Refinancing replaces your current mortgage with a new one. See your monthly savings and how long it takes to recoup the costs — your break-even point.
Refinancing has closing costs of its own. The key question is how long it takes the monthly savings to cover those costs: break-even months = refinance costs ÷ monthly savings. If you'll keep the loan well past that point, refinancing likely pays off; if you might move sooner, it may not.
A lower rate on a longer term can reduce your monthly payment while increasing total interest, because you're stretching the balance over more years. The "lifetime interest saved" figure above can go negative when that happens — compare both the monthly and the long-run numbers.
Divide the refinance's costs by your monthly savings to get the break-even in months. If you'll keep the loan past that point, it usually pays off.
It can. A new 30-year loan restarts the clock; choosing a shorter term or making extra payments avoids stretching out total interest.