# What mortgage approval can I get?

Computes the largest mortgage a lender’s housing and total debt-to-income limits allow for your income and debts, and checks whether a loan amount you want fits them.

- Page: https://www.acalculator.org/finance/mortgage-preapproval-calculator
- JSON spec: https://www.acalculator.org/finance/mortgage-preapproval-calculator.json
- Version: 5868444c3865

## Default answer

Example with the default inputs (Gross income $100,000.00, Other debt payments a month $500.00, Interest rate 6.5%, Loan term (years) 30, Tax, insurance, and HOA a month $500.00, Housing limit (front-end ratio) 30%, Total debt limit (back-end ratio) 36%): With $100,000.00 of yearly income and $500.00 of other monthly debts, you may qualify for a loan of up to $316,421.64.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| income | Gross income | Your household income before tax and deductions. |
| debts | Other debt payments a month | Monthly payments on other debts: car loans, student loans, minimum credit card payments, child support. |
| rate | Interest rate | The fixed yearly mortgage rate. The monthly rate is this ÷ 12. |
| years | Loan term (years) | The length of the mortgage, for example 30 or 15 years. |
| costs | Tax, insurance, and HOA a month | Property tax, home insurance, HOA dues, and any mortgage insurance, for one month. |
| amount | Loan you want (optional) | A loan amount to check against the limits. Leave it empty to see only the largest loan. |
| front | Housing limit (front-end ratio) | The most the housing payment may be, as a percent of gross monthly income. |
| back | Total debt limit (back-end ratio) | The most all debt payments, housing included, may be, as a percent of gross monthly income. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| maxLoan | Largest loan you may qualify for | The loan whose payment, with the other housing costs, fits both debt-to-income limits. |
| maxPayment | Principal and interest at that loan | The monthly loan payment on the largest loan. |
| housing | Housing budget a month | The most the whole housing payment may be under both limits. |
| limit | Limit | Which debt-to-income limit sets the budget. |
| payment | Principal and interest on your loan | The monthly payment on the loan you want. |
| frontRatio | Housing ratio (front-end) | The housing payment on the loan you want (or the largest loan) as a percent of gross monthly income. |
| backRatio | Total debt ratio (back-end) | That housing payment plus other debts, as a percent of gross monthly income. |
| verdict | Your loan | Whether the loan you want fits both limits. |
| room | Room below the largest loan | The largest loan minus the loan you want. |

## Method

housing budget = min(front × income ÷ 12, back × income ÷ 12 − debts); largest loan = (budget − other housing costs) ÷ a, with a = r ÷ (1 − (1 + r)^−n), r the rate ÷ 12, and n the months.

## Assumptions

- Lenders compare payments with gross (before-tax) monthly income; the limits are yours to set.
- The rate is fixed; tax, insurance, HOA dues, and mortgage insurance are one monthly amount.
- Credit score, cash reserves, residual income, employment, and down payment rules are not checked, so this is an estimate, not a preapproval.
- The default rate is an example, not a current market rate.

## Worked examples

1. income = $100,000.00, debts = $500.00, rate = 6.5%, years = 30, costs = $500.00, front = 30%, back = 36% gives housing = $2,500.00, maxPayment = $2,000.00, maxLoan = $316,421.64, frontRatio = 30%, backRatio = 36%.
2. income = $90,000.00, debts = $900.00, rate = 7%, years = 30, costs = $450.00, front = 31%, back = 43%, amount = $350,000.00 gives housing = $2,325.00, maxLoan = $281,826.69, payment = $2,328.56, frontRatio = 37.04745%, backRatio = 49.04745%, verdict = Over both limits., room = -$68,173.31. Source: FHA limits of 31% and 43% (HUD Mortgagee Letter 2014-02).
3. income = $120,000.00, debts = $2,500.00, rate = 0%, years = 30, costs = $400.00, front = 30%, back = 41%, amount = $300,000.00 gives housing = $1,600.00, maxLoan = $432,000.00, payment = $833.33, backRatio = 37.333333%, verdict = Within both limits., room = $132,000.00. Source: VA limit of 41% (38 CFR 36.4340).

## FAQ

### How do lenders decide how much mortgage I can get?

A big part is your debt-to-income ratio: your monthly debt payments divided by your gross monthly income. Lenders cap the housing payment (the front-end ratio) and all debt payments together (the back-end ratio). The loan whose payment fits both caps is the most you may qualify for.

### What DTI limits apply to my loan?

Fannie Mae allows a total ratio of 36% for manually underwritten loans, up to 45% with strong credit and reserves, and 50% through Desktop Underwriter. FHA uses 31% for housing and 43% in total without compensating factors. VA looks at a total ratio of 41% together with residual income. Set the limits on this page to match your loan.

### What is the difference between prequalification and preapproval?

Both estimate how much you can borrow. A preapproval usually means the lender has checked your credit and documents, so it carries more weight with sellers. Neither is a final approval: the lender still reviews the home, the appraisal, and your finances before closing.

### Why is the loan I want over the limits?

The payment on that loan, plus tax, insurance, and your other debts, is more than the limits allow for your income. You can borrow less, pay down other debts, find a lower rate, choose a longer term, or add a co-borrower's income.

### What should go in the monthly tax, insurance, and HOA amount?

Property tax and home insurance for one month, HOA dues, and any mortgage insurance (PMI, or FHA's annual premium). Lenders count all of these in the housing payment.

### Does this calculator check my credit score?

No. It checks only the debt-to-income ratios. Lenders also look at your credit score, savings, employment, and the down payment, so your real approval can be higher or lower.

## Sources

- Fannie Mae Selling Guide B3-6-02, Debt-to-Income Ratios (36% manual, up to 45% with credit score and reserves, 50% for Desktop Underwriter). https://selling-guide.fanniemae.com/sel/b3-6-02/debt-income-ratios
- U.S. Department of Housing and Urban Development, Mortgagee Letter 2014-02 (FHA manual underwriting: 31% housing and 43% total without compensating factors). https://www.hud.gov/sites/documents/14-02ml.pdf
- 38 CFR 36.4340, Underwriting standards (VA: debt-to-income ratio of 41% and residual income). https://www.ecfr.gov/current/title-38/chapter-I/part-36/subpart-B/section-36.4340
- Freddie Mac, How much home can I afford? (housing expense ratio ideally less than 30%). https://myhome.freddiemac.com/blog/homebuying/how-much-can-you-afford
- Consumer Financial Protection Bureau, What is a debt-to-income ratio? https://www.consumerfinance.gov/ask-cfpb/what-is-a-debt-to-income-ratio-en-1791/