Explanation
The formula to be used is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
In our case
[tex]\begin{gathered} A=13100 \\ P=6500 \\ n=4 \\ t=7 \\ r=? \end{gathered}[/tex]
Thus, we have
[tex]13100=6500(1+\frac{r}{4})^{4\times7}[/tex]
Solving for r
[tex]\begin{gathered} \frac{13100}{6500}=(1+\frac{r}{4})^{28} \\ \\ 2.01538=(1+0.25r)^{28} \end{gathered}[/tex]
solving for r
[tex]\begin{gathered} 2.01538^{\frac{1}{28}}=1+0.25r \\ 1.02534=1+025r \\ \\ 0.25r=1.02534-1 \\ \\ 0.25r=0.02534 \\ \\ r=\frac{0.02534}{0.25} \\ \\ r=0.101379 \end{gathered}[/tex]
Therefore, the rate will be 10.1379%
