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.
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. Simple Interest Formula
This formula tells a home buyer how much the total cost of a purchase is, including the purchase price and interest cost.
You find simple interest by taking the principal (p) and multiplying it times the interest rate (r) times the time frame of the loan (t) plus 1. It looks like this:
A = p (r*t + 1)
So if a buyer purchases a $100,000 home with a 30-year loan at 5% interest, the total amount paid over the course of the loan would be:
$100,000 (.05*30 + 1) = $250,000
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:
Purchase 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. Cap 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. Real Estate Math: What You Need to Know to Calculate 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]
In this formula, P = principal loan amount, i = monthly interest rate, and n = number of months required to repay the loan.
To figure out the number of months required to repay the loan, you must first figure out the loan term. Most commonly, loan terms are 15 or 30 years.
Whatever the loan term is, multiply it by 12 to determine how many months the buyer will need to pay the loan.
Once you determine the value of M, you will need to add on the cost of mortgage insurance, homeowner’s insurance, and property taxes to get the full monthly amount that your client will be paying.
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.
Next, you will need to find out the mill levy, which represents the local government’s tax rate as 1/1000 of a dollar. You can find this value at the tax assessor’s office or on your local government’s website.
Then, you will have to convert the mill levy to a percentage value. For example, if the mill levy in your area were 70, the percentage would be 70/1,000 = .070.
Once you have these two numbers, multiply the assessed value of the home by the mill levy to find the amount of property taxes the buyer can expect to pay.
For example, if the home’s assessed value was $50,000, and the mill levy was .070, then the amount of property tax would be: $50,000 x .070 = $3,500
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.
How do you feel about real estate math? Do you have a hard time with math, or find it easy to learn? Let me know in the comments below!
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