There are no bargains to be found when renting in 10 of America's most expensive counties. Renting a three-bedroom apartment in one of them could set you back anywhere from $8,000 to $4,800 a month.

Rental rates in these counties are the highest in the nation, according to an ATTOM report. And families would need to score high on the rental affordability index to qualify for them. The rental affordability index, as defined by the National Association of Realtors, uses a score of 100 to determine whether a family has enough income to qualify for a median home mortgage. Higher scores mean it is easier for families to qualify.

The most expensive is in Collier County, FL where a three-bedroom apartment leases for $8,000 a month, and the rental affordability index is 153%. In Collier County, the median home price is $770,000 and it is cheaper to buy than to rent, even though home prices are rising faster.