Appraised Value Math for Your Real Estate License Prep

OK in this episode of “Spruce Answers” we have a pretty hard math question that comes from the darkest depths of your real estate license prep. Let’s jump in and make it easy to understand!

So the question reads…

“If the mortgage loan is 80% of the appraised value of a house and the interest rate of 6% amounts to $460 for the first month, what is the appraised value of the house?”

Now there’s no “easy” way to accomplish this one. Because they want to know TWO unknowns. Real estate license prep all of a sudden seems VERY hard…

 You need to find (1) a mortgage loan amount and once we have that amount we can find (2) an appraised value… and the ONLY clues it gives is an amount of interest charged per month….

So let’s break down the question into three parts

  1. The mortgage loan is 80% of the appraised value
  2. The 6% interest rate amounts to $460 for the first month
  3. What is the appraised value of the house

Now that we see the 3 main parts of this I’d like to introduce a way of mentally converting the English wording of this question into a math equation. Breaking it down in this way allows me to make more sense of what we know and what we don’t know and honestly, I need to break this down as much as possible. Mathematical real estate license prep can become a lot easier is steps.

This English to math breakdown is actually quite easy.

English to Real Estate License Math Calculator
When you see the word “of” it means “to multiply”. When you see the word “is” it means “equals”.

There are two rules:

  1. when we see the word “of” in a question it will mean (multiply) and
  2. when we see the word “is” it will mean (equals)…

(so using this English to math translation part (1) of our breakdown would become…

 Mortgage loan = 80%  X Appraised Value 

Easy right?

Haha, no, not really because there are TWO unknown values in that equation. If we knew either the mortgage loan amount OR the appraised value then we could solve this using basic algebra, but the problem is they don’t give us that much info. We must solve for one first, so that we can then solve for another in a later step… so let’s look at part (2) of our breakdown and look for clues that can provide us with solving for one of the missing pieces in part (1).

The 2nd part reads “The 6% interest rate amounts to $460 for the first month”

Well that tells us the interest the loan charges in ONE MONTH but that’s not enough. We need to know how much interest it charges in a full year. Now, good for us converting 1 month into 12 months is easy. We simply take $460 x 12 and that’s the amount for the full year.

460 x 12 = 5,520

We now know that the loan amount produces $5,520

Ok, so that’s an important step so now that we know that the loan amount produces $5,520 of interest in a year and that’s at a rate of 6% we can work backwards and figure out the loan amount which is essential for plugging in the “mortgage loan” amount into the first part of this problem..

So how do we figure out the mortgage loan amount from knowing that the loan amount produces $5,520 in annual interest and they’re charging 6% to get that..

Well, is it fair to say   “ 6% of mortgage amount is $5520” ?

And if that’s fair to say, then let’s put that statement through the English to math translator where we substitute the words “of” and “is” and here is what we can conclude

6% x Mortgage Amount = $5,520


AND THAT MY FRIENDS IS SOLVE-ABLE real estate license prep

Because we are only missing ONE thing and when we’re missing just ONE thing we can do basic algebra. So let’s go through the basic algebra and solve for the Mortgage amount

Ok, we can write this .06 x Mortgage Amount = $5,520

Now do you remember how to isolate the one side of an equation from High School? It’s ok, it’s been a while for a lot of us, so let me refresh your memory if needed.

“It’s only fair to do to one side, what you do to the other side.”

Whatever you do to one side you HAVE to do to the other side. It’s really that simple. Doesn’t have to be complicated. I’ve been told by great mathematicians that “it’s only fair to do to one side, what you do to the other side.”

So as you can see we need to get that .06 OUT of the left side which we can do by dividing the entire left side by .06. When we do that the .06 on the left goes away (because it cancels out)…. but to do that we have to ALWAYS be fair, and do the SAME THING TO THE OTHER SIDE. So in this case we have to divide the entire right side by .06… which means we divide $5,520 by .06

Now what’s beautiful here is this now leaves JUST the Mortgage Amount on the left side and a NICE PLAIN NUMBER ON THE RIGHT SIDE which turns out to be $92,000… and that means we’ve figured out the mortgage amount! The mortgage amount is $92,000!!!

Now we can use that figure WAAAAY back in step 1 (from when we broke this down into 3 steps) so glance back at what we stated from step 1. We said

The mortgage loan is 80% of the appraised value.

So plug that statement into our brand new English to Math Translator

So plug that statement into our brand new English to Math Translator (and substitute “OF” with (multiply), and “is” with “=” and what do we have?

We have “the mortgage loan” = 80% x the Appraised Value

So let’s plug in our newfound mortgage loan amount and write this like such

92,000 = 0.8 x Appraised Value

We’re only missing ONE real estate license prep math variable!

