If the effective rate is 12.68% per annum and the compounding occurs monthly, what is the nominal rate per annum?
To find the nominal rate per annum when the compounding occurs monthly, we can use the formula:
\( \text{Effective rate} = (1 + \frac{r}{n})^n - 1 \)
Where:
- Effective rate = 12.68%
- r = Nominal rate per annum
- n = number of compounding periods per year (monthly compounding, so n = 12)
Plugging in the values, we get:
\[ 0.1268 = (1 + \frac{r}{12})^{12} - 1 \]
Solving for r:
\[ 1.1268 = (1 + \frac{r}{12})^{12} \]
\[ (1 + \frac{r}{12}) = \sqrt[12]{1.1268} \]
\[ \frac{r}{12} = \sqrt[12]{1.1268} - 1 \]
\[ r = 12(\sqrt[12]{1.1268} - 1) \]
\[ r \approx 0.1218 \]
Therefore, the nominal rate per annum is approximately 12.18%.