# Welcome to our Real Estate Math Help Section.

Math is one of those things that people either love or hate and Real Estate Math doesn’t fair any better. Unfortunately, we can’t ignore math, but we can conquer it. The school exam and the state exam are both multiple choice exams and contain only 10% math. So even if you got EVERY SINGLE MATH QUESTION WRONG, you could still pass both exams. In real life, we do use math, but most of it is very simple. We add, subtract, multiply and divide every time we write a contract or do a CMA for a buyer/seller.

We also need to know how to calculate our commission!

Our goal is to help you through the math required to pass the state exam. This is a growing library so if you have an idea for a math video or need help to a specific question, just let us know. Call us at 407-674-7477 and we’ll have an instructor walk you through it or write to us at info@REAOrlando.com.

# Loan to Value Ratio

A home was purchased with a down payment of $15,000 and a loan of $250,000 at 5.5% interest for 30 years. Monthly payments are $1419.02. What is the loan to value ratio?

## Solution

- $15,000 + $250,000 = $265,000 Sale Price
**$250,000 ÷ $265,000 = .94 LTV**

## Notes

In this example the sale price was not provided, so we had to calculate that number first. Also, be sure to read the question carefully since there may be extra information that isn’t need and is just there to confuse the test taker. The extra info here that isn’t need is the interest rate of 5.5% and the 30 year term of the loan.

# Index Lease

A building rents for $25 per square foot with an index of 1.2. The index increases to 1.5. What is the adjusted rental rate?

## Solution

**Option #1 **

- 1.5 – 1.2= .3 difference in index.
- .3 difference ÷ 1.2 = .25
**$25 per sq/ft x 1.25 = $31.25**

**Option #2 **

- 1.5÷1.2=1.25
**25 x 1.25 = $31.25**

## Notes

Another name for an index lease is a Variable Lease or Variable Rate Lease. This is similar to an adjustable rate mortgage, but in this case it’s a lease not a loan.

Watch out for half complete answers in the multiple choice answers. Be sure you’re solving the entire problem. I’ve seen some students finish step 1 in Option#1 to get the difference in the starting and new index (1.5-1.2 =.3) and then skip the 2nd step and move right to step 3 $25 x .3 = $7.5. This s the wrong answer, but if it’s one of the four multiple choices it can look pretty enticing. Don’t get fooled!

# Total Obligations Ratio

A prospective borrower has an estimated monthly housing expense of $495 and his monthly obligations total $723. If the borrower’s monthly gross income is $2125 what is the total obligations ratio?

## Solution

$723 monthly obligations ÷ $2125 Monthly Gross income = **34% Total obligations ratio**

## Notes

When you see a Total Obligations questions like this one, always be sure to read the question carefully. In this case the housing expenses of $495 are already included in the Total Obligations of $723. Where I see a lot of mistakes is students adding this to the $723 and then over-estimating the Ratio. In most cases if it says Total Obligations are $x,xxx.00 then the housing expenses are included.

Also, be sure to pay attention to the loan type and property type. If you need to add the housing expenses manually (not in this question), then look out for additional monthly housing expenses. For Example, FHA loans have an additional monthly fee for the MIP, Condos and Coop will have common charges and maintenance fees, while HOA’s will usually have a monthly HOA fee.

# Amortizing a loan

A buyer has applied for a 20-year mortgage of $65,000 at 5 5/8 % interest. How much of the $452.23 monthly payment paid in the second month will apply to principal?

## Solution

- $65,000 x .05625 = $3656.25 annual interest
- $3656.25 ÷ 12 = $304.6875 rounded to $304.69 interest Month #1
- $452.23 – $304.69 = $147.54 applied to principal Month #1
- $65,000 – $147.54 = $64,852.46 New Principal amount.
- $64,852.46 x .05625 = $3647.95 annual interest
- $ 3647.95 ÷ 12 = $303.9959 rounded to $304.00 interest Month #2
**$452.23 – $304.00 = $148.23 applied to principal Month #2**

## Notes

The good news about amortizing a loan is that in real life you never have to do it! We use mortgage calculators on our smart phones to show the amortization tables to customers if needed. Also, many times the best person to discuss the details of the financing for the buyer is the Mortgage Broker. However, it is still important for us to be knowledgeable about the details.

I’d recommend you watch the video on this one, because it’s easier to watch someone solve this type of problem, rather than a written out solution. I will say to be sure to check your work, you should have different numbers for Month 1 and Month 2, if they are the same, you missed a step.

# Prorate Prepaid Rent

A duplex is scheduled to close of Feb 15 (not a leap year). The seller collected rent for Feb at the first of the month amounting to $658 per unit. According to the purchase and sale agreement, the buyer is due the rental income for the day of closing. Calculate the proration using the actual number of days in the month.

## Solution

REMEMBER IT’S A DUPLEX 2 UNITS

- 28 days – 14 days to seller = 14 days due to buyer
- 1316 total monthly rent ÷ 28 days = $47 per day
**$47 x 14 days = $658 Credit to buyer and $658 Debit to Seller**

## Notes

When solving prorate questions like this, be sure to count the correct number of days that will allotted to the buyer and seller. I often see students assuming that if a property closes on the 15th of the month then that is always a 50/50 split between the buyer and seller. It only works in a 28 day month like Feb. Also in this example, the day of closing belonged to the buyer, this means that the seller stopped owning the property as of 11:59:59pm the night before. All rent from the day of closing forward now belongs to the buyer.

