# 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.

Интерактивная версия: https://www.calcopenly.com/ru/finance/house-affordability-calculator
Тема: Финансовые калькуляторы

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.

## Входные данные

- **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.
- **Первоначальный взнос**
- **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%.

## Результаты

- Home price you can afford — основной результат
- 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

## Формула

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

## Примеры с решением

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

- Gross household income (per year): 100,000
- Other monthly debt payments: 500
- Первоначальный взнос: 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)**
- Источник проверки: 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
- Первоначальный взнос: 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%**
- Источник проверки: 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
- Первоначальный взнос: 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)**
- Источник проверки: 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
- Первоначальный взнос: 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**
- Источник проверки: 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
- Первоначальный взнос: 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**
- Источник проверки: Python decimal search with the 31/43 ratios of HUD Handbook 4000.1 manual underwriting

## Вопросы

### 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.

### Насколько точен «House affordability calculator»?

Точность зависит от введённых данных и допущений метода. Десятичная арифметика использует 50 значащих цифр, но оценки, численные методы и исходные данные могут быть менее точными; округление на экране не устраняет эти ограничения. Решённые примеры, проверенные по независимым источникам: 5. Например, «$100,000 income, $50,000 down, 6.5%» проверяется по источнику 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.

### Откуда взята методика?

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?.

## Источники

- [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/)

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