Calculate Mortgage Affordability

---
name: calculate-mortgage-affordability
description: Use when determining how much house you can actually afford — applying the 28/36 rule, stress-testing at higher rates, and calculating required down payment and cash reserves to avoid becoming house-poor
source: Consumer Financial Protection Bureau "Know Before You Owe" mortgage guide (2023); Federal Housing Administration underwriting guidelines (28/36 rule); Bogle "The Little Book of Common Sense Investing" (2007); Urban Institute Housing Finance Policy Center research (2023)
tags: [personal-finance, mortgage, home-buying, affordability, rule-28-36, down-payment, real-estate, piti]
verified: true
---

# Calculate Mortgage Affordability

Apply the 28/36 rule to gross income, stress-test at rate +2%, calculate total required cash, and derive a maximum purchase price that leaves financial margin.

## Why This Is Best Practice

**Adopted by:** The 28/36 rule is the standard underwriting guideline used by Fannie Mae, Freddie Mac, and FHA — the three institutions that back the majority of US residential mortgages. Lenders use it as the primary affordability screen. The CFPB's "Know Before You Owe" framework (implemented by the Dodd-Frank Act) requires lenders to verify borrower's ability to repay using these or similar ratios. The rule predates the 2008 housing crisis and is the stress-tested standard for sustainable homeownership.

**Impact:** Buying based on what the bank will approve vs. what you can sustainably afford are different things. Banks approved loans up to 45% DTI in the run-up to 2008; those borrowers frequently became house-poor or defaulted when rates rose. The 28/36 rule leaves margin for savings, car payments, and unexpected expenses. Lenders approve your maximum borrowing capacity; you should choose a significantly lower purchase price.

**Why best:** The 28/36 framework is conservative by design. It prevents the single most common financial mistake in homeownership: buying at the absolute ceiling of approval and having no margin for job loss, rate increases, or major repairs. The stress test (+2% rate scenario) accounts for adjustable-rate mortgages and future refinancing risk. Total cash calculation prevents buyers from arriving at closing without enough funds.

Sources: CFPB, *Know Before You Owe* (2023) — borrower protection guidelines; FHA Handbook 4000.1 — 28/36 underwriting standard; Urban Institute, *Housing Finance at a Glance* (2023) — debt-to-income risk data; Redfin Research (2023) — closing cost ranges by state

## Steps

### Step 1: Calculate your gross monthly income
Use gross income (before taxes), not take-home pay. Include:
- Your base salary: annual ÷ 12
- Spouse/partner income (if buying jointly)
- Consistent side income that can be documented (2-year history required by most lenders)
- Do NOT include bonuses unless they have a 2-year documented history and are guaranteed

**Example:** $120,000 annual salary + $40,000 partner salary = $160,000 combined = **$13,333 gross monthly income**

### Step 2: Apply the 28% front-end ratio (PITI limit)
**Front-end ratio:** PITI (Principal + Interest + Taxes + Insurance) must not exceed 28% of gross monthly income.

PITI = mortgage payment + property tax + homeowner's insurance + (HOA fees if applicable)

Maximum PITI = gross monthly income × 0.28

**Example:** $13,333 × 0.28 = **$3,733/month maximum PITI**

To estimate property taxes and insurance before you have a specific property:
- Property tax: estimate 1.0–1.5% of purchase price annually (varies by state; check local rates)
- Homeowner's insurance: estimate $100–200/month for a median-priced home
- PMI (if down payment < 20%): estimate 0.5–1.0% of loan amount annually

### Step 3: Apply the 36% back-end ratio (total debt limit)
**Back-end ratio (DTI — Debt-to-Income):** All monthly debt payments (PITI + car loans + student loans + credit card minimum payments + any other obligations) must not exceed 36% of gross monthly income.

Maximum total monthly debt = gross monthly income × 0.36

**Example:** $13,333 × 0.36 = **$4,800 maximum total monthly debt**

If you have existing debt obligations: subtract them from the total debt limit to find what's left for housing.

**Example:** $500/month car payment + $400/month student loans = $900 existing debt. $4,800 − $900 = **$3,900 available for PITI** — which is more constrained than the front-end limit in this case. The more restrictive limit governs.

### Step 4: Back-calculate maximum loan amount from PITI

From your maximum PITI, subtract estimated taxes, insurance, and PMI to get your maximum principal + interest (P&I) payment. Then reverse-calculate the loan amount using current rates.

**Formula for loan amount from monthly payment:**

```
Loan = P&I × [(1+r)^n − 1] / [r × (1+r)^n]
```

Where r = monthly rate (annual rate ÷ 12) and n = number of payments (360 for 30-year).

**Or use the shortcut:** At 7% interest on a 30-year mortgage, each $1,000 of loan amount costs approximately **$6.65/month** in P&I. Divide your maximum P&I by 6.65 × 1,000 to get approximate loan amount.

**Example:**
- Max PITI: $3,733
- Estimated property tax: $500/month (on a $400k home)
- Estimated insurance: $150/month
- Available for P&I: $3,733 − $500 − $150 = **$3,083/month**
- At 7% / 30-year: $3,083 ÷ 6.65 × 1,000 ≈ **$463,000 loan amount**

### Step 5: Stress test at current rate + 2%
Mortgage rates can rise. If you take an adjustable-rate mortgage, or if you are planning to refinance later, you need to verify you can afford the payment at a higher rate.

