If $r_{eff}$ = effective rate of interest, $r$ = nominal rate of interest and $m$ = number of conversion periods per year, the relationship between nominal rate and effective rate of interest is:

$r_{eff}=(1+\frac{r}{m})^m – 1$

The correct answer is Option (2) → $r_{eff}=(1+\frac{r}{m})^m – 1$

Let $r$ be the nominal annual rate convertible $m$ times per year.

Rate per conversion period $=\frac{r}{m}$.

Effective annual rate:

$r_{\text{eff}}=\left(1+\frac{r}{m}\right)^{m}-1$

Final Answer: $r_{\text{eff}}=\left(1+\frac{r}{m}\right)^{m}-1$