Real estate · super (composes 3 primitives)
Mortgage refi engine
Type the current balance, rate, and term remaining; the new rate offer; and closing costs. We chain the new monthly payment, points cost-benefit, the 15-yr alternative, the after-tax interest delta, and the breakeven month.
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Inputs
Load a preset
Result
Refi — breakeven at month 28 (2.3 yrs); $239/mo savings · lifetime -$1,783.
Refi now: Sub-3-yr breakeven is the gold-standard. Lock the rate.
- 1
Current monthly payment
$1,963
$285,000 at 6.875% for 26 years remaining
- 2
New payment (30-yr at 5.875%)
$1,724
$291,500 principal (closing rolled in)
- 3
Monthly savings
$239
Recurring
- 4
Breakeven month
Month 28 (2.3 yrs)
$6,500 closing ÷ $239/mo savings
- 5
Net savings if you sell at year 8
$22,919
Positive — refi pays off in your stay window
- 6
Lifetime interest delta
-$1,783
$327,477 current → $329,260 new (full-term assumption)
- 7
15-yr alternative payment
$2,363
$133,751 total interest — saves $195,509 vs 30-yr
- 8
Tax shield delta (Y1)
N/A (std deduction)
Standard deduction makes mortgage-interest deduction moot for most filers post-TCJA.
Assumptions & notes
- Closing costs often include 0-2 discount points (1 pt = 1% of loan = ~0.25% rate reduction). Compute the in-house breakeven on points separately.
- Tax-shield delta uses Y1 interest as a proxy; the actual benefit declines over the loan as principal pays down.
- Standard deduction post-TCJA ($30k MFJ 2026) makes itemizing mortgage interest moot for most filers under $400k income unless they have very high SALT.
Continue the housing path
Keep going from Mortgage refi engine
Real-estate decisions compound: affordability changes refi risk, refi terms change investment returns, and investment math changes how much house is actually safe.
Try another scenario
Jump between the buyer, refi, and investor presets without leaving the super-calculator layer.
Affordability scenarios
Refi scenarios
Investor scenarios
Companion tools on mitchreise.com
Keep ShowMath as the formula layer, then jump to Reise Tools for richer dashboards, comparison panels, and adjacent housing workflows.
Multi-scenario comparison
What if — ±20% on one input
| Scenario | Current mortgage balance | Headline | Δ vs baseline | Magnitude |
|---|---|---|---|---|
| −20% (cautious) | $228,000 | Refi — breakeven at month 36 (3.0 yrs); $183/mo savings · lifetime -$2,895. | $-393 | |
| Baseline | $285,000 | Refi — breakeven at month 28 (2.3 yrs); $239/mo savings · lifetime -$1,783. | 0 | |
| +20% (aggressive) | $342,000 | Refi — breakeven at month 23 (1.9 yrs); $294/mo savings · lifetime -$671. | +$393 |
Try the input with the highest sensitivity (above). The Δ column shows the dollar swing from a 20% move — that's how much room you have for a counter, raise, or hedge.
Goal seek
Solve for an input value
Pick the input you want to vary and the output you care about. We'll find the input value that gets you to the target. Bisection-based; converges in < 50 iterations.
Monte Carlo simulation
Distribution under input uncertainty (500 trials)
We perturb every numeric input with normal-distributed noise (10–25% sigma depending on input type) and run 500 compute trials. The output is a probability distribution, not a single number — closer to how finance actually works.
Most-leveraged inputs (sensitivity analysis)
Where to focus — what moves the answer most
Each input perturbed ±10%; measured impact on Current monthly payment. Higher elasticity = bigger lever.
- 1
Current mortgage balance
Elasticity ↑ 1.00× — 10% change in this input increases Current monthly payment by 10.0%.
- 2
Current rate (%)
Elasticity ↑ 0.64× — 10% change in this input increases Current monthly payment by 6.4%.
- 3
Years remaining on current loan
Elasticity ↓ 0.37× — 10% change in this input decreases Current monthly payment by 3.7%.
- 4
New rate offer (%)
Elasticity ↕ 0.00× — 10% change in this input affects Current monthly payment by 0.0%.
ShowMath is the only calc site that surfaces this. Adjust the highest-leverage input first — that's where small moves create big results.
Chain payload (for the 3D constellation)
{
"slug": "mortgage-refi-engine",
"depth": 1,
"primitives": [
"mortgage-calculator",
"refi-breakeven-calculator",
"amortization-schedule"
],
"composes": [],
"chain": [
{
"key": "current_payment",
"label": "Current monthly payment",
"primitive": "mortgage-calculator",
"numeric": 1963.0672878187318
},
{
"key": "new_payment",
"label": "New payment (30-yr at 5.875%)",
"primitive": "mortgage-calculator",
"numeric": 1724.332579650586
},
{
"key": "monthly_savings",
"label": "Monthly savings",
"numeric": 238.73470816814574
},
{
"key": "breakeven",
"label": "Breakeven month",
"primitive": "refi-breakeven-calculator",
"numeric": 28
},
{
"key": "stay_period_savings",
"label": "Net savings if you sell at year 8",
"numeric": 22918.53198414202
},
{
"key": "lifetime_interest",
"label": "Lifetime interest delta",
"numeric": -1782.7348747666692
},
{
"key": "fifteen_year_alt",
"label": "15-yr alternative payment",
"numeric": 2362.5067150496407
},
{
"key": "tax_shield_delta",
"label": "Tax shield delta (Y1)",
"numeric": 0
}
]
}The chain explained
Each step above corresponds to a primitive calculator. Click any to see the stand-alone version with its own explainer + sources.
- mortgage calculatorshipping soon
- refi breakeven calculatorshipping soon
- amortization scheduleshipping soon
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