If they can not they need to make arrangements to get a friend to take the pet.

If so, there was no guarantee the title co. could get the Lender to execute the partial release, the seller would have had to arrange/negotiate that.

My question is how do I calculate interest in this arrangement.

I just arranged my bank to set up a direct deposit system with one of my tenants.

If this were an arrangement between you and the potential tenant, I would say since he doesn't have a copy of the agreement with your signature, then it's not considered executed.

My new landlord does not offer this incentive, but the lease automatically converts to a month-to-month arrangement at a much higher monthly rent when the lease is up ("negative incentive") if I don't renew the lease.

Personally I would recommend avoiding this arrangement all together.

What can I offer in return to make this a lucrative arrangement for the agent?

I was also contacted by a person here under the profile here on BP of Richard Apriot recommending a private lender and that he has an arrangement with the lender to get a point on this transaction.   

I got lost about half way through. paragraph ˈperəˌɡraf/nounnoun: paragraph; plural noun: paragraphs1. a distinct section of a piece of writing, usually dealing with a single theme and indicated by a new line, indentation, or numbering.synonyms:section, subdivision, part, subsection, division, portion, segment, passageMore"the concluding paragraph" report, article, item, sidebar, piece, write-up, mention"a paragraph in the newspaper" verbverb: paragraph; 3rd person present: paragraphs; past tense: paragraphed; past participle: paragraphed; gerund or present participle: paragraphing1. arrange (a piece of writing) in paragraphs.