Substitute $\displaystyle{A}={2},{080.8}\usepackage{cmbright}\Huge\$ , $\displaystyle{P}={2},{000}\usepackage{cmbright}\Huge\$ , and $\displaystyle{t}={1}\usepackage{cmbright}\Huge\$ into the formula: $\displaystyle{2},{080.8}={2},{000}{{\left({1}+\frac{{r}}{{2}}\right)}}^{{{2}\cdot{1}}}\usepackage{cmbright}\Huge\$

Divide both sides by 2,000: $\displaystyle{1.0404}={{\left({1}+\frac{{r}}{{2}}\right)}}^{{2}}\usepackage{cmbright}\Huge\$

Use the Square Root Property: $\displaystyle\pm{1.02}={1}+\frac{{r}}{{2}}\usepackage{cmbright}\Huge\$

Subtract 1 from both sides: $\displaystyle{1.02}-{1}=\frac{{r}}{{2}}\usepackage{cmbright}\Huge\$ or $\displaystyle-{1.02}-{1}=\frac{{r}}{{2}}\usepackage{cmbright}\Huge\$

Simplify and multiply both sides by 2: $\displaystyle{r}={0.04}\usepackage{cmbright}\Huge\$ or $\displaystyle{r}=-{4.04}\usepackage{cmbright}\Huge\$

The negative rate does not make sense, so $\displaystyle{r}={0.04}\usepackage{cmbright}\Huge\$ is the answer.