Now just like earlier WE CAN SOLVE THIS WITH BASIC ALGEBRA because we are only missing ONE THING. And we find this the same way we found the earlier missing one. We isolate one side by dividing it by the amount that is there to cancel it out and then do that to the other side as well… to be fair. 😉

So in this situation we divide the entire RIGHT side by 0.8 so we can ONLY have the Appraised Value over there… and again, anything we do on one side we HAVE to do on the other side… so we then divide the entire left side by 0.8

So this looks like this

0.8 x Appraised Value/ 0.8 (on the right side) and 92,000/ 0.8 (on the left)

When we divide the right side it cancels out the 0.8 and we are left with JUST the Appraised Value and that means that the appraised value is just one step away… by dividing 92,000 by 0.8

When we divide 92,000 by 0.8 we GET $115,000 and THAT IS THE APPRAISED VALUE and is the answer the question was seeking

To anyone mathematically skilled in real estate license prep

Now, to anyone skilled in Algebra I’m sure this explanation was tedious and you might’ve even thought that it was too many steps. But honestly this breakdown is geared for those of us who haven’t seen algebra in a while… and wanted to see the many inner workings of this fairly complicated real estate problem… Thanks for bearing with me and I hope this helps someone.

Personally, I love the English to Math translator and it will be in my arsenal of math tools in the future. “Of” means multiply and “is” means equal. This MIGHT just help with many insane math problems to come.

If you found this breakdown easy to understand and have always wanted to gain your real estate license in WV look no further! Spruce School of Real Estate has been teaching online real estate classes in West Virginia since online real estate classes “was a thing”. Seriously! Are we showing our age now? Spruce was the first school native to West Virginia to be approved to teach in the distance education method of real estate license prep. For that fact Spruce KNOWS the best ways to deliver in an online world. For more info you can check out their Facebook page here. Their business page is also found here or searched using best real estate school online. Real estate license prep is made as easy as possible with Spruce’s visual showcase of otherwise hard to convey subject matter!

Discount Point Math for your WV Real Estate Licensing Exam

Today in “Spruce Answers” I’m going over the real estate math licensing concept of the discount point. This is easier than you might think . The question is… “If a house was sold for $360,000 and the buyer obtained a mortgage loan for $288,000, how much money would the buyer pay in discount points if the lender charged two points?”

What are the steps to solving this discount point math question?

I like this one because this is a pretty easy question. That is as long as you know the concept of a discount point. And since I’m trying to show how the concepts of these questions can be related to many variations why don’t I illustrate this concept here.

That said, the discount point is one percent…. Now there’s two twists on this within this question. One, it’s giving you two numbers to try and throw you off…. One of which you ignore because, well, it wants 1% of the loan amount and only one of those numbers is the loan amount.

Discount Point is 1% of the mortgage amount
A discount point is always 1% of the loan amount

It says the guy obtained a mortgage for $288,000 and that’s the number we now take 1% of. So…

Let’s calculate that… 1% of 288,000 is $2,880

Now the second twist… it says he is getting charged two points…. So… that’s 2%…. The way I do that is simply multiplying 2,880 by 2 which is $5760. Seems way more complicated than it is but if you know that a discount point is 1% you’re good to go.

Is this an easy breakdown?

Now that you’ve seen this breakdown, If you’re looking to get a real estate license in West Virginia you’ve come to the right place. Did you know that Spruce School of Real Estate has been teaching learners how to pass the WV Real Estate License Exam for over 25 years now? It has and we take pride in our presentations and easy breakdown for every kind of learning style. If you found this video tutorial helpful I think you’ll find Spruce School of Real Estate to be a smart choice for helping you learn the sometimes difficult concepts within. Feel free to find out more at https://sprucerealestateschool.com

Feel free to also check us out on Facebook here and get more info on the best real estate school in the state of WV and access to a live instructor 7 days a week.

Real Estate License Math NW1/4 of the SE 1/4 of section

Difficult Real Estate License Math for your WV Real Estate License

When you’re dealing with difficult real estate license math that we need to get your WV real estate license look no further than the best school for your West Virginia Real Estate License to explain. Honestly, I post these after students request an explanation. Hopefully you can see that enrolling at Spruce School of Real Estate is as valuable as you have heard. We care that much, and we work hard to keep proving that. So, the question handed out was yet again on sections, so let’s go over some background of what we possibly know so we can weed down the difficult portions and leave the easy.

Sections are 640 square acres. How did I know that? Well I could’ve memorized it or I could use some things we should know already. Let me show you how we can know it with just the few memorized numbers we already know. We know that a section is 1 linear mile across AND DOWN correct? We also know that a linear mile is 5,280 feet because of our memory tips in our lovely WV Real Estate Online Class that you registered for.

