# House affordability calculator

> Find how much house you can afford: the highest home price whose payment, tax, insurance, HOA and PMI fit the 28% and 36% debt-to-income limits.

Interactive version: https://www.calcopenly.com/finance/house-affordability-calculator
Subject: Finance calculators

Lenders cap the housing payment in two ways. The front-end ratio limits principal, interest, property tax, insurance, HOA dues and mortgage insurance to a share of gross monthly income, 28% by default; the back-end ratio limits that payment plus your other monthly debts, 36% by default. The lower of the two caps is your housing budget, and the calculator finds the home price whose full payment equals it, adding PMI whenever the down payment is under 20% of the price.

With the defaults, a $100,000 household income, $500 of monthly debts and $50,000 down at 6.5% for 30 years allow a home of $332,531.51. The front-end cap of $2,333.33 a month is the tighter one.

The 28% and 36% defaults are Freddie Mac's guidelines for manually underwritten loans; Fannie Mae's automated Desktop Underwriter accepts total ratios up to 50%. Closing costs and cash reserves are not included.

## Inputs

- **Gross household income (per year)**: Before tax, for everyone who will be on the mortgage.
- **Other monthly debt payments**: Car and student loans, credit card minimums, personal loans, child support. Not rent, utilities or groceries.
- **Down payment**
- **Interest rate (per year)**
- **Loan term**
- **Property tax (per year, of home price)**
- **Homeowners insurance (per year)**
- **HOA dues (per month)**
- **PMI (per year, of loan amount)**: Added whenever the down payment is under 20% of the price.
- **Front-end ratio: housing costs, % of gross income**: 28% is Freddie Mac's guideline for manually underwritten loans (Guide 5401.1); FHA manual underwriting uses 31% (HUD Handbook 4000.1).
- **Back-end ratio: all debts, % of gross income**: 36% is Fannie Mae's maximum for manually underwritten loans, 45% with credit-score and reserve requirements, 50% through Desktop Underwriter (Selling Guide B3-6-02). FHA manual underwriting uses 43%.

## Results

- Home price you can afford — main result
- Loan amount
- Down payment as a share of the price
- Monthly housing payment
- Principal and interest
- Property tax per month
- Insurance per month
- PMI per month
- Housing budget under the front-end ratio
- Housing budget under the back-end ratio
- Limiting rule
- Front-end ratio at this price
- Back-end ratio at this price

## Formula

$$
H = \min\!\Big(\tfrac{f}{100}\,\tfrac{I}{12},\ \tfrac{b}{100}\,\tfrac{I}{12} - \text{debts}\Big),\qquad P = \frac{H - \tfrac{\text{ins}}{12} - \text{HOA} + D\,(a + m)}{a + t + m},\quad a = \frac{r(1+r)^n}{(1+r)^n - 1}
$$

## Worked examples

### $100,000 income, $50,000 down, 6.5%

- Gross household income (per year): 100,000
- Other monthly debt payments: 500
- Down payment: 50,000
- Interest rate (per year): 6.5%
- Loan term: 30 years
- Property tax (per year, of home price): 1.1%
- Homeowners insurance (per year): 1500
- HOA dues (per month): 0
- PMI (per year, of loan amount): 0.5%
- Front-end ratio: housing costs, % of gross income: 28%
- Back-end ratio: all debts, % of gross income: 36%
- **Home price you can afford: 332,531.51**
- **Housing budget under the front-end ratio: 2,333.33**
- **Housing budget under the back-end ratio: 2,500.00**
- **Monthly housing payment: 2,333.33**
- **Limiting rule: Front-end ratio (housing costs)**
- Checked against: Python decimal search: largest price whose payment (annuity P&I + 1.1% tax + 125 insurance + 0.5% PMI) stays at or below min(28% × 8,333.33, 36% × 8,333.33 − 500), found by scanning and 200 bisection steps

### Zero rate, 10-year term, back-end limit

- Gross household income (per year): 120,000
- Other monthly debt payments: 1000
- Down payment: 88,000
- Interest rate (per year): 0%
- Loan term: 10 years
- Property tax (per year, of home price): 0%
- Homeowners insurance (per year): 0
- HOA dues (per month): 0
- PMI (per year, of loan amount): 0%
- Front-end ratio: housing costs, % of gross income: 28%
- Back-end ratio: all debts, % of gross income: 36%
- **Home price you can afford: 400,000.00**
- **Loan amount: 312,000.00**
- **Housing budget under the back-end ratio: 2,600.00**
- **Limiting rule: Back-end ratio (all debts)**
- **Down payment as a share of the price: 22.00%**
- Checked against: Hand calculation: 36% × 10,000 − 1,000 = 2,600 < 28% × 10,000; 2,600 × 120 payments = 312,000 loan + 88,000 down

### Debts make the back-end cap tighter

- Gross household income (per year): 100,000
- Other monthly debt payments: 1200
- Down payment: 30,000
- Interest rate (per year): 7%
- Loan term: 30 years
- Property tax (per year, of home price): 1%
- Homeowners insurance (per year): 1200
- HOA dues (per month): 50
- PMI (per year, of loan amount): 0.6%
- Front-end ratio: housing costs, % of gross income: 28%
- Back-end ratio: all debts, % of gross income: 36%
- **Home price you can afford: 233,471.96**
- **Housing budget under the back-end ratio: 1,800.00**
- **Limiting rule: Back-end ratio (all debts)**
- Checked against: Python decimal search as above: 36% × 8,333.33 − 1,200 = 1,800 is below the 2,333.33 front-end cap

