Real Estate Math Assessments

A buyer takes out a loan for $50,000 at 5% simple annual interest. The buyer informs the lender that over the first two years, he can only afford to pay off the interest and none of the principal amount. Given this information, the lender charges the buyer a 2-point loan discount up front and reduces the annual interest rate on the loan to 4%. How much more profit will the lender make in the first two years than she would if she hadn't charged the discount?

$0?

If a lender charges a 2-point discount on a $50,000 loan, what is the amount of the discount?

$1,000

If a deposit of $1,200 is posted to an account with a 5% annual compound interest rate, what will the balance of the account be after three years?

$1,389.15

How much does the buyer owe the seller for a 2-year $8,760 insurance policy that runs out August 12 if prorations are carried to the day of closing, April 12 of the same year? Assume a calendar year with no leap-years involved.

$1,476

A broker recently sold his client a home for $100,000. He charged the client a 6.5% commission and agreed to pay 25% of that amount to the listing salesperson and 25% to the selling salesperson. What amount of the commission will the listing salesperson receive from the sale?

$1,625

If an insurance policy costs $500 a year, what is the daily rate of the policy, given a statutory year?

$1.30 per day

If a lot that sells for $114,000 makes the seller a 14% profit, what was the original price of the lot?

$100,000

What is the monthly net operating income of a building whose value is $9 million, if the annual rate of return is 15%?

$112,500

What is the approximate value of a business venture that makes $2.8 million annually and capitalizes on its worth at a rate of 22%?

$12.73 million

A house on Pecan Street is valued at $100,000. The local annual tax rate is $1.50 per $100 appraised value. What will the amount of monthly taxes paid on the house be?

$125

If an account has a $100,000 balance and a simple interest rate of 10%, what will its balance reach if left alone for 4 years?

$140,000

After two years, what is the balance on a $150,000 loan with 5% annual interest if monthly payments are $1,000?

$140,775?

After three years, what is the amount of interest accrued on a $1,200 loan with an annual simple interest rate of 5%, assuming that the loan recipient makes no payments during that time?

$180

If a lender charges a 3-point loan discount on a $78,000 loan, what is the amount of the discount?

$2,340

If a lot depreciated at an average annual rate of 1.75% over the last twelve years and was originally valued at $26,000, how much is it worth now?

$20,540

If a lot that sells for $228,000 makes the seller 14% profit, how much was the original price of the lot?

$200,000

If an investor purchases a property for $20,000 and intends to make a 5% profit, how much should he sell the property for, not factoring in taxes and closing costs?

$21,000

In a statutory year, what is the daily tax rate on a house appraised at $18,000 if the annual rate is 6%?

$3 / day

A lease calls for a minimum monthly rent of $1,000 plus 12% of the yearly gross in excess of $500,000. How much is one month's rent if a company grosses $750,000 annually?

$3,500

A borrower wants to know how much she owes in mortgage loans. The interest portion of her last monthly payment was $300. If she is paying interest at the annual rate of 12%, what was the outstanding balance on her loan before that last payment was made?

$30,000

If a loan of $30,000 accrues 5% compound interest, what is the loan balance after 3 years if we consider that the loan recipient has not made any payments during that time?

$34,728.75

What is the cost of a parcel of land that is being sold at $150 per frontage foot with measurements of 233 feet by 417 feet?

$34,950

A percentage lease on an office building stipulates a $3,000 monthly base rent plus 3.5% of gross profit in excess of $250,000. If the company renting the building grosses $375,000 in its first year, what is the total annual rent for that year?

$40,375

What is the total sale price of a house if a seller nets $45,000 on the sale after paying a 5% commission to a broker and another 5% on other expenses?

$50,000

A new lot is valued at $1,500, but an investor succeeds in buying it for $1,000. Five years later, he sells it at market value. How much has the investor lost if the property has been depreciating at an average annual rate of 7.5% of the original value?

$62.50

What is a building's annual NOI if its net worth is $820,000, and it capitalizes on its worth at a rate of 9% annually?

$73,800

IRS documentation shows that a particular building has depreciated at a constant rate of 3% every year. Suppose that an investor buys the property in September for $100,000 and from September to the end of the first year, the property depreciates at a prorated 1%. Say that for the next eight years, the property depreciates at a constant rate of 3%, so in April of the tenth year (after taxes have been paid), the owner sells the property for $150,000. If during that last year the prorated depreciation was 1%, how much taxable income on capital gains will the owner receive from the property following the sale?

$76,000

Which of the following is equivalent to 5%?

.05

What percentage of the original value of a lot is its appreciated value?

1 + the total appreciation rate

A certain house has proved difficult to sell. The salesperson has suggested that it might sell faster if the owners enclosed a portion of the backyard with a privacy fence. If the area of the rectangular lot to be fenced is 400 square feet and the frontage is 10 feet, what is the number of running feet of fence needed to enclose the area?

100?

During a leap year, how many days are there in a banker's year from January 1 to April 20th?

110

144 inches is equivalent to which of the following?

12 feet

If a house sells for $50,400, and its original cost was $36,000. What is the percentage of cost sold?

140%

If a house that originally cost $78,000 sells for $102,000, what fraction of the original price is equal to the profit?

17/13

102/120 reduces to which of the following fractions?

17/20

For how many days does a seller owe the buyer for accrued items in the month of April, if the contract stipulates prorations through the closing date, April 19?

19 days

The distance around a rectangle (its perimeter) is given by which one of the following formulas?

2 x (length + width)

A 2-point loan discount is what percentage of the loan itself?

2%

How many square yards are in a room that measures 12 feet by 17 feet?

22.67

0.25 is represented as a fraction by which of the following?

25/100

A house is valued at $56,000 at the time of purchase. If after five years, an appraisal finds that the house is worth $64,400, what was the average annual rate of appreciation?

