In the formula you provided, \( EPR = \left(1 + \frac{r}{n}\right)^n - 1 \), the variable \( n \) represents the number of compounding periods per year. For example:
- If interest is compounded annually, \( n = 1 \).
- If compounded semi-annually, \( n = 2 \).
- If compounded quarterly, \( n = 4 \).
- If compounded monthly, \( n = 12 \).
- If compounded daily, \( n = 365 \).
However, when interest is compounded continuously, \( n \) approaches infinity, and we can use a different formula to find the effective annual rate (EAR):
\[ EPR = e^r - 1 \]
where \( e \) is the base of the natural logarithm (approximately equal to 2.71828), and \( r \) is the nominal interest rate (as a decimal).
In your case, with an interest rate of 9.00% (or 0.09 as a decimal), we can calculate the effective annual rate (EAR) using the continuous compounding formula:
\[ EPR = e^{0.09} - 1 \]
Let's do the calculation:
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Calculate \( e^{0.09} \): \[ e^{0.09} \approx 1.09417 \]
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Now subtract 1: \[ EPR \approx 1.09417 - 1 \approx 0.09417 \]
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Convert to percentage: \[ EPR \approx 0.09417 \times 100 \approx 9.42% \]
So, the effective annual rate (EAR) when the interest is compounded continuously at a rate of 9.00% is approximately 9.42%.