Becky Anderson bought a television set with money borrowed from the bank at $5 \%$ interest compounded semiannually. What effective interest rate did she pay?
The effective interest rate is $\square \%$.
(Round to the nearest hundredth as needed.)
\(\boxed{5.06 \%}\) is the effective interest rate that Becky Anderson paid.
Step 1 :Becky Anderson borrowed money from the bank at an interest rate of 5% compounded semiannually.
Step 2 :The nominal interest rate \( r \) in decimal form is 0.05.
Step 3 :The number of compounding periods per year \( n \) is 2.
Step 4 :The number of years \( t \) is 1.
Step 5 :We calculate the effective interest rate using the formula \( (1 + r/n)^{n*t} - 1 \).
Step 6 :The effective interest rate in decimal form is approximately 0.0506.
Step 7 :We convert the effective interest rate to percentage form and round to the nearest hundredth to get 5.06%.
Step 8 :\(\boxed{5.06 \%}\) is the effective interest rate that Becky Anderson paid.