Why does Miss Havisham invite Pip to Satis House?

The correct answer why Miss Havisham wants Pip to visit her at 'Satis House' is found in Ch.7.

Mrs.Joe Gargery, Pip's sister tells her husband Joe,

When Joe asks her how Miss Havisham came to know of Pip, she replies that Pumblechook who was a tenant of Miss Havisham recommended Pip's name to Miss Havisham when she asked him if he knew of some boy who could amuse her by coming to Satis House and play there:

Isn't it just barely possible that Uncle Pumblechook may be a tenant of hers, and that he may sometimes -- we won't say quarterly or half-yearly, for that would be requiring too much of you -- but sometimes -- go there to pay his rent? And couldn't she then ask Uncle Pumblechook if he knew of a boy to go and play there? And couldn't Uncle Pumblechook, being always considerate and thoughtful for us -- though you may not think it, Joseph,' in a tone of the deepest reproach, as if he were the most callous of nephews, that I have for ever been a willing slave to?'