One division, two ratios, and the reason clearing the right debt can raise what a lender will let you borrow by more than the debt itself.
Add up every monthly debt payment and divide by your gross monthly income, before tax. On an illustrative salary of $64,800, which is $5,400 a month, payments of $2,176.53 give a debt-to-income ratio of 40.3 per cent. At the 36 per cent limit many lenders use, the same person can carry a housing payment of at most $1,217.47, and the cheapest way to raise that is not the debt with the highest rate.
Worked in full in Personal Finance for Beginners by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A renter is thinking about a mortgage. The figures are illustrative. Debt payments are the contractual monthly amounts: the loan instalments and the card's minimum payment, not what you choose to pay above it. Living costs such as groceries, utilities and insurance are not debts and stay out of the ratio.
| Item | Amount |
|---|---|
| Gross salary, a year | $64,800 |
| Gross income, a month | $5,400 |
| Rent | $1,450.00 |
| Car loan payment (balance $9,800) | $385.00 |
| Student loan payment | $260.00 |
| Credit card minimum (balance $3,200) | $81.53 |
| Total monthly payments | $2,176.53 |
Debt-to-income ratio = total monthly debt payments ÷ gross monthly income
= 2,176.53 ÷ 5,400 = 40.3%
Excel: =SUM(B2:B5)/(B1/12)
Lenders usually look at two versions. The front-end ratio counts housing only: $1,450 ÷ $5,400 = 26.9 per cent. The back-end ratio counts everything, the 40.3 per cent above. Strip out the rent and the other debts alone are $726.53, or 13.5 per cent of gross pay.
Online calculators often include rent, as here, because it is a fixed monthly obligation. A mortgage lender will instead replace the rent with the payment on the home you are buying, which is why the useful question is not "what is my ratio?" but "what housing payment does a given ratio allow?"
Turn the ratio around. Multiply gross income by the limit, then subtract the debts that will still be there after the move.
Front-end cap = 28% × 5,400 = $1,512.00
Back-end cap = 36% × 5,400 − 726.53 = 1,944.00 − 726.53 = $1,217.47
At a 43% ceiling = 2,322.00 − 726.53 = $1,595.47
The lower of the caps that apply is the one that binds.
On the common 28 and 36 per cent rules, this household can carry $1,217.47 a month of housing, $232.53 less than the rent it already pays. That is the back-end ratio doing its job: the car, the student loan and the card take 13.5 points of income before the house gets any. To bring today's 40.3 per cent down to 36 per cent, payments would have to fall by the same $232.53, or gross income would have to rise to $6,046 a month, $72,551 a year.
A housing payment is not a loan amount. If taxes and insurance take $350 a month and the mortgage costs an illustrative 6.5 per cent over 30 years, $1,217.47 leaves $867.47 for principal and interest, which supports a loan of about $137,243. Each $100 a month of extra room is worth about $15,821 of borrowing on those terms. The monthly payment arithmetic is in how a loan's monthly payment is calculated.
Paying a debt off removes its monthly payment from the ratio, not its balance. That changes the usual order.
| Debt cleared | Balance repaid | Payment removed | DTI with rent | Housing allowed | Loan supported |
|---|---|---|---|---|---|
| None | $0 | $0.00 | 40.3% | $1,217.47 | $137,243 |
| Credit card | $3,200 | $81.53 | 38.8% | $1,299.00 | $150,142 |
| Car loan | $9,800 | $385.00 | 33.2% | $1,512.00 | $183,841 |
| Both | $13,000 | $466.53 | 31.7% | $1,512.00 | $183,841 |
Per $1,000 repaid, the car loan frees $39.29 a month and the card $25.48, because the car's instalment is large against its balance and the card's minimum is small. Clearing the car lifts the borrowing it supports by $46,598; clearing the card, by $12,899.
Two further points sit in that table. Once the car is gone, the back-end ratio would allow $1,602.47, but the 28 per cent front-end cap of $1,512 now binds, so $90.47 of the freed payment buys nothing. And clearing the card as well changes the ratio but not the housing allowed. Past the point where the other cap binds, paying down more debt improves your finances but not your application.
For your finances, the card, at an illustrative 22.9 per cent APR, is still the expensive debt and usually the one to clear first. For a mortgage application in the next few months, the ratio may point elsewhere. Run both before deciding.
| Back-end limit | Total payments allowed | Housing allowed |
|---|---|---|
| 36% | $1,944.00 | $1,217.47 |
| 43% | $2,322.00 | $1,595.47 |
The step from 36 to 43 per cent adds $378 of housing room, but it means 43 cents of every gross dollar committed before tax, food or saving. On this salary that leaves very little margin if a car repair or a rate rise arrives. A ratio a lender accepts is a ceiling, not a target.
The blank calculator in the free workbook for this book shows, for any one debt, how much of the payment is interest and how long it takes to clear.
On gross income, before tax and deductions. On the worked example, $2,176.53 of monthly payments against $5,400 of gross pay is 40.3 per cent; against the $4,310 that actually reaches the bank account it would be 50.5 per cent. Using net pay makes your ratio look worse than the one a lender computes, which is useful for your own budget but not for predicting an application.
Common lender rules of thumb are 28 per cent for housing alone and 36 per cent for all debts, with 43 per cent a ceiling often quoted for mortgages; each lender and loan programme sets its own limits. On $5,400 a month, 36 per cent allows $1,944 of total payments and 43 per cent allows $2,322. Below about 36 per cent most of your income is still free for living costs and saving.
Yes, by the minimum payment, not by the balance. Clearing a $3,200 card with an $81.53 minimum takes the example's ratio from 40.3 to 38.8 per cent. Clearing a $9,800 car loan with a $385 payment takes it to 33.2 per cent, so per dollar repaid the car loan does more: $39.29 of monthly room per $1,000 cleared against $25.48.
This article is one calculation from Personal Finance for Beginners. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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