What type of mortgage would Greg and Joyce likely receive with a $5,000 closing incentive from their builder?

The correct answer is a buydown mortgage. This type of mortgage involves reducing the interest rate on a loan temporarily by paying an upfront fee, often funded through incentives like a closing cost concession from the builder. In this scenario, the $5,000 closing incentive can be effectively used to lower the initial interest rate on Greg and Joyce's mortgage, making their monthly payments more affordable and easing the financial burden right after purchase.

In a buydown, the builder might contribute the $5,000 as a method to attract buyers by making financing more appealing. This is particularly useful for buyers who want reduced payments in the early years of the mortgage, aligning well with their financial planning.

While reverse annuity mortgages, shared equity mortgages, and sale and leaseback arrangements are alternative financing options, they do not fit the context of this scenario where the primary goal is to lower the mortgage interest rate and monthly payment using a closing incentive from the builder. Those options serve different purposes in mortgage lending and real estate transactions.