Real Estate Math

Question 1

Mark’s gross income is $10,250 a month. To qualify for most loans, what is the maximum monthly house payment Mark can make (using the 28/36 rule)?

Answer 1

$10,250 x 0.28 = $2,870

Question 2

If Mandy’s gross income is $8,550 a month, she would need to spend less than how much in total household debt a month to qualify for most loans?

Answer 2

(28/36 rule)
8,550 x 0.36 = $3,078

Question 3

Lizzie’s groos income is $7,050 a month. What is the maximum total household debt she could have to qualify for most loans?

Answer 3

(28/36 rule)
7,050 x 0.36 = $2,538

Question 4

Assuming there are no extra fees, and the broker is representing the buyer and the seller, what was the final sales price of a property if the commission rate was 6% and the broker received $24,000?

Answer 4

24,000 / 0.06 = $400,000

Question 5

Find the annual GRM. A 9-unit building in Cleveland, Ohio, with an asking price of $2,000,000 and gross annual rents of $105,000 (round to the nearest hundredth)

Answer 5

GRM = Price / Gross Yearly Rental Income = how many years it would take to pay off the property.

2,000,000 / 105,000 = 19.05 years

Question 6

Find the annal GRM. A 10-unit building with an asking price of $5,000,000 and gross annual rents of $225,000 (round to the nearest hundredth)

Answer 6

GRM = Price / Gross Yearly Rental Income = how many years it would take to pay off the property

5,000,000 / 225,000 = 22.22 years

Question 7

An agent is going to receive a 50% share of a 3% gross commission. The property sold for $350,000. How much commission will the agent receive?

Answer 7

350,000 x 0.03 = 10,500
10,500 / 2 = $5,250

Question 8

During the listing agreement, a commission of 6% is established. The house is sold for $450,000. What is the commission?

Answer 8

450,000 x 0.06 = 27,000

Question 9

An agent was to receive a 35% share of a 3% gross commission. The salesperson received $4,500. What did the property sell for?

Answer 9

4500 / 0.35 = 12857.14
12857.14 / 0.03 = 428571.43

Question 10

A property’s market value is $250,000. The assessment rate for the house is 15% with 27.50 mills. Find the annual property taxes.

Answer 10

Market value x assessment rate
250,000 x 0.15 = 37,500

Convert mills to mill rate by moving decimal over 3 places
27.50 = 0.0275

Multiply
37,500 x 0.0275 = $1,031.25 annual property taxes

Question 11

A property’s market value is $350,000. The assessment rate for the house is 25% with 27.50 mills. Find the annual property taxes.

Answer 11

Multiply market value by assessment rate:
350,000 x 0.25 = 87,500

Convert mills to mill rate by moving decimal over 3 places:
27.50 = 0.0275

Multiply:
87,500 x 0.0275 = $2,406.25 annual property taxes

Question 12

A property’s market value is $200,000. The assessment rate for the house is 45% with 65 mills. Find the annual property taxes.

Answer 12

Multiply Market Value by assessment rate:
200,000 x 0.45 = 90,000

Convert mills to mill rate by moving decimal over 3 places:
65 = 0.065

Multiply:
90,000 x 0.065 = $5,850 annual property taxes

Question 13

A property’s market value is $400,000. The assessment rate for the house is 25% with 22.75 mills and a $30,000 property tax deduction. Find the annual property taxes.

Answer 13

Market value x assessment rate:
400,000 x 0.25 = 100,000

Subtract property tax deduction from assessed value:
100,000 - 30,000 = 70,000

convert mills to mill rate by moving decimal over 3 places:
22.75 = 0.02275

Multiply:
70,000 x 0.02275 = $1,592.50

Question 14

A property’s market value is $500,000. The assessment rate for the house is 25% with 55.75 mills and a $25,000 property tax deduction. Find the monthly property taxes.

Answer 14

Multiply market value by assessment rate:
500,000 x 0.25 = 125,000

Subtract property tax deduction from assessed value:
125,000 - 25,000 = 100,000

Multiply by mill rate:
100,000 x 0.05575 = 5,575

Divide by 12 to get MONTHLY taxes:
5,575 / 12 = 464.58

Question 15

The value of a property is $180,000 today. What was the original cost of the property if it has lost 20% of its value over the past three years?

