There are several mathematical formulas borrowers should understand when applying for a mortgage, to help them get the best possible mortgage with the lowest mortgage interest rate.
So, here are 4 important things every borrower should understand about mortgage math.
#1 Loan-To-Value Ratio (LTV)
The loan-to-value ratio is the loan amount divided by the value of the property being purchased or refinanced.
So, if you are buying a $100,000 home with a 20% down payment ($20,000), you have a loan amount of $80,000, and the loan-to-value is $80,000/$100,000 or 80%.
This formula is important because mortgage guidelines and interest rates may differ depending upon the loan-to-value ratio. Interest rates are often better for lower loan-to-value ratios. Also, loans with higher loan-to-value ratios (above 80%) generally require mortgage insurance.
#2 Debt-To-Income Ratio (DTI)
The debt-to-income ratio is one of the most significant qualifying factors that a lender will review when determining whether you meet the mortgage guidelines. This formula is:
Monthly Obligations/Gross Monthly Income
Understanding your debt-to-income ratio, and what components make up the numerator and denominator of this ratio, is important in understanding how much you may qualify for in buying a home.
Monthly obligations include all of your monthly debts typically reflected on your credit report, such as car payments, student loans, credit card minimum monthly payments, existing mortgages that will not be paid off prior to the home purchase; plus, the new mortgage, taxes, insurance and home owner association fees that are expected on the home being purchased.
Gross income is the borrower’s income before deduction of payroll taxes.
Example: Borrower has the following debts:
Car payment $450
Student Loans $150
Credit cards $300
Estimated expenses of the home they are buying:
Principal and interest $1120
Taxes $240
Homeowners insurance $265
HOA Fees $100
Total debts $2625
Income – Annual Salary $75,000 – monthly income $6250
Debt-to-income ratio in this example is $2625/$6250 = 42%
The required debt-to-income ratio varies by loan program. Your lender can help you to understand your debt-to-income ratio, and what is required for various loan programs.
#3 Paying Points to Buy Down the Interest Rate
Borrowers often hear their lender say that they can get a lower interest rate by paying points.
Each point is 1% of the loan amount. For example, if you have a loan of $200,000 and the rate is 4.25% with no points, you may be offered a lower rate, possibly 4% with 1 point. The cost of that point is 1% of the $200,000 loan, or $2000.
In order to determine whether it is worth paying $2000 for the lower rate, you should consider the monthly savings at the lower interest rate vs. the $2000 cost of obtaining the lower rate. In our example, a $200,000 loan for 30 years at 4.25% will have a monthly principal and interest payment of $984. The same loan at 4.0% will have a monthly principal and interest payment of $955, thus a savings of $29 per month.
In this example, it will take approximately 69 months to recoup that additional cost ($2000/$29). Whether or not that expenditure makes sense for the borrower depends on many factors, such as how long they intend to live in the home, and personal preferences such as what other uses they may have for the funds.
#4 Monthly Payment
The more complicated mathematical formula is, “What will my payment be on a $200,000 loan at 4%?”
Fortunately, there are numerous mortgage payment calculators online, as well as spreadsheet functions, to help you easily come up with that number rather than calculating it by hand. Also, most spreadsheets have a PMT function (payment function) which allows you to put in the interest rate, number of periods, and principal balance to come up with a payment amount.
However, borrowers should also understand how their monthly payment is allocated between principal and interest, and the fact that in the early years of making their mortgage payments a higher amount will be allocated to interest rather than principal. That is because each month the interest is calculated on the principal balance remaining after the last payment. As the principal balance is reduced, the interest portion of the payment is reduced also, allowing a larger amount of the monthly mortgage payment to be applied to principal.
This is demonstrated as follows:
$200,000 loan at 4% interest to be paid over 30 years. Monthly payment $954.83.
In the first month the payment of $954.83 will be allocated as follows:
Interest – $200,000 x 4% divided by 12 months = $666.67. The remainder $288.16 goes to principal.
The following month, the principal balance is now lower because you have paid down $288.16.
The new interest calculation is: $199,711.84 ($200,000-$288.16) x 4% divided by 12 months = $665.71. That leaves $289.12 to apply to principal.
As you can see in the example above, more of the monthly payment is applied to principal each month, as the principal balance is paid down. And eventually, you will see a larger portion of the monthly payment applied to principal than to interest.
This is why making extra payments on your mortgage helps to reduce the overall interest paid over the life of the loan, and helps pay off the loan more quickly. In our example, anything paid over the $954.83 required monthly payment would be applied direct to the principal amount of the loan, requiring less interest to be paid over the life on the loan and paying the mortgage off more quickly. Here is an example:
Let’s say in the first month you paid $3954.83 – an extra $3000.
The calculation for the interest would not change. You would still pay $666.67 toward interest, but now you have a principal reduction of $3288.16 instead of only $288.16.
Let’s look at how that changes the second month calculation, if you pay your regular payment of $954.83.
The interest calculation is now $196711.84 x 4% divided by 12 months = $655.70. That leaves $299.13 to apply to principal rather than $289.12. That may seem like a small amount, but continuing to make additional principal payments over time will result in significant savings in interest and shortening of the mortgage term.
Your lender / mortgage broker should be willing to spend the time necessary to explain these mathematical formulas, and show you how they affect your mortgage. You are not expected to know these calculations and how to come up with them on your own, but a good understanding of these calculations will help you make wise financial decisions.
Marimark Mortgage
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