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.

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. I’m constantly adding material to this site so please come back often.

Proration Practice Examples (Blog Post)

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.

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

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.

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

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.)

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.

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%

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** +

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

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)
- 15 + 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 $0.70 = $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, (30 – 24 = 6 days) October 25th through 30th (day of closing goes to the seller).
- 60 + 6 = 66 days

**UPDATED 12/06/14:** For more examples for proration of taxes please click here. There are 20 examples to help you build your understanding and skill set for prorating.

Now we multiply the daily rate of $4.50 x 66 days and $297.00 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

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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

You’re welcome I had to see how this worked

Excuse me Admin- is this related to the T method

Donny – the T method is another way to get the same results. It’s easy to use and will defintely help illustrate my examples. I will write a post about it soon. Thanks again, I really appreciate your feedback. Travis

hello, this will be my third attempt to pass the real estate exam. There are at least 6-12 math questions and I never get any correct. do you have any advice or math drills that I can practice to get an idea of what I am doing wrong. most of the questions are about prorating taxes and using certain months or calculating period and I am very confused on the steps. Are the same steps used in every calculating problem? Kirsten

Hey Kirsten, please give me a few days and I will pull some material together for you. Thank you for reaching out to me. Travis

Hey Kirsten, I just added a new post with some math exercises to help you (click here). Please check it out and let me know if it helps. If you have any other questions please let me know and I’ll try to provide some more help. Thanks for reaching out to me. Travis

Thanks Travis this was so helpful. I just a little confused with the dates for the buyer. My answers were 1 day off because I always thought if you are figuring out what the buyers owes at closing, for example with taxes, you always count the next day, because the seller was responsible for the day of closing. Ex: Closing May 2nd. I would count May 3rd thru May 30 = 27 days, then June – December = 30 x 7 = 210 days. Am I doing that incorrectly? I’m also having a hard time with the math and will be taking my exam soon, so I would appreciate any help.

Q. Purns,

Thank you for the comments and questions regarding proration and the calculating of number of days. The rule I like to use is essentially this:

– For the Seller – use the date of closing as the number of days in the month. Example – if the closing date is June 24th then I would give 24 days in June to the seller. That’s the easy part.

– For the Buyer – I take 30 days and subtract the date of closing. For a June 24 closing, I take 30 – 24 = 6 days to use for the buyer calculation.

In your comment, you used the example of May 2nd of closing. Take 30 days minus 2 days (30 – 2 = 28 days). You are correct with my assumption that the seller is responsible for the day of closing. So yes, you should count May 3rd for the buyer calculation so try think of it this way – if May 1st and 2nd go to the seller then the other 28 days in the 30 day month go to the buyer.

If you haven’t already, please check out my latest post (click here) and look at the examples there to see if that helps. If there are any other math topics that you’d like for me to address I’d be glad t provide more examples. Thanks! Travis

Hello, Thank you so much for creating this page. It was unbelievably helpful. I did get a little confused with one little part with the proration examples. I did the math as well, and I could be wrong so I just need an explanation. For the first example I got the buyer only owing for 224 days. 14+210= 224. Which led to owing 156.80 for the buyer. Then in the second example october 25th-30th is only 5 days not 6, which leads the buyer to owing for 65 days. Thank you again for your help, please respond at your convenience.

Angelica

Angelica,

First of all, let me say THANK YOU! I had a typo in that first example. It should read “15” + 210 = 225. The 14 was not correct and I updated the page. But let’s take another look at the number of days in the two examples you mention:

If closing if May 15th and we’re assuming a 30 day/month calendar then the seller gets the first 15 days (including the day of closing) and the buyer gets the last 15 days of the month. 30 days in the month minus the date of closing since it goes to the seller is 30 – 15 = 15 days to the buyer.

This works for your second question as well – If closing is October 24th then the seller gets 24 days and the buyer gets (30 – 24 = 6) 6 days.

Does that help? Please check out my response to Q. Purns question and my latest post (click here) for more examples on proration.

Also, please let me know if you find more typos :-).

Thanks again,

Travis