If the long term rate of inflation is 2-3% (and the Fed has taken extraordinary measures in recent times to try and induce that), and you're locked in at 4.0%, you're borrowing money at an effective rate of 1-2%.

While there is currently a migration towards the Sun Belt, which is great for real estate there for the time being, they were mentioning that the future migration flow will be climate-induced and the best place in the US will be the Great Lakes Area and the city of Chicago as its main center is already preparing for that.

other inducements?  

That s/he grossly mislead you or lied to you about a fact or facts to induce you into closing.As others have also stated, ARV is a subjective opinion and as such it may be impossible to prove a fraudulent behavior. 

The main reason being that factors that contributed to an increase in mortgage rates in the first place, such as wage-induced inflation and employment patterns, remain largely unchanged.

I replaced a bad contactor in one of the condenser units in my house, and bad inducer fans in both furnaces.

Im not sure if I have anything to induce them to come with. 

FHA Financing;Single Family Residence or The rental units are an owner-occupied two (2), three (3) or four (4) unit property Maximum Basic Standard FinancingSingle - $271,050Duplex - $347,000Triplex - $419,425Fourplex - $521,250FHA Basic High Cost area limits are:Single - $625,500Duplex - $800,775Triplex - $967,950Fourplex - $1,202,925Financing for Hawaii, Alaska, Guam, Virgin Islands -Single - $938,250 Duplex - $1,201,150Triplex - $1,451,925Fourplex - $1,804,375Here is the site to search by county for the maximum financing. https://entp.hud.gov/idapp/html/hicostlook.cfmMaximum Financed Properties The maximum of four financed properties includes the subject property.Inducements to Purchase Certain expenses, paid by the seller and/or another interested third party, on behalf of the borrower, are considered “inducements to purchase” and result in a dollar for dollar reduction to the lesser of the sales price or appraised value of the property before applying the appropriate LTV factor.

While it has had LOTS of ulcer inducing moments, financially it has been so amazing.

Part of sellers claims are FRAUD BY INDUCEMENT, victimizing the elderly, violation of 475.43, etc.