Problem

Find the effective interest rate. Round to two decimal places when needed.
Rate: $10 \%$ Compounded: Semiannually
The effective rate is $\%$

Answer

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Answer

\( \boxed{The effective interest rate is 10.25\%} \)

Steps

Step 1 :Calculate the effective interest rate using the formula: \( (1 + \frac{Nominal Rate}{Number of Compounding Periods})^{Number of Compounding Periods} - 1 \)

Step 2 :Plug in the values: \( (1 + \frac{0.10}{2})^{2} - 1 \)

Step 3 :Simplify the expression: \( (1 + 0.05)^{2} - 1 \)

Step 4 :Evaluate the expression: \( 1.1025 - 1 \)

Step 5 :Find the effective interest rate: \( 0.1025 \)

Step 6 :Convert to percentage and round to two decimal places: \( 10.25\% \)

Step 7 :\( \boxed{The effective interest rate is 10.25\%} \)

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