Real Estate Math Prep Guide

Math Prep Guide

Real estate agents are frequently faced with math calculations to determine commission, interest rates, and monthly mortgage payments, profit, and more. While some people are wary of math, it does not have to be challenging. In this session, you will look at basic concepts and formulas necessary to respond to the most typical calculations.

You’ll learn how to:

  • Measure square footage and acreage.
  • Calculate commission.
  • Calculate the net to seller.
  • Calculate annual interest.
  • Calculate percentage of profit and loss.

Measurements

There will be times when it’s necessary to calculate the area of property. For instance, when figuring market values of properties in the area, some properties may list the square footage of a bedroom, others may just provide dimensions. Real estate licensees will have to convert one or the other to make a comparison. The same is true for lot dimensions. Perhaps the dimensions of a lot are listed, but the client wants to know the size in acres. First, here is some key information:

Linear Measurement

12 inches1 foot
3 feet1 yard
16 1/2 feet1 rod, perch, or pole
5,280 feet1 mile, 80 chains

Cubic Measurement

27 cubic feet1 cubic yard
1 cubic foot7.48 gallons

Square Measurement

43,560 square feet1 acre, 10 square chains
2.47 acres1 hectare (10,000 square meters)
640 acres1 square mile
1 square mile1 section
36 sections1 township
9 square feet1 square yard

Area Measurement

To determine the area of a square or rectangular parcel, the equation is:

Area = Width x Length (AWL)
Area ÷ Width = Length
Area ÷ Length = Width

If given the area and length and asked to find the width, for example, divide the area by the length:

33,750 Square Feet ÷ 225 Feet (Length) = 150 Feet (Width)

Front Feet

Front feet, or frontage, is that portion of the lot that faces the street. In a measurement, the frontage is always the first number.

In this example, the lot is 125’ x 200’, so the frontage is 125 feet.

Triangular-Shaped Lots

Triangular, or pie-shaped, lots are also fairly common. There are two common ways to figure the square footage of a triangle:

Multiply half of the base measurement times the height: (200 ÷ 2) x 350 = 35,000 Sq. Ft.
Multiply the base times the height and divide by 2: (200 x 350) ÷ 2 = 35,000 Sq. Ft.

Irregular Lots

Like houses, irregular lots tend to be a collection of many squares, rectangles, and sometimes triangles. In the most basic sense, the total square footage can be determined by separating the house into individual shapes, figuring the square footage for all parts, then adding them together. In this simple example, the total measurement would be 1,775 square feet (1,250 + 150 + 375).

Acreage

There are 43,560 square feet in an acre. To find the acreage of a lot:

Square Footage ÷ 43,560 = Acres

For example:
George and Judy are looking for an empty lot to build a custom home, and they want at least half an acre. You have found a lot that you think is suitable for them. It measures 120’ x 200’. Will this lot meet their size request?

First, find the total square footage: 120 x 200 = 24,000 Total Square Feet
Then divide to find the acreage: 24,000 ÷ 43,560 = .55 Acres

Yes! This lot is just over half an acre. George and Judy should be pleased.

Perimeter (Linear Footage)

To find the perimeter of a lot, add the length in feet around the outside of all sides of the lot.

For example:

A 75’ x 50’ back yard would require 250 linear feet of fencing (75 + 50 + 75 + 50).

Cubic Measurement

Cubic measurement may be needed to determine the volume of something, for example, the airspace in a room or the amount of water in a pool.

Length x Width x Height = Volume

For example:
A pool is 12’ long, 8’ wide, and 6’ deep. The volume of the pool is:

12’ x 8’ x 6’ = 576 Cubic Feet
To convert cubic feet to cubic yards, it’s necessary to divide by 27:
576 Cubic Feet ÷ 27 = 21.33 Cubic Yards


Commission

When working with commission, the commission is the part, the commission rate is the percent, and the sale price is the whole:

Sale Price x Rate = Commission
Commission ÷ Rate = Sale Price
Commission ÷ Sale Price = Rate

For example:
Albany Real Estate sells one of its listed properties for $211,000. If the commission rate is 6%, what is the total commission?
0.06 x $211,000 = $12,660
The total commission is $12,660.

T-Math

Many real estate situations require the ability to calculate percentages, for example, commissions or property assessment. An easy method for solving these problems is called T-math. When using T-math, the horizontal line means divide and the vertical line means multiply.

When calculating percentages, the part goes on the top of the T. The percent goes on the bottom, and the whole goes on the bottom opposite the percent. When you know any two variables, you can easily find the third:

Percent x Whole = Part
Part ÷ Percent = Whole
Part ÷ Whole = Percent


Net to Seller

A seller’s share, or net to seller, is an estimate of the money a seller should receive from a real estate transaction, based on a certain selling price after all costs and expenses have been paid. This is not a guarantee but an approximation of what the seller should receive. The purpose of computing the net to seller is to let the seller know how much money he can expect to make from a transaction after everything has been paid. This is important information when considering both a listing price for the property and deciding whether to accept an offer.

For example:
Laney wants to sell her home. She must pay off her existing $35,000 mortgage and pay $3,200 in closing costs. She wants to have $40,000 left so she can buy another home. If she pays a 6.5% commission, what is the minimum offer she can accept? First, subtract the known commission rate from the total sale price to find the percentage of the sale the seller will net:

100% – 6.5% = 93.5%

Total up the other known expenses: $35,000 + $3,200 + $40,000 = $78,200

Finally, divide the total expenses by the net to seller percent: $78,200 ÷ 0.935 (93.5%) = $83,636.36

Laney must sell her house for a minimum of $83,637.


Principal and Interest

Interest is the cost of borrowing money, while principal is the balance of the loan. The T-math strategy can be used to solve problems involving interest. The annual interest is the part, so it goes on the top. The principal is the whole, so it goes on the bottom with the interest rate. If you know any two factors in the equation, you can easily find the third.

For example:
If the loan balance (principal) is $135,000 and the interest rate is 7.5%, the annual interest would be:

.075 x $135,000 = $10,125

That number, divided by 12, indicates the monthly interest on the loan balance. If the borrower makes a monthly mortgage payment of $985, it’s possible to see how much of that payment is applied to the principal that month:

$10,125 ÷ 12 = $843.75 Monthly Interest
$985 – $843.75 = $141.25 Applied to Principal


Return on Investment

If you know the original purchase price of the property and the eventual sale price, you can calculate the return on investment, also known as the percent of profit.

Profit ÷ Original Purchase Price = Percentage of Profit
or
Loss ÷ Original Purchase Price = Percentage of Loss

For example:
A parcel of land is purchased for $100,000 and later sold for $115,000. What is the percent of profit?

$115,000 (Sale Price) – $100,000 (Original Price) = $15,000 (Profit)
$15,000 ÷ $100,000 = 0.15 or 15% Profit

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