What are discount points and should I pay for them?

One discount point costs 1% of the loan amount and typically lowers the interest rate by 0.25%. Paying for points makes mathematical sense only if your expected holding period is long enough to exceed the point recovery break-even horizon.

What is the 1% Rule of Thumb in mortgage refinancing?

Traditionally, refinancing was considered viable if the interest rate dropped by at least 1.0% (100 basis points). However, on larger loan balances ($400,000+), an interest rate drop of even 0.50% to 0.75% can yield substantial net savings after closing costs.

Mortgage Refinance Break-Even Calculator

Timeline	Current Loan Cost	Refinanced Cost	Net Savings
Year 1	$30,358	$32,422	-$2,065
Year 2	$60,716	$58,845	+$1,871
Year 3	$91,074	$85,267	+$5,806
Year 4	$121,432	$111,690	+$9,742
Year 5	$151,789	$138,112	+$13,677
Year 6	$182,147	$164,535	+$17,613
Year 7	$212,505	$190,957	+$21,548
Year 8	$242,863	$217,380	+$25,483

Mortgage Actuarial Science & Debt Structuring10 min readToro Quantitative Credit Analytics

The Quantitative Mathematics of Mortgage Refinancing: Break-Even Horizon Analysis, Points Amortization, and Tenor Arbitrage

Mortgage refinancing is an actuarial arbitrage trade: exchanging existing high-interest debt obligations for lower periodic financing costs at the expense of upfront closing transaction friction. Below is an exhaustive quantitative walkthrough of the break-even equation, points capitalization, and tenor compression strategies.

1. The Actuarial Break-Even Equation

The fundamental viability test for any debt refinancing transaction is the Break-Even Horizon (BEH): the exact number of months required for cumulative monthly cash savings to exceed total transaction closing fees (origination fees, title insurance, appraisal, and discount points).

Formula 1: Mortgage Refinancing Break-Even HorizonAmortization Arbitrage

BEH = Total Closing Costs / ( E_current − E_refinance )

BEH = Number of elapsed months required to recoup upfront transaction costs.

E_current = Scheduled monthly payment under existing loan contract.

E_refinance = Scheduled monthly payment under new refinanced contract.

2. Avoiding the "30-Year Reset" Amortization Trap

A widespread mistake made by homeowners is refinancing a loan that has already been serviced for 5 to 7 years back into a brand new 30-year term. While this dramatically lowers immediate monthly payments, it resets the front-loaded reducing-balance interest curve, often increasing total lifetime interest paid.

Tenor Matching Maxim:Always refinance into a tenure equal to or less than your remaining duration (e.g. refinancing 23 remaining years into a 20-year or 15-year fixed loan) to capture both rate reductions and rapid equity accumulation.

Frequently Asked Questions & Quantitative Reference

An ideal break-even period is 24 to 36 months or less. If you plan to stay in the home longer than the break-even timeline, refinancing is mathematically beneficial.

Mortgage Refinance & Break-Even Calculator

Existing Loan Parameters

New Refinanced Loan Terms

Cumulative Cost Progression (First 10 Years)

The Quantitative Mathematics of Mortgage Refinancing: Break-Even Horizon Analysis, Points Amortization, and Tenor Arbitrage

1. The Actuarial Break-Even Equation

2. Avoiding the "30-Year Reset" Amortization Trap

Frequently Asked Questions & Quantitative Reference