"In checking advertisements by mortgage lenders, several showed APRs on fixed-rate mortgages that were lower than the interest rate. Is that possible…?”
On adjustable rate mortgages (ARMs), the APR can be below the initial interest rate if the fully-indexed rate (index plus margin) is below the initial rate. See Annual Percentage Rate Below Interest Rate on ARM.
On fixed-rate mortgages (FRMs), the APR and the interest rate will be the same if the lender charges no fees of any kind. Third party fees, such as title insurance or appraisal cost, are not included in the APR. If the lender charges fees, the APR will be above the rate. This is the most common case.
On high-rate loans, lenders pay rebates (negative points), which can be used to pay lenders fees and third party fees. If a rebate just covers the lender fees, the APR will be the same as the interest rate. Lenders sometimes do this because, when the APR and the interest rate are the same, borrowers are much less likely to ask them to explain what the APR is.
If the lender’s rebate is large enough to cover third party fees as well as all the lender fees, the APR should be below the interest rate. Evidently some lenders do calculate it in this way. But all the lenders I know interpret the rules to mean that, since third party charges are not included in the APR, paying them out of the lender's rebate does not affect the APR. Under this interpretation, the APR on an FRM can't be below the interest rate.
A consequence of this interpretation is that the APR overstates the true cost of any loan on which the lender's rebate exceeds the lender's fees. This means that the APR on a “no-cost” mortgage where the lender pays all the settlement costs is misleadingly high.