Equate the formula for compound interest with the added interest rate
6% => 0.06
[tex]\begin{gathered} 1+0.06=(1+\frac{r}{n})^2 \\ 1.06=(1+\frac{r}{2})^2 \end{gathered}[/tex]Get the square root of both sides.
[tex]\begin{gathered} \sqrt[]{1.06}=\sqrt[]{(1+\frac{r}{n})^2} \\ \sqrt[]{1.06}=1+\frac{r}{2} \\ \sqrt[]{1.06}-1=\frac{r}{2} \\ r=2(\sqrt[]{1.06}-1) \\ r=0.0591260282 \end{gathered}[/tex]Converting the result to percentage, and rounding it off to the nearest tenth of a percent. The rate is 5.9%.