Ok, so the next step. We know how to calculate square footage which is length times width.  That means 5,280 x 5,280 is 27,878,400 and that means that that all sections are 27,878,400 square feet. Yes ALL of them 😉

Now we also know that a square acre is 43,560 feet because of our study tips in class. So if we divide 27,878,400 by 43,560 we get 640. So that means that ALL sections are 640 acres in total. Yes, ALL of them.

Now You See Why a Section is 640 Acres?

So that’s how I knew a section represented 640 acres.  OK so lets see what we can do with that number. Sections can be divided into halves (320 acres) and quarters (160 acres). So that’s the easy part. Then it has to get more confusing because EACH of those portions can then be divided again into halves and quarters. But its not terribly hard…. Its basic math. 40 acres here, 40 acres here, 40 acres here, 40 acres here. Do you see the logic? Good!Sections explained by WV Real Estate School

Now, there a reason I went into all this BEFORE I broke down the super confusing question. And that’s because the super confusing question doesn’t have to be that confusing question IF WE KNOW WHAT I JUST STATED.  In the end the question wants us to know how many acres. They give us a bunch of gibberish in there but the reality is they want you to calculate an acreage amount by the price per acre and tell them what that total price was.

So lets look at the question and tear it apart. Let’s make this real estate license math make sense!

If a farm described as “the NW 1/4 of the SE 1/4 of section 10, Township 2 North, Range 3 West of the 6th P.M.”

It reads, If a farm described as “the NW 1/4 of the SE 1/4 of section 10, Township 2 North, Range 3 West of the 6th P.M.” sold for $4,500 an acre, what was the total sales price?

Ok, so lets think about this? They want to know the NW 1/4 of the SE 1/4 . Lets place that on our sections grid to illustrate it. North, south, east, west to help us think it through. We start with the south east quarter so that here. And then they want the north west quarter of THAT, so that’s here.

Now you wanna know something that is crazy? We didn’t even need to map that out. I did because it makes more sense to explain the real estate license math IF we map it out but ALL we needed to know here was that they wanted to know a quarter of a quarter size… Does this look familiar from earlier in the video? Good 😊

So You See the Size is 40 Acres

And guess what? A quarter of a quarter of a section. will ALWAYS BE 40 acres. It doesn’t matter if it said it wanted the SE ¼ of the NW ¼ or the NE ¼ of the SW ¼, or any of that gibberish because all sections are divided up like this and they’re ALL a liner mile up and down, and they’re always gonna be a fixed size.

It also doesn’t matter if the question read:

A farm on Planet Neptune described as “the NW ¼ of the SE ¼ of section 40, Township 20, of the eastern coast of the Bahamas, past the 400th Meridian to the southern lake” BECAUSE IN THE END THEY JUST WANTED TO KNOW THE NUMBER OF ACRES IN A QUARTER OF A QUARTER OF A SECTION. Real Estate License Math Sections

Basically everything AFTER the description of “NW ¼ of the SE ¼” is totally irrelevant to the size of the acreage we need. We KNOW the size is 40 acres and then just do basic math here. 40 acres times $4,500 is $180,000

Now why did I go over all these steps to show you this? I did it so you can plug in a wide variety of numbers, prices, and scenarios , like they might throw at you at the national testing center and you can still get an answer, regardless of them changing details. Knowing these steps can allow you to answer a wide variety of real estate license math that is dealing with sections and land descriptions now.

By the way, you CAN enroll now to take Spruce’s online real estate classes by visiting https://www.spruceschoolofrealestate.com and clicking “enroll now” It’s THAT easy. You’ll then have access to the instructor for your real estate education needs all the time during your enrollment!

Real Estate Math Walk-Through Part 1 to help you get that WV Real Estate License

There are a few real estate math topics in your real estate license textbook that are very hard to make sense of

At Spruce School of Real Estate we have forums dedicated to JUST explaining real estate math and the instructor takes requests for more! Here’s a taste of what we produce to show you how we can take a math concept that’s seemingly impossible and by the end of the walk-through I’m fairly certain it will make sense. Spruce is all about high quality, clear explanations, of otherwise difficult real estate exam content. No gimmicks, just clear, concise real estate classes that anyone can understand.

Ok, so the question reads

How many acres are contained in the tract described as “beginning at the NW corner of the SW 1/4, then south along the west line to the SW corner of the section, then east along the south line of the section 2,640 feet, more or less, to the SE corner of the said SW 1/4, then in a straight line to the POB”?

And the answers they give are

  1. 80 acres
  2. 90 acres
  3. 100 acres
  4. 160 acres

First thoughts of mine are “are they trying to kill me with this!?”

But in reality this question really is quizzing us on what we understand about a section… in a LOT of detail. And believe it or not you DO actually know how to do this once we decipher their wording.

