To find the nominal rate of interest per annum compounded monthly that is equivalent to an effective interest rate of 12.60% per annum, we can use the formula for converting the effective interest rate to the nominal interest rate:
\[ \text{Effective Annual Interest Rate (EAR)} = (1 + \frac{r}{n})^n - 1 \]
Where:
- EAR = Effective Annual Interest Rate (given as 12.60%)
- r = Nominal rate of interest per annum
- n = Number of compounding periods per year (12 for monthly compounding)
Substitute the given values into the formula:
\[ 0.126 = (1 + \frac{r}{12})^{12} - 1 \]
Now, solve for r:
\[ 1.126 = (1 + \frac{r}{12})^{12} \]
\[ (1 + \frac{r}{12})^{12} = 1.126 \]
\[ 1 + \frac{r}{12} = \sqrt[12]{1.126} \]
\[ \frac{r}{12} = \sqrt[12]{1.126} - 1 \]
\[ r = 12(\sqrt[12]{1.126} - 1) \]
\[ r \approx 12 \times (1.010483 - 1) \]
\[ r \approx 12 \times 0.010483 \]
\[ r \approx 0.1258 \text{ or } 12.58\% \]
Therefore, the nominal rate of interest per annum compounded monthly equivalent to the effective interest rate of 12.60% per annum is approximately 12.58% per annum.
Find the nominal rate of interest per annum compounded monthly, equivalent to the effective interest rate of 12.60% per annum.
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