ \\ 1+\frac{r}{100}=\sqrt[4]{\frac{10}{7}} \\ \\ \frac{r}{100}=\sqrt[4]{\frac{10}{7}}-1 \\ \\ r=100\sqrt[4]{\frac{10}{7}}-100 \\ \\ r=9.326\cong9.33\% \end{gathered}[/tex]So the correct answer is 4th option: 9.33 percent