# Percentage of Profit

A Developer purchased two 150-front-foot lots for $37,500 net each and divided them into three 100-front-foot lots. The developer sold the lots for $340 per front-foot. Calculate the developer’s percentage of profit (round answer to nearest whole percent).

## Solution

- $37,500 x 2 lots =
**$75,000 Cost** - 100 x 3 lots = 300 front feet
- $340 x 300 front feet =
**$102,000 Revenue** - $102,000 – $75,000 =
**$27,000 profit** **$27,000 ÷ $75,000 = .36 rounded to 36%**

**Amount made on sale (profit) ÷ total cost = Percent Profit**

## Notes

The video above does a great job of illustrating what is happening with the lots. I always recommend drawing a visual to help yourself organize what is happening in the question. While this is a percentage of profit question, we would solve the percentage of loss the same way except we would take **TOTAL LOSS ÷ TOTAL COST = % LOSS**

# Reproduction Cost New

You are appraising a three year old, single-family residence. The total square footage of the livable area is 2,250. The garage is 550 square feet. According to figures obtained from a cost estimating service, the base construction cost per square foot of livable area is $57 and $38 per square foot for the garage. Calculate the reproduction cost new of the structure.

## Solution

- 2,250 square feet x $57 = $128,250
- 550 square feet x $38 = $20,900
**$128,250 + $20,900 = $149,150 reproduction cost new**

## Notes

This is a pretty straightforward multiplication problem. Luckily in this question we kept it tame and didn’t add any geometry like calculating the area of a rectangle (length x width). However, one variation of this type of question could require you to calculate the square footage of each space. If so, just break down complex shapes into squares and rectangles.

# Calculate Commission

A sales associate, while working for the broker, acquired a listing for $325,000 at a 6% commission rate. A second sales associate, who works for another brokerage office, found the buyer for the property. The listing and selling brokers agree to a 50-50 split between the two offices. The property sold for the listed price. The selling broker kept 40% of the commission received by the selling office. How much did the selling office sales associate receive?

## Solution

- $325,000 sale price x .o6 =
**$19,500 total commission** - $19,500 ÷ 2 =
**$9,750 selling office split** **$9,750 x .60 = $5,850 Selling office sales associate’s commission**

## Notes

This is everyone’s favorite question and you better get this right:) The only stumbling block I see often is in the terminology of who is who in the transaction. Many often confuse the Selling Agent with the Listing Agent. Remember, the Selling Agent represents the Buyer and the Listing Agent represents the Seller. Without a buyer, no selling is going to happen. Also, remember we don’t get paid to take listings, they have to sell too. So be sure to choose your listings carefully and price them correctly.

# Vacancy and Collection Loss

A multifamily unit consists of 7 two-bedroom apartments that rent for $950 per month and 13 three bedroom apartments that rent for $1,250 per month. The vacancy and collection loss is estimated to be 8%. Management is 5% of effective gross income. What is the annual vacancy and collection loss allowance for this property?

## Solution

- $950 x 7 units = $6650 x 12 months = $79,800
- $1250 x 13 = $16,250 x 12 months = $195,000
- $79,800 + $195,000 = $274,800 PGI
**$ 274,800 x .08 V&C = $21,984 Vacancy and collection loss**

## Notes

While this is a pretty simple math problem (PGI x 8%), it does require you to understand the larger context here of calculating both PGI: Potential Gross Income and EGI: Effective Gross Income. We’ll do another video shortly to explore these in greater detail which will lead to us solving for NOI: Net Operating Income. For now, watch out for extra info that isn’t needed for the answer. In this question, we don’t need to know the 5% Management fee and we’re not even calculating the EGI.

**Here is the Full Formula to solve for EGI and NOI: Net Operating Income**

PGI

-V/C

EGI

– OE: Operating Expenses

NOI: Net Operating Income

# Doc Stamps & Intangible Tax

Calculate all applicable documentary stamp taxes and intangible taxes for a property located in Orange County:

- Purchase price: $72,525
- Earnest Money: $3,000
- Recorded first mortgage (assumed): $29,700
- Second Mortgage (new): $15,800
- Cash at closing: $27,025

## Solution

**Doc stamps on deed:**

- $72,525 purchase price ÷ $100 = 725.25 ROUNDED UP = 726
- 726 x .$70 rate = $508.20 Doc Stamps on Deed

**Doc stamps on note assumed:**

- $29,700 ÷ 100 = 297 x .35 rate = $103.95

**Doc stamps on note new:**

- $15,800 ÷ 100 = 158 x .35 rate = $55.30

**Intangible Tax on new mortgage:**

- $15,800 x .002 = $31.60

**Total Taxes paid = $508.20 + $103.95 + $55.30 + $31.60 = $699.05 **

## Notes

This one is a pain in the butt, because it requires you to remember a few important things, the rate of each tax, what the taxes are for and are we multiplying the rate by Sale Price or Loan Amount.

**Each of these taxes are assessed against a certain document presented at the closing table.**

- The DEED: This is taxed at $.70 per $100 of Sale Price or fraction thereof.
- The Mortgage: Think of this as a recording fee and is taxed at $.002 per $1 of Loan Amount.
- The Note (promissory note): This is taxed at 1/2 of the Deed or $.35 per $100 of Loan Amount