To calculate the effective annual rate (EAR) when interest is compounded semi-annually, you can use the following formula:
\[ \text{EAR} = \left(1 + \frac{r}{n}\right)^n - 1 \]
Where:
- \( r \) = nominal annual interest rate (as a decimal)
- \( n \) = number of compounding periods per year
Given:
- \( r = 8.00% = 0.08 \)
- \( n = 2 \) (since interest is compounded semi-annually)
Now, substitute these values into the formula:
\[ \text{EAR} = \left(1 + \frac{0.08}{2}\right)^2 - 1 \]
\[ = \left(1 + 0.04\right)^2 - 1 \]
\[ = (1.04)^2 - 1 \]
\[ = 1.0816 - 1 \]
\[ = 0.0816 \]
To express this as a percentage, multiply by 100:
\[ \text{EAR} = 0.0816 \times 100 = 8.16% \]
Thus, the effective annual rate when interest is compounded semi-annually is 8.16%.
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