# Real Estate Math: Can you Crunch the Numbers?

When you’re helping clients navigate one of the most important financial decisions of their life, you must be confident dealing with numbers. Take this test to measure your skills.

Excerpted from Real Estate Math: What You Need to Know

Virtually every real estate transaction involves numbers; therefore, it follows that everyone in the real estate business should be proficient with numbers. This book will help both prospective and experienced real estate professionals perform numerical calculations with confidence. It will assist in sharpening the use of simple arithmetic in general — and in the field of real estate in particular.

The following pretest is intended to help you determine areas needing the greatest amount of study. Do not look at the answer key at the end of this pretest until you have finished all of the answers.

1. A broker keeps 60 percent of sales commissions and pays the sales associate the other 40 percent. A sales associate sells 50 acres of land at \$900 per acre with a gross sale commission of 10 percent of the sale price. What is the broker’s commission?

a) \$1,800
b) \$2,700
c) \$4,500
d) \$4,700

2. A broker earned a \$3,120 commission for selling a residential lot at \$52,000. What was the sale commission rate?

a) .06
b) .08
c) .60
d) 16.67

3. What is the annual premium for an insurance policy in the amount of \$25,000 if the cost is \$.60 per \$100?

a) \$15
b) \$150
c) \$416
d) \$500

4. A developer is subdividing a 12-acre tract into lots measuring 80' × 110'. Each lot has a perimeter of 380 feet and a sale price of \$4,500. She has allowed 126,720 square feet for required streets, sidewalks, and recreational facilities. How many salable lots are there?

a) 14.4
b) 59.4
c) 45.67
d) 116.6

5. Mr. Garcia’s monthly mortgage payment for principal and interest is \$264.60. If his annual property taxes are \$780 and his homeowner’s insurance premium is \$198, what is his total monthly payment, including taxes and insurance?

a) \$329.60
b) \$346.10
c) \$379.10
d) \$527.60

6. An investor is considering the purchase of a duplex for \$215,500 cash. She wants an investment that will produce a first-year 12 percent net return on investment. How much net income must the duplex generate during the first year to produce this investor’s required return on investment?

a) \$9,625
b) \$11,550
c) \$12,500
d) \$25,860

7. You have sold a residential property for \$98,500. Your employment contract specifies that you receive 55 percent of the total sale commission for properties you sell. If the rate of commission is 8 percent, what amount will you receive?

a) \$3,546
b) \$3,940
c) \$4,334
d) \$7,880

8. A buyer has made an earnest money deposit of \$7,000 on a home selling for \$139,900. A bank has agreed to lend the buyer 80 percent of the sale price. How much additional cash must the buyer furnish to pay the total required down payment?

a) \$7,000
b) \$11,920
c) \$20,980
d) \$27,980

9. Mr. Jones borrowed \$85,000 at 7.5 percent interest per year and paid a total of \$3,187.50 in interest. How long was the term of this loan?

a) Two months
b) Three months
c) Four months
d) Six months

10. A seller received \$52,000 from the sale of his home. He paid \$2,500 in settlement costs in addition to an 8 percent commission. What is the selling price of the home? (Round to the nearest dollar.)

a) \$54,500
b) \$56,522
c) \$58,860
d) \$59,239

11. The loan-to-value ratio offered by a local financial institution is 75 percent. If a buyer wishes to acquire a property selling for \$129,500, what will her down payment need to be?

a) \$1,727
b) \$5,180
c) \$32,375
d) \$97,125

12. A property has an assessed value of \$125,500. What is the property tax based on a rate of 25 mills?

a) \$313.75
b) \$3,125
c) \$3,137.50
d) \$3,150

13. The city is proposing to pave the streets in your neighborhood at a cost of \$40 per foot of frontage. The city will absorb 25 percent of the cost. Your lot has footage on the street of 130 feet. Assuming there are homes on both sides of the street, what is the amount of your paving assessment?

a) \$1,950
b) \$2,600
c) \$3,900
d) \$5,200

14. The N½ of the NE¼ of the SW¼ and the S½ of the SE¼ of a section contains how many acres?

a) 2.5
b) 20
c) 80
d) 100

15. A duplex is scheduled to close on September 10. The seller collected rent for September on the first of the month amounting to \$950. According to the sale contract, the buyer is due the rental income for the day of closing. What is the proration?

a) \$285 debit to seller, \$285 credit to buyer
b) \$633.33 credit to seller, \$633.33 debit to buyer
c) \$665 debit to seller, \$665 credit to buyer
d) \$665 credit to seller, \$665 debit to buyer

1. b) \$2,700
How to do it: 50 acres × \$900 per acre = \$45,000 total sale price; \$45,000 sale price × .10 commission = \$4,500 total commission; \$4,500 × .60 broker’s share = \$2,700 broker’s commission

2. a) .06 or 6 percent
How to do it: \$3,120 commission ÷ \$52,000 sale price = .06 rate or 6 percent

3. b) \$150
How to do it: \$.60 ÷ \$100 = .006 premium rate; .006 × \$25,000 policy = \$150 premium

4. c) 45
How to do it: 43,560 square feet per acre × 12 acres = 522,720 total square feet – 126,720 square feet for streets, sidewalks, etc. = 396,000 available square feet; 80 feet × 110 feet = 8,800 square feet per lot; 396,000 available square feet ÷ 8,800 = 45 lots

5. b) \$346.10
How to do it: \$780 ÷ 12 months = \$65.00 taxes per month; \$198 per year ÷ 12 months = \$16.50; \$264.60 principal and interest payment + \$65.00 + \$16.50 = \$346.10

6. d) \$25,860
How to do it: .12 net return × \$215,500 purchase price = \$25,860 net income

7. c) \$4,334
How to do it: \$98,500 sale price × .08 commission rate = \$7,880 total commission; \$7,880 total commission × .55 sales associate’s share = \$4,334 commission due sales associate

8. c) \$20,980
How to do it: \$139,900 sale price × .80 = \$111,920 loan; \$139,900 sale price – \$111,920 loan = \$27,980 down payment; \$27,980 – \$7,000 earnest money deposit = \$20,980

9. d) Six months
How to do it: \$85,000 loan × .075 interest rate = \$6,375 interest per year; \$6,375 interest ÷ 12 months = \$531.25 per month; \$3,187.50 ÷ \$531.25 = 6 months

10. d) \$59,239
How to do it: \$52,000 sale proceeds + \$2,500 settlement costs = \$54,500; \$54,500 ÷ .92 = \$59,239.13 or \$59,239 sale price

11. c. \$32,375
How to do it: \$129,500 sale price × .75 LTV = \$97,125 loan; \$129,500 sale price – \$97,125 loan = \$32,375 down payment

12. c) \$3,137.50
How to do it: \$125,500 × .025 property tax rate = \$3,137.50

13. a) \$1,950
How to do it: \$40.00 × .75 homeowner’s share = \$30.00 homeowner’s cost per foot of frontage; \$30.00 × 130 feet of footage = \$3,900 ÷ 2 = \$1,950

14. d) 100
How to do it: 640 acres ÷ 4 ÷ 2 = 80 acres; 640 acres ÷ 4 ÷ 4 ÷ 2 = 20 acres; 80 + 20 = 100 acres

15. c) \$665 debit to seller, \$665 credit to buyer
How to do it: \$950 ÷ 30 days = \$31.666667/day; \$31.666667 × 21 days = \$665.00; Seller has collected the rent in advance; Seller owes buyer; Debit seller and credit buyer