How much lower does your rate need to be to refinance?

By Rustin, maker of Gross Profit Calculator · Published July 24, 2026 · Last updated July 24, 2026

Between 0.77 and 1.85 percentage points, depending almost entirely on your loan balance — not the flat "1% rule" you'll read everywhere else. Small loans need a bigger drop than 1 point; large loans need a smaller one. That number comes from a closed-form solution derived by economists Sumit Agarwal, John Driscoll, and David Laibson and published as NBER Working Paper 13487, later in the Journal of Money, Credit and Banking. This page explains that formula in plain English, gives you the computed threshold for every common balance, and is honest about the three things it does not tell you.

What is the Agarwal–Driscoll–Laibson refinance threshold?

It is the exact amount your mortgage rate must exceed today's market rate before refinancing becomes optimal, accounting for closing costs and the option value of waiting for a better rate.

Nearly every piece of refinance advice on the internet hands you a rule of thumb — one percentage point, or half a point, or three-quarters. Those numbers were never derived from anything. They are conventions that got repeated until they sounded like facts.

The real question has an actual answer, and it has had one since 2007. Agarwal, Driscoll and Laibson framed refinancing the way it deserves to be framed: not as a comparison between two payments, but as an option. You hold the right to refinance once, cheaply, at a moment of your choosing. Using it today means you can't use it next month if rates fall further. So the correct threshold is not "when do I save money" — you save money the instant rates dip below yours. It is "when is the money on the table big enough that I should stop waiting for more."

Their contribution was to solve that problem in closed form. In their own words:

"We derive the first closed-form optimal refinancing rule: Refinance when the current mortgage interest rate falls below the original rate by at least 1/ψ [φ + W(−exp(−φ))]." Agarwal, Driscoll & Laibson, Optimal Mortgage Refinancing: A Closed Form Solution, NBER Working Paper 13487, October 2007

That "W" is the Lambert W function — the inverse of f(w) = w·e^w. It shows up whenever a variable appears both inside and outside an exponential, which is exactly what happens when you try to solve for the moment an option is worth exercising. Before this paper, getting the answer required numerical simulation. After it, it's arithmetic.

Why is the 1% rule wrong?

Because the threshold scales with your loan size. A flat rule refinances small balances far too early and leaves large balances waiting far too long.

Closing costs are mostly fixed. Appraisal, title, origination, recording — those run roughly $2,000 plus a percentage of the balance. But the savings from a rate drop scale directly with the balance. Drop 1 point on $100,000 and you save about $1,000 a year against roughly $2,750 of costs. Drop 1 point on $800,000 and you save about $8,000 a year against roughly $8,000 of costs. Same rate drop. Completely different decisions.

A single threshold cannot be right for both. Here is what the popular rules actually recommend, side by side with what the math says:

Notice the pattern. The sites that debunk the rules are right to debunk them, and then they stop. The reader is told the rule is wrong and handed a division problem. The replacement has existed in the literature for nineteen years.

What is the actual formula?

Refinance when your rate exceeds the market rate by x*, where x* = (1/ψ)·[φ + W(−e^−φ)] and W is the Lambert W function.

That τ = 0 deserves a note, because it's where a 2007 paper meets 2026 reality. Agarwal, Driscoll and Laibson calibrated with a 28% marginal rate, assuming the household itemizes and deducts mortgage interest. After the 2017 standard-deduction change, the large majority of US filers take the standard deduction and deduct no mortgage interest at all. Setting τ = 0 is the right call for most people today, and it lowers the threshold — an itemizer at 24% needs a noticeably bigger drop, because the government is already paying part of their interest. Numbers for both cases are below.

What is the threshold for my loan balance?

For a 7-year expected stay it runs from 1.70 points at a $100,000 balance down to 0.93 points at $1,000,000. Longer expected stays lower it further.

This is the table the rest of the internet doesn't have. Every cell is the formula above, solved exactly with the Lambert W function — not interpolated, not rounded off a rule of thumb. Closing costs are estimated as $2,000 + 0.75% of the balance, which tracks Freddie Mac's roughly $5,000 average on a typical loan while staying sensible at both extremes.

Read the top-left and bottom-right corners against each other. A homeowner with $100,000 left who might move in five years needs a 1.85-point drop. A homeowner with a million-dollar balance who is never leaving needs 0.77. Those are the same decision under the 1% rule. They are not remotely the same decision.

The one variable people underestimate is the third column group: how long you'll stay. Going from a 5-year to a 30-year expected stay knocks roughly a quarter of a point off the threshold at every balance, because a longer horizon means more months to collect the savings and less chance you exit the loan before the option pays off.

How much do closing costs move the threshold?

Enormously. On a $300,000 balance, cutting costs from $6,000 to $3,000 drops the required rate gap from 1.41 points to 0.96 — a 45-basis-point swing.

This is the single most actionable line in the whole model, and it has nothing to do with rates: shopping your closing costs down is mathematically equivalent to waiting for a better rate. Knocking $1,250 off your costs on that $300,000 loan moves your threshold by 20 basis points — the same as the market moving 20 basis points in your favor, except you control it.

