Maximum Affordable Loan
Maximum Affordable Loan
The largest loan whose payment fits within a debt-to-income limit: income times the allowed DTI ratio per period, less existing debt payments, is the payment capacity; the loan is that capacity converted to a principal at the rate and term.
When to use: Use to see how much house or car a given income supports under a lender's DTI rule (commonly 36% to 43% for mortgages), and how existing car or student payments shrink it.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| MaxLoan | Maximum Loan | Largest principal the payment capacity supports | $ |
| AnnualIncome | Annual Gross Income | Household income before tax | $ |
| DTI | Debt-to-Income Limit | Maximum share of income allowed for all debt payments, as a decimal | % |
| OtherDebt | Other Debt Payments | Existing debt payments per period (car, student, cards) | $ |
| k | Interest Rate | Annual interest rate on the new loan | % |
| n | Loan Term | Term in years | years |
| m | Payments per Year | Number of payments per year | integer |
Real-Life Examples
Example 1: Mortgage at 36% DTI
$120,000 income, 36% DTI limit, $600 a month of other debt, 6.5% over 30 years.
Given
Step-by-Step
About $475,000 of mortgage. Without the $600 car payment the capacity would be $3,600 and the loan about $570,000: existing debt costs nearly $95,000 of house.
Example 2: Stretching to 43%
$75,000 income, 43% DTI, $900 a month of other debt, 7% over 30 years.
Given
Step-by-Step
Even at the more permissive 43% limit, $900 of existing payments and a 7% rate hold the maximum to about $269,000.
Frequently Asked Questions
Rules vary by lender and loan program. Conventional mortgages often use 36% (sometimes 43% or more with strong credit); the DTI here counts all debt payments, including the new loan, as a share of gross income.
Not unless you fold them in. Lenders usually count property tax, insurance and HOA dues as part of the housing payment, which reduces the loan this formula shows.