The 9 Common Real Estate Math Formulas You Should Know
Whether you’re studying to pass the real estate exam or computing the mortgage payment for a client, you’ll need to know a basic level of math as a real estate agent.
This guide will walk you through the type of real estate math skills you’ll find in the state exam, as well as in every real estate transaction you take on once you earn your license.
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Real Estate Math: What You Need to Know to Work as an Agent
1. Loan-to-Value Ratio
This is the most common math problem that you will likely come across in your real estate career. The loan to value ratio follows this formula:
Loan Amount / Assessed Value of the Property = Loan-to-Value Ratio
The answer to this basic math problem gets expressed in a percent. So a home with a $100,000 value and an $80,000 loan would have a loan-to-value ratio of 80% because 80,000/100,000 equals .8 or 80%.
2. 28/36 Rule (Qualification Ratios)
When working with a homebuyer, knowing how much they potentially qualify for is extremely important. The 28 side of the 28/36 Rule says the buyer can qualify for 28 percent of their gross monthly income (before taxes). So for example, if the homebuyer earns $10,000 monthly they would qualify for a mortgage payment of around $2,800.
The 36 side of the rule takes into account additional debt payments (car loans, student loans, credit cards, etc.). Here you can still multiply the $10,000 by 36 percent to get $3,600. This means that their total debt payments plus mortgage need to be below $3,600.
3. Down Payments
Whether a buyer is buying an investment property or a home to live in, they will need a down payment.
To determine the down payment, use this math formula:
Sales Price x Percentage Down = Down Payment Amount
So if the purchase price is $100,000 and the buyer is using the traditional 20% down payment, you will have:
$100,000 x .2 = $20,000
4. Capitalization Rate
In an investment property, the cap rate is the amount the investor makes and takes home as income on the property. Knowing the cap rate helps an investor figure income and keep cash flow positive while managing rental properties.
Use this formula:
Net Operating Income / Purchase Price = Cap Rate
For example, say you have an income-generating rental property that costs $500,000 and brings in $50,000 in rent. However, it costs $15,000 to maintain over the year. Calculating the cap rate would look like this:
($50,000 – $15,000) / $500,000 = 7%
5. Return on Investment
ROI tells you how much you make on a particular investment when you sell it. Calculate ROI using this formula:
ROI = (Final Value – Initial cost) / Cost
So if you purchase a property for $250,000, then sell it later for $280,000, your ROI would look like this:
($280,000-$250,000) / $250,000 = 12%
Keep in mind that this is gross income on the sale. Any repairs the investor put into the property would also impact how much you make on the sale.
6. Prorated Taxes
Usually, most buyers will pay a prorated tax amount at closing. To prorate taxes, you must determine how much tax is remaining on the property for the calendar year.
To do this, find the remaining number of days in the year, and divide it by 365. This will give you the percentage of the tax bill that the buyer needs to pay.
Then, take that percentage and multiply it by the amount left on the tax bill. This will give you the amount of property tax due at closing.
7. Calculating Mortgage Payments
Principal and Interest
The mortgage principal is another name for the initial loan amount. This is the full amount that the buyer is borrowing from the bank. For example, if the buyer had $150,000 in cash to make a 25% down payment on a $600,000 home, they would need an initial loan amount of $450,000 from the bank.
To determine the monthly interest rate on a home, you’ll need to know the annual interest rate for mortgages in your area. You can get this number from any mortgage lender in your market.
Then, divide that number by 12 to get the monthly percentage. So for instance, if the annual interest rate were 3%, then the monthly rate would be 0.25%.
Calculating Monthly Mortgage Payment
To calculate the monthly mortgage payment (not including insurance and taxes) you can use this formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
M = monthly mortgage payment
P = loan amount
r = monthly interest rate (divide your annual interest rate by 12 to get this number)
n = number of payments ( usually, this is 30 years)
For our example above, let’s say the annual interest rate was 5%. To calculate the monthly mortgage payment, you would use:
M = $450,000(.00416(1+.00416)^360)/((1+.00416)^360-1)
M = $2,416
Obviously, if you’re working with a client and not answering a question on a real estate exam, it’s much easier to simply use a mortgage payment calculator. I like to use Zillow’s Mortgage Payment calculator as you can add in PMI, Insurance, HOA, Taxes, etc… Or if you’re looking to download an app to your phone, here is the app for iPhone and Android.
Private mortgage insurance (PMI) is required if the buyer makes a down payment below 20% of the home’s purchase price. This cost is added to the monthly mortgage payments.