3%

The circumference of a circle is approximated by which one of the following formulas?

3.142 x Radius^2

If a borrower has initially taken a loan of $100,000, then what percentage does she owe if her current balance is $30,000?

30%

The management of an apartment wants to replace the vinyl in the kitchen of one of the apartments. The kitchen floor is 15 feet by 20 feet. How many square feet of vinyl will the management need to purchase?

300

A homeowner is planning to construct a rectangular patio in his backyard. If the dimensions of the patio are 20 feet by 30 feet and the cement is to be poured as a 6-inch slab, how many cubic feet of cement will be poured for this patio?

300 cubic feet

A banker's year has how many days in it?

360

How many days are in a banker's year?

360

A lease calls for a minimum monthly rent of $1,000 plus 12% of yearly gross in excess of $500,000. How much is one month's rent if a company grosses $850,000 annually?

4,500

The total linear footage to enclose a lot measuring 75' × 125' is which one of the following amounts?

400'

A rectangular room is 12 feet wide, 12 feet long and the distance from its floor to the ceiling is 10 feet. What is the total square footage of wall space in the room?

480 square feet

If a lot sells for $50,000 and the salesperson receives a $2,500 commission, what is the rate of commission?

5%

If a lot is worth $50,000 and appreciates an average of 2% each year over the next 5 years, what will its new value be?

55,000

How many square inches are in an area of 4 square feet?

576

Seven points are equal to which percentage?

7%

Using a calculator, what process would yield 5% of $73,260?

73,260 multiplied by .05

In the fraction 7/8 how many parts of the whole are there?

7?

If an investor puts $6,000 into a business venture and expects a profit of $18,900 in four years, what is the annual rate of return he expects?

80.75% ??

What is the area, in feet, of a triangle with a base of 12 inches and a height of 18 inches?

9 square feet

A lender charges a 3-point discount on a $50,000 loan and sets the annual interest rate at 3%. The loan recipient agrees to pay the loan off in 10 years by paying 10% of the original principal plus interest every year. How much will the lender make in net profits if the borrower is able to meet these terms?

??

Rate is expressed as _______.

???

Suppose that a seller has prepaid an insurance policy through November at a yearly premium of $876 and is closing on July 31. With calculations based on a calendar (non-leap) year, if the buyer assumes this insurance policy and the closing agreement stipulates prorated terms through the day of closing, what does he or she owe the seller?

???

What is the value of a building that grosses $700,000 annually with $52,000 in annual expenses and a 2% rate of return?

???

Which of the following equations properly describes the relationship between the Net Operating Income, Value, and Annual Rate of Return for an income-producing property?

???

Prepaid items are costs that have already been paid by whom?

??? (not the buyer)

If a lot has appreciated by A dollars in one year at a rate of R, what was its original value?

A / R

An unused insurance policy assumed by the buyer at closing is considered which one of the following choices?

A prepaid item at closing

When a change in value of an appreciating property is expressed as a percentage of the original cost, it is characterized by which of the following choices?

Always greater than 1

13/8 is an example of _______.

An improper fraction

An example of a prepaid item might be which one of the following choices?

An insurance policy with two more months remaining in effect

Annual NOI equals which one of the following functions?

Annual Effective Gross Income - Annual Expenses

If a contract stipulates that prorating will be calculated to the day of closing, then who will pay property taxes for the day?

Buyer

Volume is expressed in which of the following terms?

Cubic units

Volume is measured in________.

Cubic units

If a loan is amortized, the principal balance of the loan _____ with each payment.

Decreases

In the fraction 6/7, the number 7 is the _______.

Denominator

Fractions can be converted to equivalent decimals by _______.

Dividing the numerator by the denominator

Which of the following is not a typical item of proration?

Home improvement charges

When amortizing a loan which of the following choices apply?

Interest payments and principal payments are tax deductible.

Straight-line depreciation is defined in which of the following ways?

Is used for tax purposes to adjust an owner's taxable basis in a property

Which of the following steps would you take to convert a decimal to a percentage?

Move the decimal 2 places to the right and add the % sign ??

In order to find the area of a circle one must solve in which of the following ways?

Multiply the radius squared by pi

The area of a triangle can be determined by performing which of the following functions?

Multiplying the base by the height and dividing by 2

If the sale price of a house is known, in addition to the percentage of gross sales required to account for expenses, a person can determine the seller's net profit by which one of the following methods?

Multiplying the sale price by the percentage used for total expenses and then subtracting the resulting amount from the sale price.

NOI stands for which one of the following terms?

Net Operating Income

"Percent" (%) means which of the following?

Per hundred

Which of the following steps would you take to change a percentage to a fraction?

Place the percentage over 100

The percentage rent is equal to which of the following?

Portion sales subject to the percentage x percentage stipulated in the lease

Which of the following is not a T-rule?

Rate = Total / Part

A lender charges a loan discount in order to achieve which of the following actions?

Reimburse the recipient of the loan for accrued items

Profit is derived by which of the following functions?

Sale price - Cost

The cost of an item times the percentage of cost sold is represented by which of the following terms?

Sale price?

Linear measurements are used to express which one of the following choices?

The length of an object

Amortization is defined in which of the following ways?

The repayment of loan principal plus interest over time

Area is defined as which one of the following?

The two dimensional surface of an object

Consider the question: How many cubic yards of dirt will it take to fill a hole? This question asks that we solve using which one of the following measurement units?

The volume of the hole

Using the T-method, what is the formula to find the part?

Total x rate

Volume is typically expressed in which of the following terms?

cubic units

Interest is the cost of the use of _______.

money

What is the formula for the volume of a cylinder?

p x Radius^2 x Length

The area of a circle is calculated by which formula?

pr^2