Spruce can help

You know a section is a square mile correct? Yes. So it’s a mile up and down, and a mile, left and right… which creates a square mile. You know that a linear mile is 5,280 feet (because you listened to me in class and you have the memory tip for that from your online real estate license class) … so one way it is 5,280 feet and the other way it is ALSO 5,280 feet. So, lets draw that out

When we draw it out we can basically just draw a square. We know that each side is 5,280 feet long. Now the confusing thing about the square isn’t that terribly confusing as long as you know north south east and west. The square is first divided into those portions.

The top right is North East ¼

The bottom right is south east ¼

The top left is North West ¼

And the bottom left is South West ¼

Say it in English!

Looking at the question we can pull from the cryptic wording that they’re interested in the South West portion so let’s make this easier now that we know WHERE the SW portion is and ONLY work within that area.

Now that we’re working JUST in that area we can now break THAT square up into regions using the same logic of north, south, east and west… so let’s draw that out to help illustrate it in your mind

We’ll start with the NW ¼

… and you see how the North West Quarter of the South West Quarter now makes sense and doesn’t make you cry? Yes, me too 😊. SO lets run with that and we’ll add the other three. We now can easily add the North East Quarter of the South West Quarter. Now the South West Quarter of the South West Quarter. And lastly the South East Quarter of the South West Quarter.

NOW, let’s look at the question and sort out where they want this “map” to happen. They say they want the map to begin at “NW corner of the SW ¼” sooooooo, we’re working IN the SW ¼ and we want to put a marker in the NW CORNER.

Then the question states to “go south along the west line to the SW corner of the section”. So where’s the SW corner of this section? It’s simply the bottom left. So, lets place another marker there. Now for point 3 it says to “go east along the south line of the section 2,640 feet, more or less, to the SE corner of the said SW 1/4,”

Huh?

Now, 90% of that is cryptic gibberish because we KNOW that a section is 5,280 feet long (in its entirety) and they want us to go HALF that at 2,640 feet to the right (seeing that they want us to go east… SOOOOO, place a marker half way across the section (which is 2,640 feet and places the marker here).

It’s a Triangle, it’s Connect the Dots! Do NOT Fear!

Now they say “in a straight line” go back to the point of beginning… which is easy… ITS CONNECT THE DOTS!!!! Let’s connect the remaining dots and this is the area they actually want to know how many acres it is!

So, why has FEAR all of a sudden crept into your brain? Because it’s a TRIANGLE BILLY!!!! But honestly this triangle thing is worth noting because I’ve heard of people seeing more and more on PSI (the testing facility that administers your WV Real Estate Exam) where they want you to calculate square footage within a triangle. So, let’s calm your fears

What is a triangle? Its half a square, is it not? Yes, and can you calculate square footage of a square? Yes, you can, so you can actually calculate the square footage of a triangle (half of a square) by simply calculating the square footage like it WAS A SQUARE and then dividing that in half! Wham, brain explosion stopped.

Real Estate Math Clearly Explained

So, using our memory tips

We know that the linear feet of the section is a mile, 5,280 feet… Look at the grid… are we using the whole mile? No, we’re using HALF OF IT so we are using 2,640 feet in the math and now doing what I just said above we can calculate the square footage like we would with a square but then divide that in two to get the triangles square footage sooooo

2,640 x 2,640 = 6,969,600 square feet (IF it was a square)

But it’s a triangle , which we know is half of a square, so divide by two

6,969,600/2= 3, 484,800

And we now know that THAT triangle has 3,484,800 square feet in it. BUT GEEEESH, WHAT DO WE DO WITH THAT NUMBER!!!! Well, we need one very important memory number. Remember the 43,560 memory tip, which is the square feet in an acre…. REMEMBER? Sure you do… Well that’s how many square feet are in ONE acre… so we can use that to figure this out

We have 3,484,800 square feet in our triangle so let’s take that number and divide it by 43,560

3,484,800/43,560

WAAAAAAAL AAAAAAA we get 80

There are 80 acres in that triangle.

What Did We Really Need to Know?

…to answer that super messed up hard question?

  • We needed to know what a section was in a very deep way.
  • We needed to remember our memory numbers 5280 and 43560 (which like in the course I stressed were very important for a multitude of application)
  • We needed to know the basics of a compass (N,S, E, and W)

Compass
A section can be broken down into the basics of a compasses direction.

Now I realize the wording of that was a BEAST but isn’t it amazing what we DO know, if we can just apply it? If you’re considering getting a WV real estate license look no further than Spruce School of Real Estate. We are as professional as the national corporations BUT with the added benefit of it being a small business, able to be there for you, answer questions when you need, without waiting on hold. Spruce School of Real Estate has offered pre-licensing courses so you can get your WV Real Estate License for 28 years now! No Gimmicks, just clear explanation and presentation. Whether it’s real estate math or real estate terms Spruce is the absolute best online real estate class in all 50 states, offered to you in WV simply because we live here! Sign up now by clicking the “sign up button” https://sprucerealestateschool.com/index.html