If the effective rate is 12.68% per annum and the compounding occurs monthly, what is the nominal rate per annum?

Answer 1

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%.