Real Estate Mathematics - Chapter 86

Question 1

amortization table

Answer 1

The percentage formula can also be used in loan calculation problems.
Cost of using the lenders money = cost
Interest rate = percent
Principal amount of the loan = principal

When calculating problems involving simple interest, the interest rate is the rate of interest over one year. Interest can be further broken down into months by dividing the annual interest rate by 12, and in two ways by dividing the interest rate by 360 ( months are uniformly considered to be 30 days to avoid awkward numbers).

Financial calculators and amortization tables make interest calculations easier. An amortization table is a schedule of monthly loan payments would show the amount of principal and the amount of Interest which comprises each constant payment until it is paid in full by the end of the term. Early in the amortization schedule, a majority of the monthly payment is applied to interest. However, towards the end of the schedule, most of the monthly payment is applied towards the diminishing principal balance.

In loan problems, time is an important factor and is part of the percentage formula. Thus, the percentage formula is modified slightly for loan problems as follows:

Cost of borrowing money (C) = Interest Rate (%) x Time (T) x Principal (P)

C= % x T x P

When dealing with interest rates for different periods, remember the following:

• for ANNUAL INTEREST, the interest rate is the percent given
• for MONTHLY INTEREST, the interest rate is equal to the interest rate given / 12
• for DAILY INTEREST, the interest rate is equal to the interest rate given / 360

Question 2

area

Answer 2

The amount of space within the boundaries of a parcel of real estate. The formula for area is:

Area = Length x Width

Area of a Triangle
Area = (BxH) / 2

Question 3

capitalization rate

Answer 3

CAPITALIZATION RATE (CAP RATE) is the annual rate of return on investment produced by the operations of an income property or sought by an investor on the investment of capital.

The cap rate is calculated by dividing the net operating income by the price asked or offered for income property.

Example with income-producing property, the value of the property is determined by capitalizing the net operating income (1000) generated by the property (rental income minus operating expenses ( .

The rate of return an investor expects on their investment after rental operating expenses are subtracted from rental income is called the capitalization rate – cap rate.

Net Operating Income or loss (NOI) = Capitalization Rate % (rate of return) x Purchase Price (P)

Cap Rate = NOI / Purchase Price

Question 4

percentage formula

Answer 4

The percentage formula is a basic calculation used in real estate mathematics. It is typically used to determine the amount of a broker’s fee on a transaction. As compensation for services, a broker is entitled to a broker’s fee typically stated as a percentage of the:

• sales price
• loan amount
• total rents

the percentage formula is easily converted to suit a variety of situations. Usually, two of the three variables will be known, leaving the third to be determined. Understanding the basic formula make solving problems a question of mechanics.

The percentage formula is as follows:
Fee = Percent (%) x Principal

Percent (%) = the rate charged
Principal (P) = the dollar amount of the price, loan or rents

Question 5

net operating income

Answer 5

The NET OPERATING INCOME (NOI) is the net revenue generated by an income-producing property as the return on Capital, calculated as the sum of a property’s gross operating income less the properties operating expenses.

Question 6

basic units of land measurement in real estate

Answer 6

Township = 36 sq miles broken up into 36 sections
Section = 640 acres = 1 square mile
Half Section = 320 acres
Quarter Section = 160 acres
Quarter of a Quarter Section = 40 acres
Acre = 43,560 square feet
Mile = 5,280 feet
Square mile = 27,878,400 sq feet (5280ft x 5280ft)
Square mile = 640 acres (27,878,400sf/43,560sf)
Square acre = approx 209ft x 209ft
1 yard = 3 feet
1 square yard = 9 sq ft (3ft x 3ft)
1 mile = 320 rods = 5,280 ft
1 rod = 16.5ft or 5.5 yards (16.5ft x 3ft)

Question 7

fractions

Answer 7

It is beneficial to convert all fractions to decimals during the DRE exam, and then use the calculator to complete the computations.

A fraction is composed of a NUMERATOR (top number) and a DENOMINATOR (bottom number).

When converting a fraction into a decimal, divide the numerator by the denominator.  Examples:
4/5 = 0.8
1/2 = 0.5
3/4 = 0.75
3/100 = 0.03
667/100 = 6.67

Question 8

The main real estate math equations to know

Answer 8

Area of a Rectangle
A = L x W
Area = Length x Width

Area of a Triangle
A = (B x H) / 2
Area = (Base x Height) / 2

Percentage Formula
F = % x P
Fee = % Rate Charged x Principal

Loan Calculation Percentage Formula
C = % x T x P
Cost of borrowing money =
% Interest Rate on the Loan x Term of Loan (Time) x Principal amount