It also explains why "no closing cost" refinances are less of a free lunch than they sound. The lender folds the cost into a higher rate, which raises the rate you're refinancing to, which eats the gap you were trying to capture. The threshold falls, but so does your actual saving.

Does the mortgage interest deduction change the answer?

Yes — an itemizing household needs a bigger rate drop, because deducting the interest means the government is already absorbing part of the cost of the old rate.

Is there a version I can do on a calculator?

Yes. The square-root approximation is x* ≈ √( σ·√(2(ρ+λ))·κ / [M(1−τ)] ), and it lands about 10 to 25 basis points below the exact answer.

The paper offers a back-of-envelope version for people who don't have a Lambert W function handy. It's useful, and it's biased in a specific direction you should know about — it consistently understates the threshold, meaning it will tell you to refinance slightly earlier than is optimal:

The error shrinks as the balance grows, because the approximation is a leading-order expansion that gets better as the cost-to-balance ratio gets smaller. If you're using it, add roughly 15 basis points and you'll be close. Or just use the calculator, which solves it exactly.

Why does the option value of waiting matter so much?

Because refinancing is a one-shot move. Spending your option on a small dip forfeits the larger dip that might arrive next quarter.

This is the part every rule of thumb misses, and it's the reason the thresholds above are as high as they are. If refinancing were free and repeatable, you'd do it the instant rates ticked below yours. It isn't. You pay thousands of dollars and you reset the clock, so you get to do it meaningfully once in a given rate cycle.

That makes rate volatility — the σ in the formula — a real input to your decision. In a market that moves a lot, waiting is worth more, and the threshold rises. In a dead-calm market, waiting is worth little, and the threshold falls toward simple break-even. The 2026 market has been anything but calm: the 30-year fixed ranged from about 5.98% to 6.95% in the last eighteen months, touching its low in February. Anyone who refinanced on the first small dip of that run gave up the better one.

What does this threshold NOT tell you?

Three things: whether you'll qualify, whether you're resetting your term, and what the rate you're quoted will actually be.

Being honest about a model's limits is more useful than overselling it, so:

1. It assumes you can refinance. The formula has no term for credit score, debt-to-income, appraisal risk, or being underwater. A threshold you can't act on is trivia.
2. It says nothing about term reset. The model compares interest costs, not payment schedules. Refinancing a loan with 22 years left into a fresh 30-year loan lowers your payment while potentially raising your lifetime interest — the threshold can say REFI while the honest same-payoff-date comparison says otherwise. Our calculator runs both and reports the matched-term number, which is why its "interest saved" figure is often smaller than what other tools show.
3. It uses a market average, not your quote. The threshold tells you how big a gap you need. What you actually get depends on your credit tier, loan-to-value, loan type, and which lender you walk into. A national survey rate is a benchmark. Get quotes.

There's also a fourth, softer one: the model is about money. It doesn't know that you want the payment lower because a kid starts college in September, or that you'd sleep better trading an ARM for a fixed rate at a threshold the math doesn't justify. Those are legitimate reasons. The math is an input to your decision, not a replacement for it.

What happens to people who ignore this?

About 20% of households who should refinance never do, forgoing a median of roughly $11,500 each — a failure of attention, not arithmetic.

The companion finding to the ADL formula comes from Benjamin Keys, Devin Pope and Jaren Pope (NBER Working Paper 20401, later in the Journal of Financial Economics). Examining a large sample of US mortgages, they found roughly 20% of households for whom refinancing was clearly optimal simply failed to do it. Median forgone savings: about $160 per month, or roughly $11,500 in present value per household — about $5.4 billion across their sample.

A 2024 University of Chicago Booth working paper models the mechanism directly as inattention. People aren't running the numbers and deciding wrong. They aren't running the numbers at all.

Which is a strange thing to lose money over, because the window opens and closes fast. When the 30-year dipped in early 2026, ICE counted nearly 5 million homeowners moving "in the money" on a move of a few tenths of a point. Most of them did nothing, and the window shut.

How we compute it

Every number on this page comes from the closed-form solution above, solved exactly. The Lambert W function is evaluated with Halley's method to a tolerance of 1×10⁻¹⁴ — no lookup tables, no approximation. Market rates come from the Freddie Mac Primary Mortgage Market Survey and the Optimal Blue Mortgage Market Indices, both via FRED®.

Assumptions used throughout this page: ρ = 0.05, σ = 0.0109, τ = 0 unless stated, λ = 1/(expected years in home) + 0.047, and closing costs estimated as $2,000 + 0.75% of balance. Agarwal, Driscoll and Laibson's own 2007 calibration used τ = 0.28 and costs of one point plus $2,000, which produces higher thresholds than the tables above — the difference is almost entirely the mortgage-interest deduction, which most households no longer take.

The tables here refresh as market conditions change. The calculator runs the same math against your actual balance, costs, credit tier, equity, and expected stay, and returns one word.