The PMI cost will depend on what the lender states in the loan estimate, but it is typically between 0.2% and 2% of the mortgage principal. Usually, the PMI ends once the buyer has 20% equity in the home.
Some factors that determine PMI cost are:
- Loan term length – a shorter term means monthly payments will be higher, but 20% equity will be reached sooner.
- Loan-to-value ratio – if the buyer makes a down payment above 20%, PMI isn’t needed at all.
- Credit score – a higher credit score will get the buyer a better deal on a PMI cost.
There are four types of PMI you should generally be aware of:
- Borrower-paid mortgage insurance
- Single-premium mortgage insurance
- Split-premium mortgage insurance
- Lender-paid mortgage insurance
Next, you need to determine the cost of homeowner’s insurance. This will depend on a variety of factors, including:
- Home’s location
- Potential exposure to natural disasters
- Home’s value
- Coverage level
- Deductible amount
- Age of Home
- Roof condition
- Past claims
- Type of policy (there are eight types of homeowner’s insurance)
On average, homeowners in the U.S. can expect to pay around $1,000 a year for homeowner’s insurance. But to get an accurate assessment of how much this will cost your buyer, you will need to get a quote from an insurance company.
Buyers may also be able to qualify for cheaper insurance rates by adding some safety features to their homes, such as smoke detectors, storm shutters, or a new roof. However, ultimately the price will depend on the above factors.
Lastly, you’ll need to know how to calculate property taxes. While the government will charge property taxes automatically, it’s still a good idea to understand how much the buyer can expect to pay.
How much the buyer owes will depend on two numbers: the tax rate in the area they live in and the value of the home.
The home’s value isn’t just the purchase price that the buyer paid. To find the home’s assessed value, you will have to get in touch with the tax assessor who determined its value or look up the relevant property records.
Once you have the assessed value, multiply it by the tax rate to get the yearly property tax bill. This number is then divided by 12 to get the monthly amount that will be added to the buyer’s mortgage payment.
Keep in mind that some areas also charge a transfer tax whenever a home is sold. This is generally paid by the seller, but it’s still something you should be aware of.
8. Gross Rent Multiplier
The gross rent multiplier (GRM) is a calculation used to determine a property’s value. It takes into account the annual rent income and the property’s purchase price.
To use the GRM, you will need to know the following:
- The annual rent income
- The purchase price
The GRM formula is: GRM = Purchase Price or Value / Gross Rental Income
For example, if a property is purchased for $200,000 and the annual rent income is $24,000, the GRM would be: GRM = 200,000 / 24,000 = 8.3
This number can then be compared to similar properties in the area to see if the purchase price is fair. Generally speaking, a lower GRM is better, as it indicates the property is undervalued.
9. Price Per Square Foot
This is likely one of the easiest but most used real estate math problems you’ll solve throughout your career. You’ll use it when valuing both commercial and residential properties. To calculate the price per square foot, simply take the sales price or value of the property and divide it by the square footage.
For example, if a home is 2,000 square feet and is purchased for $400,000, the price per square foot would be: 400,000 / 2,000 = $200
This calculation can also be used to find how much a property is worth per square foot. So if you know the sales price or value, you can use this equation to find out the approximate square footage of a property.
Real Estate Math: What You Need To Know to Prepare For the Exam
There are many mortgage calculators out there that you can use to double-check your math and see if you’re on the right track.
However, you’ll need to know all of these real estate math concepts in order to pass the real estate license exam successfully. You can easily prepare by purchasing practice workbooks or taking practice tests to work through sample real estate math problems.
Check out my other post to learn more tips for passing the real estate exam.
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Thank you for sharing knowledge and good information.
I know the PSI National Salesperson and Broker exam outline we have is as follows:
XI. REAL ESTATE CALCULATIONS (Salesperson 10%; Broker 8%)
A. Basic math concepts
1. Loan-to-value ratios
2. Discount points
4. Down payment/amount to be financed
B. Calculations for transactions
1. Property tax calculations
3. Commission and commission splits
4. Seller’s proceeds of sale
5. Buyer funds needed at closing
6. Transfer fee/conveyance tax/revenue stamps
7. PITI (Principal, Interest, Taxes and Insurance) payments
C. Calculations for valuation, rate of return (BROKER ONLY)
1. Net operating income
3. Capitalization rate
4. Gross Rent and gross income multipliers
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Thanks! That’s great info.