What factors (appraisal value, home equity/LTV) affect the rate I'm offered when refinancing?

Yes. On a conventional loan, the equity your appraisal establishes feeds directly into your rate. On government loans, it mostly does not. Conventional loans (Fannie Mae and Freddie Mac, plus most jumbo and portfolio money) price through loan-level price adjustments, a grid that tiers your rate by loan-to-value and credit score together. The direction is what to remember: more equity means better pricing, with the strongest tiers at the lowest loan-to-values. The exact breakpoints shift as the agencies revise the grids, so treat the tiers as a framework and confirm live pricing when you apply. Government loans work differently. Loan-level price adjustments are a Fannie and Freddie construct. FHA, VA, and USDA do not use equity-tiered or credit-tiered pricing adjustments; they price through their own mortgage insurance, funding fee, and guarantee fee structures. Apart from cash-out limits, a lighter appraisal does not ding your rate on those programs the way it can on a conventional loan. The appraisal sets the value that drives all of this, which is why a reputable lender estimates your value conservatively up front rather than assuming the home comes in well above a recent purchase price. You get quoted a rate that holds up, instead of an artificially good one that falls apart when the appraisal lands.