# Real Estate Math

Hello All,

One of the main reasons that I launched this site is to provide a resource for aspiring agents to learn more and/or get a quick refresher on essential math skills that will be needed to pass a real estate exam and then be used in every practice of being an agent.

Currently, I have the written posts on the following subjects. Please click on the links below to see more about each topic. As always, I appreciate your input and welcome any comments to improve this sight.

#### Foundational Skills:

#### Financial Math in Real Estate:

#### Proration (Prorating Fees, Taxes, etc.)

**Starting with the Basics (Fundamental Math Concepts)**

**Building on a Solid Base**

A home that stands firmly up to the elements and time is most likely built on a solid foundation. The purpose of this post is to help establish a solid foundation of the basic math skills needed to kick start your understanding of real estate math.

**ROUNDING DECIMALS**

Basic rule for rounding is this – the digit you want to round is less than 5 then round down. Conversely, if the digit is 5 or greater then round up.

**Example 1:**

Round the following number to 2 decimal places:

1.33345 = 1.33 (because the 3^{rd} digit is a 3 you should keep the second digit the same).

**Example 2: **

Round the following number to 2 decimal places:

1.33645 = 1.34 (because the 3^{rd} digit is a 6 you should round up the second digit, 3 becomes a 4).

Since most of you will use calculators for solving your math problems you will have some rounding that will need to take place. For this post and all of the examples we will assume the decimals will be rounded to the 4^{th} decimal.

Example:

Let’s say that you have to calculate 600 divided by 7 = 85.71428571…

Rounded to the 4^{th} decimal place will be 85.7143

The 5^{th} digit after the decimal is an 8 so you round up the 3^{rd} digit from a 2 to a 3.

Now you round the examples below to the 4^{th} decimal:

- 8 ÷ 3
- 7 ÷ 3
- 12 ÷ 11

Answers: a) 2.6667, b) 2.3333, c) 1.0909

**CONVERTING FRACTIONS**

A fractions top number is the numerator and the bottom number is the denominator. To convert fractions to numbers simply take the numerator and divide it by the denominator.

Examples: 1/2 = 1 ÷ 2 = 0.5

2/3 = 2 ÷ 3 = 0.6667

3/4 = 3 ÷ 4 = 0.75

Real Life Example:

Mr. Buyer would like your help finding a lot that is at least a 3/4 of an acre. A fellow agent tells you that he may have the perfect lot for your client that is 5/8 of an acre.

Will the lot meet the requirement of your client?

Answer: Mr. Buyer wants a lot to bigger than 3/4 of an acre (3 ÷ 4 = 0.75 acres). The lot that your fellow agent mentioned to you is 5/8 of an acre (5 ÷ 8 = 0.625 acres).

So the answer is **no.** The lot is not big enough for your client.

**PERCENTAGES**

Converting a percentage is as simple as moving the decimal place two digits to the left.

50.3% = 0.503

Let’s say you have a percentage without a decimal such as 6%. The procedure is still the same:

6% = 0.06

To convert a number to a percentage the process is just reversed.

0.654 = 65.4%

Example:

You have a buyer that has placed an offer on a $130,000 home and your commission rate is 3%. How much is your commission?

3% = 0.03

0.03 x $130,000 = $3,900

**MEASUREMENTS**

Here are some basic units of measure that you should commit to memory:

1 foot = 12 inches

1 yard = 3 feet

1 Square yard = 9 feet

1 acre = 43,560 square feet

(Helpful hint: Something that helped me remember it was my real estate professor told us to think of the store Seven Eleven to remember how many feet are in an acre, 4+3=7 and 5+6=11 so on acre is 43,560.)

1 mile = 5,280 feet

1 square mile = 640 acres (5,280ft (1 mile) x 5,280ft (1 mile) = 27,878,400ft ÷ 43,560ft (1 acre) = 640 acres.

(You probably don’t need to commit the square mile to memory but understanding how it’s calculated is good to know.)

**Financial Math in Real Estate**

As a real estate agent you will have many conversations with loan officers. Some of the common terms you will hear include interest rates, LTV, discount points and debt to equity income. Below, I give a few examples of each of these and try show the relevance to real estate agents.

**INTEREST RATES**

Probably the most common term you will hear is **interest rate**. Every loan will most likely have an interest rate. The interest income generated from the loan is a vital source of revenue for the lender. For the borrower, it is cost associated with borrowing money. Let’s look at some examples of calculating simple interest:

Your buyer wants to borrow $100,000 to purchase their home and the lender is charging 4.5% interest per year. How much will your buyer pay in interest the first year of the loan?

$100,000 x 4.5% = $100,000 x 0.045 = $4,500 of interest the first year.

Since educators like to mix things up on exams let’s change things around a bit:

If we know that your borrower is being charged $9,000 for her first year of interest on a loan of $225,000, then what is the interest rate the lender is charging?

$9,000 (interest) divided by $225,000 (loan amount)= 0.04 = 4.0%

**LOAN TO VALUE RATIO**

LTV stands for **Loan to Value**. Lenders are concerned with how much money they will lend your borrower as a percentage of the appraised value of the desired home.

For example, if your borrower wants to buy a home for $100,000 and has $5,000 available to use as a down payment, the bank will have to lend $95,000 ($100,000 minus $5,000) for the loan to happen.

The Loan to Value calculation will be:

$95,000 (loan amount) divided by $100,000 purchase price = 95% LTV

Let’s think about it a different way:

If your buyer wants to purchase a $300,000 home and the lender will lend up to 90% of the loan, how much will your borrower need as a down payment?

$300,000 x 90% = $270,000 loan amount

$300,000 (purchase price) – $270,000 (loan amount) = $30,000 needed for a down payment.

