Mortgage payments are built from three moving parts: the loan amount, the interest rate, and the term. A lower rate lowers the payment, but a higher price raises the loan amount and everything tied to it, including property taxes, insurance, and sometimes mortgage insurance. Buyers often compare two houses on principal and interest alone and conclude the pricier one is the better deal. That comparison leaves out the costs that arrive every month regardless of the rate. Run the full housing payment for both options before you let the lower rate make the decision.
Price differences also show up at the closing table. A larger loan usually means a bigger down payment if you want to avoid extra mortgage insurance, and closing costs tend to scale with price as well. Once that money is spent, you may have less left for repairs, moving expenses, or an emergency fund, and a thin cushion turns a manageable house into a stressful one. Rates can also be bought down temporarily or permanently, and a lender can show you whether paying points would change the math. Ask your loan officer to model the payment, remaining reserves, and the break-even point side by side.
Refinancing is the reason many buyers stretch, and it is also the reason to be careful. A future refinance depends on rates being lower at that time, your credit and equity being solid, and the closing costs of the new loan being worth paying again. Waiting for rates to fall can take longer than expected, and the house you buy today will cost what it costs in the meantime. If you expect to stay in the home for many years, a higher price paired with a better rate may pencil out well. If you might move sooner, a lower price with a smaller loan usually gives you more room to maneuver.
The right answer depends on the full monthly cost, the cash you will have after closing, and how long you plan to live in the home. A lower rate can make a bigger house work, but only if the rest of your budget holds up.