CHAPTER TWENTY-FOUR
MATH - SECTION 5 - Proration Problems
INTRODUCTION TO REAL ESTATE MATH
Math is a part of the real estate profession, as it is of most careers. The amount of math and the complexity of the math will vary, depending on the area of real estate chosen. Today, we have calculators and computers that are great time-savers, but we still need to have a good basic knowledge of math. It is a matter of taking the math concepts we were taught in school and adapting them to the real estate profession.
People react differently to the word math. Some people like math. Some people are comfortable with math. Some people, though, are uncomfortable with math and become very anxious and stressed when they encounter numbers. If you're that kind of person, you will find the approach taken here very comfortable and helpful. Even if you're someone who's comfortable working with numbers, this clear and simple review will reinforce what you know—and maybe teach you a few tricks and shortcuts, too.
This chapter covers the basics of real estate math to prepare you for those real-world situations you will encounter as well as the math problems you will be most likely to find on your real estate licensing examination.
Study, review, and practice will help you overcome stress and anxiety so you can become comfortable with math. Each time you review and practice your real estate math, you will find that your confidence and ability will increase.
USING THIS CHAPTER AS A MATH REVIEW
This brief chapter on math is designed to provide you with a quick check of your math knowledge and to help you reinforce what you already know. It's organized in a way that makes it easy for you to look up just the information you need, and the subject matter is presented in as straightforward a manner as we could think of, with a minimum of wordy explanations and a maximum of quick tips, examples, formulas, memory aids, and shortcuts to help you overcome any remaining "math phobias."
Divided into sections, this chapter is organized into the following five general subject areas:
1) Calculators
2) Fractions
3) Percentages
4) Measurement
5) Proration
Within each general subject heading are a series of frequently asked questions (FAQs) and brief, clear explanations. If you read the Math FAQs in this chapter through from start to finish, you'll get a good, general review of real estate math principles. You also can use the Math FAQs for last-minute review of difficult issues or even as a memory-jogger in your daily real estate practice. Simply check Math FAQs Table of Contents in each chapter to see if your question is listed: if it is, go directly to that page. If your question is more complicated or fact-specific, you may have to look at several different items to find your answer. Either way, you'll probably find it here.
SPECIAL FEATURES
Throughout the text you will find Math Tips that offer insight into the trickier aspects of real estate math in general and the real estate exam's math content in particular. The For Example feature applies formulas and concepts to practical situations to show how the concept works in the real world. A generous collection of practice problems at the end of the review gives you the opportunity to apply your understanding in an exam-style context, and the simple T -Bar method is offered as a shortcut that's both easy to understand and easy to apply.
We hope this math review helps you master real estate math. Good luck!
S E C T I O N 1 - Introduction to Calculators
• What kind of calculator do I need?
• What are the specific real estate functions I should look for?
• How do I use the percent key?
INTRODUCTION TO CALCULATORS
Calculators are permitted when taking most state licensing examinations. The rules usually state that the calculator must be silent, hand-held, battery-operated, and nonprinting. Many states will not allow a real estate or financial calculator to be used while taking the real estate exam. Check with your state in regard to the appropriate calculator for your exam.
WHAT KIND OF CALCULATOR DO I NEED?
A calculator that will add (+), subtract (–), multiply (x), and divide (÷) is all that is needed for licensing examinations. In fact, only simple calculators will be allowed into the test site. Programmable calculators or calculators that have built in real estate problem solving functions will not be allowed into the test site.
Simple calculators are available in many sizes, shapes, and colors. The keys and display may be small or large. Some are battery-powered, some are solar-powered, and others are solar-powered with a battery backup. A calculator with a battery only or solar power with a battery backup is recommended over solar-powered only. Choose a calculator that is most comfortable for you; allow yourself time to learn to use it correctly and to become comfortable with it before you take the licensing examination.
WHAT ARE THE SPECIFIC REAL ESTATE FUNCTIONS I SHOULD LOOK FOR?
There are many business or financial calculators available that have additional functions that are very beneficial to the real estate professional. Some of the keys you would want are "N" (number of interest compounding periods/number of payments), "I" (interest rate per period), "PV" (present value of money/loan), "PMT" (amount of payment), and "FV" (future value of money). Business or financial calculators vary according to brand and/or model; therefore, the user's manual should always be followed to use the calculator properly. For example, some have "TERM" instead of "N"; therefore, you enter the number of years of the term instead of the number of payments or compounding periods. Some have "LOAN" instead of "PV". Some instruct you to enter the interest rate as an annual rate instead of a monthly rate. You may wish to purchase a business or financial calculator that contains these extra functions. Check with your state real estate commission to see if you will be permitted to use them during the exam.
► MATH TIP Be careful! Business or financial calculators are often set to round to two decimals at the factory. Follow the user's manual and set the decimal to float or to a minimum of five decimals. This will enable you to arrive at an answer with enough decimals to match multiple choice answers on exams. No matter which calculator you choose, read the user's manual.
The calculator preferred by the Career Institute would be any of three calculators by Calculated Industries designed specifically for real estate. The Real Estate Master IIIX Real Estate Finance Calculator will calculate complete payment solutions, amortization, combo loans, ARMs, rent versus buy comparisons, and much more. The Real Estate Master IIIX (model 3405) performs nearly every post-qualifying real estate calculation right there in front of the client to help boost sales.
You'll be able to calculate mortgage payments, terms, interest, PITI payments, future value, as well as purchase price, and down payment figures. Permanently store local property tax and property insurance rates for customized calculations that will help buyers and sellers develop an informative financial outlook--it even figures mortgage insurance. It also performs numerous "what-if" calculations from variables like purchase price, down payment amount, and loan amount financing.
Other features include bi-weekly and monthly loan comparisons, automatic sales price and down payment calculations, and completion of taxes, insurance, and mortgage insurance for true PITI payments. It also offers a built-in date-math function for closing and expiration dates, triple zero key that saves time and keystrokes.
There are actually two other calculators by the same company that offer even more advanced features. Calculated Industries Qualifier Plus IIIX Real Estate Finance Calculator (model 3415) and the top of the line Calculated Industries Qualifier Plus IIIFX Real Estate Finance Calculator (model 3430)
A pocket user guide stores conveniently inside the back of all three in a built in slot. They are powered by two LR44 batteries, which provide up to 800 hours of battery life, and the all have an auto shut-off feature that turns the calculator off after about 8 to 12 minutes of non-use. The device measures 5.75 x 3 x 0.6 inches and weighs 3.2 ounces, and it's backed by a one-year limited
HOW DO I USE THE PERCENT KEY?
Regardless of your choice of calculators, if you use the "%" key on calculators to solve percentage problems, read the user's manual for proper use of it. Some calculators require the use of the "%" key
or the "=" key but never both in the same calculation. Other calculators require the use of both the "%" key and the "=" key to get a correct answer. No matter which calculator you choose, read the user's manual.
FOR EXAMPLE If a property sold for $100,000 and a 7% commission was paid to the broker, how much was the broker paid?
This question may be worked two ways, as illustrated below.
Convert 7% to the decimal .07. (How to convert percents to decimals is shown in Section 2 of this Math Unit.) Touch $100,000 into your calculator, then the x or multiplication key, then .07, then the = key to read $7,000.
or
Touch in $100,000, then the x or multiplication key, then 7, then the % key. If your calculator now reads $7,000, you've finished the question. If when you touch the % key, it reads 0.07, then you must touch the = key to complete the question.
The use of the percent key allows the calculator to convert to the proper decimal place, and there's no question about the placement of the decimal. The choice is yours: you can convert the percent to a decimal or use the percent key for the conversion.