Helpful Math Formulas

Helpful Math Formulas

1. Loan-to-value ratio

The loan-to-value ratio (LTV) is a measure used to compare the amount of your client’s mortgage to the value of the home they wish to purchase. Mortgage lenders will often use the LTV to determine their risk in extending credit to your client as a borrower. 

Lenders favor a loan assessment with a low LTV because they see it as a lower risk. Contrarily, lenders see a high LTV loan assessment as a higher risk and may require your client to purchase mortgage insurance to offset that risk. 

As a real estate agent, you commonly use this equation to help your clients. 

Loan to Value Ratio Formula:

Loan Amount / Assessed Value of the Property = Loan to Value Ratio

The LTV ratio is typically expressed as a percent. For example, if the home value is appraised at $100,000 and your client’s mortgage lender offers them a loan for $80,000, then the Loan to Value Ratio for this house would be 80%.

2. The 28 / 36 rule (Qualification Ratio)

The 28/36 rule is used to determine how much house your client may qualify for based on their income. 

The 28 in this rule suggests the home buyer can qualify for 28% of their gross monthly income (before taxes). For example, if your client earns $12,000 monthly, they would qualify for a mortgage payment of $3,360. 

On the other hand, the 36 in this home buyer rule considers your client’s additional debt payments (student loans, car loans, etc.). In this case, you would multiply their monthly earnings of $12,000 by 36% and get $4,320. Your client’s total debt payment and the mortgage must be below $4,320.

3. Down payments

Purchasing a property, whether for living or investing, will require your client to provide a down payment. You can help your client determine their down payment with the formula below. 

Down Payment Formula:

Sale Price x Percentage Payment = Down Payment Amount

For example, if the house is worth $500,000, and the home buyer plans to provide the traditional 20% payment upfront, their total down payment amount will be $100,000.

4. Capitalization rate

The cap rate measures a real estate investment property’s profitability. It helps investors figure out how much money they can make and keep cash flow positive while managing rental properties without taking on too much risk.  

Capitalization Rate Formula:

Net Operating Income / Purchase Price = Capitalization Rate

Let’s say, for example, you have a rental property that costs $800,000 and generates $80,000 in rent. It costs $20,000 to maintain it over the year. All costs considered, the cap rate would look something like this:

($80,000 – $20,000) / $800,000 = 7.5%

5. Return on investment (ROI)

ROI is a measure of how much is made on a real estate investment when it’s sold. You can calculate ROI using the below formula. 

ROI Formula:

(Final Value – Initial Cost) / Cost = ROI

For instance, if you buy a property for $400,000 and sell it later for $450,000, the ROI would be:

($450,000-$400,000) / $400,000 = 12.5%

6. Prorated taxes

If you’re working with home buyers, they will typically pay a prorated tax amount at closing. To find this amount, you must first determine the amount of tax remaining on the property for the calendar year. 

By identifying the number of days remaining in the year and dividing it by 365, you’ll get the percentage of the tax bill that your buyer will need to pay. 

You can then multiply the above percentage by the amount remaining on the tax bill to get the final amount of property tax due at closing.

7. Mortgage payments 

Principal and interest 

The mortgage principal is the initial loan amount your home-buying client borrows from the bank to purchase a property. 

For instance, if your client has $160,000 cash to make a 20% down payment on a house of $800,000. Then, the initial loan amount they need from the bank would be $640,000. 

To determine the monthly interest rate, you’ll need to work with a mortgage lender to understand the annual interest rate for the mortgages in your area. Once you have the annual interest rate, you can divide the number by 12 to get a monthly rate. 

So, if the annual rate is 3%, the monthly interest rate will be 0.25%.

Monthly mortgage payment 

Use the formula below to determine how much your home-buying client will pay monthly on their mortgage. You can also use a free mortgage calculator to get this information. 

Monthly Mortgage Payment Formula:

P [ i(1 + i)^n ] / [ (1 + i)^n – 1] = M

M = monthly mortgage payment

P = loan amount

i = monthly interest rate 

n = number of payments (assume 30-yr, fixed)

Using the above example, let’s say the annual interest rate is still 3%, the mortgage payment will be:

M = $640,000(.0025(1 + .0025)^360)/((1 + .0025)^360 – 1)

M = $2,698

Private mortgage insurance

If your client plans to front less than the traditional 20% down payment, lenders will require them to secure private mortgage insurance (PMI). Your client should factor this cost into their total monthly mortgage payments. 

Homeowner’s insurance

Your client will need to consider the cost of homeowner’s insurance for their property. The price will vary based on several factors (e.g., location, home value, roof condition, etc.), but typically U.S. homeowners can expect to pay approximately $1000 per year for homeowners insurance. They may be able to qualify for cheaper insurance rates by adding certain safety features to their home. However, they will need to work with an insurance company to get an accurate quote. 

Property taxes 

You’ll also need to know how much a home buyer can expect their property taxes will be. The government charges them automatically, but it’s still important for buyers who understand this number because they may run into some unexpected costs down the road if those numbers change or go up unexpectedly. You can determine this using the below formula.

Annual Property Tax Formula:

Assessed Home Value x Local Tax Rate = Annual Property Taxes  

8. Price per square foot

Price per square foot helps you find the value of residential and commercial properties. To calculate this, take the property’s sales price and divide it by the square footage.

For instance, if the home has 2,000 square feet and the sales price is $400,000, then the price per square foot would be $400,000 / 2000 = $200.

9. Price-to-rent ratio

The price-to-rent ratio can help your clients estimate whether it’s cheaper (or more expensive) to rent or own property in their area. You can use the below formula to calculate this ratio. 

Price to Rent Ratio formula:

Median Home Price / Median Annual Rent = Price to Rent Ratio

10. Gross rent multiplier

Calculating the gross rent multiplier (GRM) will help determine a property’s value. To get this information, you’ll need the annual rental income and property purchase price.

Gross Rent Multiplier formula:

Purchase Price or Value / Gross Rental Income = Gross rent multiplier

For instance, if the property’s value is $200,000 and the annual rent income is $24,000, then the GRM for the property would be:

GRM = 200,000 / 24,000 = 8.3

Compare it to the other properties in the area to see if the purchase is fair. Generally, you’ll want a lower GRM because it indicates the property is undervalued.

11. 70% Rule

The 70% rule helps you and your client determine whether or not they should invest in a property. Generally, a buyer should not invest in a property for more than 70% of the After Repair Value (ARV) minus any renovation costs. 

70% Rule formula:

(ARV) x .70 − Estimated repair costs = Maximum buying price

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