### PMI cliff at 20% down (edge)

- Gross household income (per year): 100,000
- Other monthly debt payments: 500
- Down payment: 72,000
- Interest rate (per year): 6.5%
- Loan term: 30 years
- Property tax (per year, of home price): 1.1%
- Homeowners insurance (per year): 1500
- HOA dues (per month): 0
- PMI (per year, of loan amount): 0.5%
- Front-end ratio: housing costs, % of gross income: 28%
- Back-end ratio: all debts, % of gross income: 36%
- **Home price you can afford: 360,000.00**
- **PMI per month: 0.00**
- **Down payment as a share of the price: 20.00%**
- **Monthly housing payment: 2,275.36**
- Checked against: Python decimal search: a price of 360,000 (20% down, no PMI) costs 2,275.36 a month; any higher price adds PMI and exceeds the 2,333.33 cap

### FHA-style ratios 31% and 43%

- Gross household income (per year): 100,000
- Other monthly debt payments: 500
- Down payment: 50,000
- Interest rate (per year): 6.5%
- Loan term: 30 years
- Property tax (per year, of home price): 1.1%
- Homeowners insurance (per year): 1500
- HOA dues (per month): 0
- PMI (per year, of loan amount): 0.5%
- Front-end ratio: housing costs, % of gross income: 31%
- Back-end ratio: all debts, % of gross income: 43%
- **Home price you can afford: 365,194.11**
- **Housing budget under the front-end ratio: 2,583.33**
- Checked against: Python decimal search with the 31/43 ratios of HUD Handbook 4000.1 manual underwriting

## Questions

### What is the 28/36 rule?

Housing costs should take no more than 28% of gross monthly income, and all debt payments including housing no more than 36%. These are Freddie Mac's guideline ratios for manually underwritten mortgages (Seller/Servicer Guide 5401.1 and 5401.2). On $100,000 a year, gross monthly income is $8,333.33, so housing may cost $2,333.33 and all debts $3,000.

### How much house can I afford on a $100,000 salary?

About $332,500 with $50,000 down, $500 of other monthly debts and a 6.5% 30-year rate, under the 28/36 rule, including 1.1% property tax, $1,500 a year of insurance and 0.5% PMI. With FHA-style ratios of 31% and 43%, the same inputs allow $365,194.11. Other debts up to $666.67 a month leave the price unchanged, because the 28% front-end cap stays the tighter one.

### What debt-to-income ratio do lenders allow?

Fannie Mae's maximum is 36% for manually underwritten loans, 45% with credit-score and reserve requirements, and 50% for loans run through Desktop Underwriter (Selling Guide B3-6-02). FHA's manual-underwriting limits without compensating factors are 31% for housing and 43% in total (HUD Handbook 4000.1). The CFPB suggests keeping total debt payments at 36% or less.

### How does the down payment change how much house I can afford?

Each dollar of down payment adds a dollar to the price, and more once PMI drops away at 20% down. On a $2,333.33 budget at 6.5%, $50,000 down allows $332,531.51 with PMI, while $72,000 down allows exactly $360,000: at 20% down there is no PMI, but any higher price would bring PMI back and push the payment over the budget.

### How accurate is the house affordability calculator?

Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 5 worked examples whose answers come from independent sources; for example, “$100,000 income, $50,000 down, 6.5%” is checked against Python decimal search: largest price whose payment (annuity P&I + 1.1% tax + 125 insurance + 0.5% PMI) stays at or below min(28% × 8,333.33, 36% × 8,333.33 − 500), found by scanning and 200 bisection steps.

### Where does the method come from?

Freddie Mac Single-Family Seller/Servicer Guide 5401.1: monthly housing expense-to-income ratio (28% guideline, manual underwriting); Freddie Mac Single-Family Seller/Servicer Guide 5401.2: monthly debt payment-to-income ratio (36% guideline); Fannie Mae Selling Guide B3-6-02, Debt-to-Income Ratios (36%, 45%, 50%); HUD Single Family Housing Policy Handbook 4000.1 (FHA manual underwriting ratios 31/43); Consumer Financial Protection Bureau: When can I remove PMI from my loan?.

## Sources

- [Freddie Mac Single-Family Seller/Servicer Guide 5401.1: monthly housing expense-to-income ratio (28% guideline, manual underwriting)](https://guide.freddiemac.com/app/guide/section/5401.1)
- [Freddie Mac Single-Family Seller/Servicer Guide 5401.2: monthly debt payment-to-income ratio (36% guideline)](https://guide.freddiemac.com/app/guide/section/5401.2)
- [Fannie Mae Selling Guide B3-6-02, Debt-to-Income Ratios (36%, 45%, 50%)](https://selling-guide.fanniemae.com/sel/b3-6-02/debt-income-ratios)
- [HUD Single Family Housing Policy Handbook 4000.1 (FHA manual underwriting ratios 31/43)](https://www.hud.gov/hud-partners/single-family-handbook-4000-1)
- [Consumer Financial Protection Bureau: When can I remove PMI from my loan?](https://www.consumerfinance.gov/ask-cfpb/when-can-i-remove-private-mortgage-insurance-pmi-from-my-loan-en-202/)

_Note: financial information, not professional advice._