Given:
- r = 0.10 (10% annual rate),
- n = 12 (monthly compounding).
To calculate the effective interest rate over a 6-month period:
EIR = \left(1 + \frac{0.10}{12}\right)^{12} - 1
This simplifies to:
EIR = \left(1 + \frac{0.10}{12}\right)^{12} - 1
EIR = (1.00833)^{12} - 1
EIR = 1.0512 - 1
EIR = 0.0512
So, the effective interest rate over the 6-month period is approximately 5.12%.
\boxed{EIR \approx 5.12\%}