Real life, however may not always be so clean cut. Let’s use the example above and say that the sales contract was written with a $100,000 sale price but the appraised value is comes $97,000. What does this mean to the buyer?

It’s likely the lender will only finance up to the appraised value of $97,000 minus any required down payment. So, if the lender requires 5% down payment and the house appraised for $97,000 what are the buyers options?

The buyer can walk away from the contract which can mean the loss of earnest money and/or any due diligence/option fees already paid.

The buyer can go back to the seller and ask to renegotiate since the house did not appraise for the asking price.

The buyer can go ahead with the contract as it stands and come up with the difference needed to make the deal happen. So let’s calculate what the buyer will need to do this:

Appraised value = $97,000

Bank requires 5% down payment = 5% x $97,000 = ** $4,850** from buyer

To satisfy the contract the buyer will need to make up the difference between the appraised value and the contract price. $100,000 (contract price) – $97,000 (appraised value) = *$3,000*

So the buyer will need to bring to closing ** $4,850** +

**=**

*$3,000***$7,850**

**DEBT TO INCOME RATIO**

The debt to income ratio is a great calculation that every buyer should be aware of and know how to calculate. It will help them understand how much of a monthly home payment they can afford and still buy groceries and pay other bills. It compares the gross income with the recurring debt (car payments, child support, student loans, etc).

If your buyer’s annual gross income is $65,000 and is using a lender that has a limit of 31% of income used for housing and a 43% total monthly debt limit, what is their maximum monthly house payment they can have and how much additional debt will the lender allow?

Housing Calculation (31%) – $65,000 x 31% = $20,150 / 12 months = $1,679

Total Debt Calculation (43%) – $65,000 x 43% – $27,950 / 12 months = $2,329

Total Allowable Debt $2,329 – Housing Debt $1,679 = $650 remaining for other Debt

What if the buyer above has $1,100 in monthly debt? How much will the lender allow for monthly house payments?

Total Allowable Debt $2,329 – $1,100 monthly debt = $1,229 remaining for housing.

Thank you for stopping by and reading this post. I hope it was helpful, and welcome your questions. Please leave comments on how I can make it better and more useful to you. Real Estate math can be a big stumbling block for people. My goal is to make it easier for people to understand and put it into practice.

Blessings,

Travis

**Proration (Prorating Fees, Taxes, etc.)**

One common type of math calculation that you will make as a real estate agent is called a proration. Proration for our purpose here is simply the portion or percentage that the buyer and seller pay/owe for various items at closing, such as HOA fees, taxes and fuel.

One common proration calculation is the HOA (Home Owner Association) fees that each the buyer and seller will pay at closing. Let’s look at an example:

Closing is May 15th and the HOA fees are $252 for the calendar year. They are based on the calendar year and have not been paid for the current year. The buyer and seller must divide up this fee by the amount of time each will be

in the home for the current year.

*Please note: I will use the “Bankers Calendar” which says that each month has 30 days and each year has 360 days (makes it much simpler to remember and was used in my own pre-licensing course).*

So let’s break this down into smaller steps:

First let’s calculate what the daily expense is for HOA fees:

- Annual fee is $252 divided by 360 days = $0.70/day.
- Now we will calculate the number of days each party will owe for the year
- The seller will pay for HOA Fees from Jan 1st through May 15th (day of closing)
- The buyer will pay for HOA Fees from May 16th through December 31st.

How may days does the seller have to pay for HOA fees?

- January through April (30 days x 4 months = 120 days) plus the 15 days in May.
- 120 days + 15 days = 135 days

Now what about the buyer?

- May 16th through May 30th (30 days – 15 days from seller = 15 days) plus June through December (30 days x 7 months = 210 days)
- 14 + 210 = 225 days

So as a check, let’s make sure we did it correctly; 135 + 225 = 360 days in a year. Looks like we’re good!

The last thing to do is to multiply the days each person is responsible for by the daily rate:

- The seller owes 135 days x $0.70 = $94.50
- The buyer owes 225 days x $0.56 = $157.50

Now, let’s check the math to make sure that the total $252 get’s paid:

- $94.50 + $157.50 = $252.00, Yeah! I am all about checking the math to avoid errors.

Another common example of what prorations will be used for is calculating taxes owed. So let’s look at a tax example:

Let’s say that the property tax for a house is $1,620/annually and have already been paid for by the seller. Closing is October 24. Since the taxes have already been paid, the buyer will have to reimburse the seller for the taxes paid for October 25 through December 31st.

To start let’s calculate the daily rate:

- Taxes are $1,620/annually. So now we divide $1,620 by 360 days = $4.50/taxes per day

Now, how many days will the buyer own the home for this year?

- All of November and December (30 days x 2 months = 60 days)
- After closing on October 24th there will be 6 remaining days, October 25th through 30th (day of closing goes to the seller).
- 60 + 6 = 66 days

Now we multiply the daily rate of $4.50 x 66 days and $296.00 is what the buyer will pay at closing back to the seller for property taxes.

I hope this helps you better understand how proration works. If you have any questions please feel free to leave a message and I’ll get back with you soon.

Blessings,

Travis

ok , good for sales, what about property management,i.e GST and Management fee. Calculated monthly on total rent.

Andrew, so very sorry for the delayed response. I will include some helpful property management math examples in an upcoming post.

I will us this. Great source

Thanks Gloria. Please let me know if there is a topic that you would like for me to address in a future post.

Travis

Thanks for the sight, but I noticed that you have an error in the LTV section. 90% of $300,000 is $270,000 not $280,000.

Karen – Thank you very much for catching the errors and I’ve made the corrections. Please let me know if have any other feedback. I’m always open to ideas on how to improve this site.