FLORIDA | with informations from Brian Bandell | City National Bank of Florida reported improved earnings in the second quarter of the year as it announced plans for four new branches. The Miami-based bank earned $10.3 million in the second quarter, up from $9.4 million in the first quarter. Its net interest income grew to $30.6 million in the second quarter from $30.2 million. Still, figures are 8.8 percent lower than last year in the same…