By definition, a nominal interest rate $r$ is given as $q,$

$r=($ interest rate per time period ${)}^{\text{n}\text{u}\text{m}\text{b}\text{e}\text{r}of\text{p}\text{e}\text{r}\text{i}\text{o}\text{d}\text{s}}$

$r=$ interest rate per time period $$ number of periods

$r=\frac{\text{n}\text{u}\text{m}\text{b}\text{e}\text{r}of\text{p}\text{e}\text{r}\text{i}\text{o}\text{d}\text{s}}{\text{i}\text{n}\text{t}\text{e}\text{r}\text{e}\text{s}\text{t}\text{r}\text{a}\text{t}\text{e}\text{p}\text{e}\text{r}\text{t}\text{i}\text{m}\text{e}\text{p}\text{e}\text{r}\text{i}\text{o}\text{d}}$

$r=\frac{\text{i}\text{n}\text{t}\text{e}\text{r}\text{e}\text{s}\text{t}\text{r}\text{a}\text{t}\text{e}\text{p}\text{e}\text{r}\text{t}\text{i}\text{m}\text{e}\text{p}\text{e}\text{r}\text{i}\text{o}\text{d}}{\text{n}\text{u}\text{m}\text{b}\text{e}\text{r}of\text{p}\text{e}\text{r}\text{i}\text{o}\text{d}\text{s}}$