To begin with, the nail BED doesn't grow - only the nail plate can grow. The nail plate cells are developed in the root/Matrix and it can take anywhere form 3-6 months for it to completely replace itself from root to free edge - this depends entirely on your genetics for nail growth and if it is a fingernail or a toenail and which fingernail it is. The larger and longer the nail, the longer it takes for complete replacement.