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
- The mortgage loan is 80% of the appraised value
- The 6% interest rate amounts to $460 for the first month
- 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.
There are two rules:
- when we see the word “of” in a question it will mean (multiply) and
- 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
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.
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