Recalculate P&I payment using rate + 2% on the same loan amount. If the resulting PITI exceeds 28% of gross income, the purchase is not affordable under stress conditions — reduce the purchase price.

**Example:** $463,000 loan at 9% (stress test): monthly P&I ≈ $3,726. PITI = $3,726 + $500 + $150 = $4,376 — exceeds the $3,733 limit. Reduce loan amount to ~$340,000 to remain safe under stress conditions.

### Step 6: Calculate maximum purchase price
Maximum purchase price = loan amount + down payment.

**Down payment options:**
| Down payment | PMI required? | Notes |
|-------------|--------------|-------|
| < 20% | Yes (adds cost) | FHA allows 3.5%; conventional allows 3–5% |
| 20% | No | Eliminates PMI; standard recommendation |
| > 20% | No | Lower monthly payment; improves debt ratios |

**Example (20% down):** $463,000 loan ÷ 0.80 = **$578,750 maximum purchase price**

### Step 7: Calculate total cash required at closing
Knowing your purchase price isn't enough — you need the total cash required to close.

| Item | Amount |
|------|--------|
| Down payment | 20% of purchase price |
| Closing costs | 2–5% of purchase price (varies by state; avg ~3%) |
| Pre-paid items | 2–3 months property tax + insurance escrow (~$2,000–5,000) |
| Moving costs | $1,000–5,000 depending on distance |
| Immediate repairs reserve | Recommend 1% of purchase price |
| **Emergency fund (post-purchase)** | Maintain 3–6 months expenses |

**Example (on $578,750 purchase):**
- Down payment (20%): $115,750
- Closing costs (3%): $17,362
- Pre-paids: $3,000
- Moving + reserve: $8,000
- **Total cash needed at closing: ~$144,000**

If you don't have this cash, reduce your purchase price — not your down payment (lower down payment adds PMI and increases monthly payment).

### Step 8: Derive your realistic price range
Your affordable purchase price is the lowest of:
1. Price derived from front-end (28%) ratio
2. Price derived from back-end (36%) ratio minus existing debt
3. Price that passes the rate +2% stress test
4. Price for which you have the total cash to close plus post-purchase emergency fund

## Rules

- The bank's pre-approval amount is their maximum, not your target. Borrow 20–30% less than what you're approved for.
- Never deplete your emergency fund for a down payment. Post-purchase financial emergencies are common (HVAC, roof, plumbing). Maintain 3–6 months of expenses in liquid savings after closing.
- Do not buy with less than 10% down unless constrained by market (3–5% programs exist but increase risk and monthly cost significantly via PMI and higher loan balance).
- Include property taxes at the actual local rate. A $400k home in New Jersey ($8,000–12,000/yr tax) is not the same as in Texas ($5,000–7,000/yr) or California (Prop 13 capped rate).
- Run the stress test every time. Rates change faster than house prices.

## Examples

**Household income $180k, 30-year at 7%, 20% down, $1,200/yr existing debt:**
- Gross monthly: $15,000
- Max PITI (28%): $4,200
- Max total debt (36%): $5,400 → less $100 existing = $5,300 housing available → not binding
- P&I available: $4,200 − $600 tax est − $175 ins = $3,425 → loan ≈ $515,000
- Purchase price (20% down): $644,000
- Stress test at 9%: P&I = $4,142 + $600 + $175 = $4,917 > $4,200 → over limit
- Adjusted loan for stress: ~$380,000 → purchase price $475,000
- Cash needed: $95,000 down + $14,250 closing + $6,000 = ~$115,000

**First-time buyer, $75k income, renting, no existing debt:**
- Gross monthly: $6,250
- Max PITI (28%): $1,750
- P&I available: $1,750 − $250 tax − $100 ins = $1,400 → loan ≈ $210,000
- With 10% down: purchase price ~$233,000 (PMI adds ~$150/mo → reduces P&I to $1,250 → loan ~$188k → price ~$209k)
- Cash needed with 10% down: $23,000 + $7,000 closing + reserves = ~$35,000

## Common Mistakes

**Buying at maximum pre-approval:** Pre-approval is based on what you can technically qualify for, not what is financially sustainable. Lenders don't account for your other goals (retirement savings, college, travel).

**Forgetting closing costs:** Many first-time buyers budget for the down payment but arrive at closing underfunded. Closing costs of 2–5% on a $400k home = $8,000–20,000.

**Ignoring PMI:** At less than 20% down, PMI costs $100–400/month and is pure cost with no equity benefit. Model its impact before accepting a low-down-payment loan.

**Not stress-testing the rate:** A $400k loan at 6.5% costs $2,528/month. At 8.5%, the same loan costs $3,076/month — a $548/month increase. If your budget is tight at 6.5%, you cannot afford this home.

**Buying based on "what we can afford now":** A home purchase is a 30-year commitment. Model your payment assuming income stays flat (job loss, parental leave, career change) — not assuming it grows.

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> **Financial disclaimer:** This skill encodes professional best practices for educational purposes. It is not financial or legal advice. Mortgage affordability depends on your specific financial situation, local tax rates, credit score, and lender guidelines. Consult a licensed mortgage professional and financial advisor before making a purchase decision.