A debt-to-income ratio is a number that compares how much money you are making to how much money you are spending. One of the first numbers a bank wants to look at is your debt-to-income ratio before they help you get the money to buy a house. Town and city budgets also should consider their debt-to-income ratio before taking on any more debt for a project.
The debt-to-income ratio is a straightforward calculation. Divide your debt by your income. Make sure your debt and your income are measured in the same time period, as it would not make sense to divide your monthly debt by your yearly income.
\[\text{debt-to-income ratio } = \frac{\text{debt}}{\text{income}}\]
1.
A family has the following monthly bills and wants to buy a
house:
$140 for two car insurance payments $90 for electricity $340 for heating (averaged throughout the year) $420 for two car payments The loan they are looking at will mean their housing payment will be $1,000 per month
The family has $68,000 in yearly income. What will their debt-to-income ratio be if they purchase this home?
We can first calculate our total monthly debt.
\[\$140 + \$90 + \$340 + \$420 + \$1,000 = \$1,990\]
The income is yearly income. We can convert our monthly debt to yearly debt by multiplying by \(12\).
\[\$1,990 \text{ per month} \cdot 12 \text{ months in a year} = \$23,880\]
Their debt-to-income ratio is
\[\text{debt-to-income ratio } = \frac{\text{debt}}{\text{income}} = \frac{\$23,880}{\$68,000} \approx 0.3511764\], or approximately \(35\%\).
2.
The mortgage lender in town will only pay for a home if the family
has a debt-to-income ratio of \(37\%\)
or less. Does the family qualify for a home loan?
Yes, as the family has a debt-to-income ratio of \(35\%\). That is less than the highest debt-to-income ratio tolerated by this lending institution.
3.
If the mortgage lender will allow a loan that causes a family’s
debt-to-income ratio to be 37%, what’s the above family’s maximum
monthly payment that they can afford?
The equation we have used for debt-to-income is
\[\text{debt-to-income ratio } = \frac{\text{debt}}{\text{income}}\]
We can substitute \(0.37\) (the decimal form of the percentage) for the debt-to-income ratio. We can convert the $68,000 yearly income to monthly income to make the calculation easier. \(\$68,000 \div 12 \approx \$5,666.67\). We can replace the $1,000 payment with \(x\) as we now want to calculate the new monthly payment that’s possible.
\[0.37 = \frac{\$140 + \$90 + \$340 + \$420 + x}{\$5,666.67}\]
We can add all the numbers in the numerator.
\[0.37 = \frac{\$990 + x}{\$5,666.67}\]
The numbers \(\$990 + x\) are being divided by \(\$5,666.67\). We can do the opposite to \(\$5,666.67\) by multiplying it to both sides.
\[0.37 \cdot \$5,666.67= \frac{\$990 + x}{\$5,666.67} \cdot \$5,666.67\]
\[\$2,096.67= \$990 + x\]
Subtract $990 from both sides to get \(x\) by itself.
\[\$2,096.67 - \$990 = \$990 - \$990 + x\]
\[\$1,106.67 = x\]
The most the family can afford is a home with a \(\$1,106.67\) monthly payment.
1. A family has the following yearly bills:
$2040 a year for two car insurance payments $1200 for electricity $3600 for heating (averaged throughout the year) $10800 for housing $5040 for two car payments $1440 for water and sewer
The family has $6,000 in monthly income. What is their debt-to-income ratio?
2. The mortgage lender in town will only pay for a home if the family has a debt-to-income ratio of \(37\%\) or less. Does the family qualify for a home loan?
3. If the mortgage lender will allow a loan that causes a family’s debt-to-income ratio to be 37%, what’s the above family’s maximum monthly payment that they can afford?
1. Do some light research on the web. Does the federal government limit debt-to-income ratios for lending institutions?
2. If one family makes \(\$50,000\) a year and another family makes \(\$ 200,000\) a year, should they have different debt-to-income ratios? Why or why not?
3. What is one quick way to lower a debt-to-income ratio?
4. What is one long-term strategy for lowering a debt-to-income ratio?