A researcher wants to estimate the mean household income in a city of 50,000 households within ±$500 margin of error at 95% confidence. Prior studies suggest σ ≈ $6,000. What is the minimum sample size accounting for finite population correction?

$n_0 = \left(\frac{z^* \sigma}{ME}\right)^2; \quad n = \frac{n_0}{1 + n_0/N}$

(Use z* = 1.96)