Answer 15

subtract depreciation percentage from 100%:
1.0 - 0.2 = 0.8 (so the property is worth 80% of what it used to be)

Divide property value by calculated percentage:
180,000 / 0.8 = 225,000

Question 16

Robin bought her home 5 years ago for $190,000. She sold her home last month for $199,000. How much did the house appreciate?

Answer 16

190,000 - 190,000 = 9,000

Question 17

The value of a property is $91,000 today. What was the original cost of the property if it has lost 35% of its value over the past five years?

Answer 17

subtract depreciation value from 100%:
100 - 35 = 65%

Divide property value by calculated percentage:
91,000 / 0.65 = 140,000

Question 18

A lot purchased 25 years ago for $40,000 has appreciated a total of 45% since its purchase. What is it worth today?

Answer 18

Add appreciation percentage to 100%
100 + 45 = 145%

Multiply original price by total appreciation percentage:
40,000 x 1.45 = $58,000

Question 19

A lot purchased 5 years ago for $100,000 has appreciated a total of 10% since it s purchase. How much per year did the property appreciate for?

Answer 19

Add appreciation percentage to 100%
100 + 10 = 110

Multiply original price by calculated percentage:
100,000 x 1.10 = 110,000

Subtract original price from new property value:
110,000 - 100,000 = 10,000

Divide by 5:
10,000 / 5 = 2,000

Question 20

What is the interest rate on a $150,000 loan that requires an annual interest payment of $6,500?

Answer 20

6500 / 150,000 = 0.0433 or 4.33%

Question 21

What is the interest rate on a $200,000 loan that requires an annual interest payment of $8,000?

Answer 21

8,000 / 200,000 = 0.04 or 4%

Question 22

What is the annual interest rate on a $10,000 loan that requires a semiannual interest payment of $450?

Answer 22

Semi-annual = 2 times a year

450 x 2 = $900

900 / 10,000 = 9%

Question 23

What is the annual interest rate on an $80,000 loan that requires a semiannual interest payment of $1,000

Answer 23

Semi-annual = 2 times a year

1,000 x 2 = 2,000

2,000 / 80,000 = 0.025 or 2.5%

Question 24

What is the annual interest rate on a $300,000 loan that requires a monthly interest payment of $500?

Answer 24

500 x 12 = 6000 yearly interest

6000 / 300,000 = 0.02 or 2%

Question 25

A lot in a subdivision is being sold for $5.00 per sqft. It is 100ft wide and 120ft deep. How much does the lot cost?

Answer 25

100 x 120 = 12,000sqft

12,000 x 5 = $60,000

Question 26

A lot in a subdivision is being sold for $8 per sqft. It is 200ft wide and 400 ft deep. How much does the lot cost?

Answer 26

200 x 400 = 80,000 sqft

80,000 x 8 = $640,000

Question 27

A lot in a subdivision costs $300,000. It is 100ft wide and 150ft deep. How much is the price per sqft?

Answer 27

100 x 150 = 15,000 sqft

300,000 / 15,000 = $20 per sqft

Question 28

What is the price per square front foot for a 50’ wide x 100’ long lot that sold for $75,000?

Answer 28

75,000 / 50 = $1,500 per front foot

Question 29

Judy is considering buying a lakefront property. She learns that a property there just sold for $550,000 and had frontage on the lake, totaling 550 feet. About how much did the property sell per front foot?

Answer 29

550,000 / 550 = 1,000 per front foot.

Question 30

If the LTV is set at 80% and the purchase price is $500,000 what is the down payment required by the borrower?

Answer 30

500,000 x 0.8 = 400,000

500,000 - 400,000 = 100,000

Question 31

A property closed for $210,000 and the seller made a 20% profit. How much had the seller paid for the property, assuming they did nothing to the property?

Answer 31

Appreciation problem! add 100% to the profit percentage:
100 + 20 = 120% or 1.20

Divide to find the original purchase price
210,000 / 1.20 = 175,000

Question 32

Some of the closing costs on a $300,000 transaction are as follows: Commission of $15,000, title insurance fee of $5,000, mortgage pay-off of $245,000. Based on that info, what is the seller’s proceed of sale?

Answer 32

300,000 - 245,000 - 15,000 = 40,000

The $5,000 title insurance fee is paid by the buyer, not the seller.

Question 33

A listing on the MLS offers a 3% cooperation amount to a buyer’s broker. What is the sales price if the buyer’s broker collects a $6,000 commission?

Answer 33

6,000 / 0.03 = $200,000

Question 34

The tax assessed value of a property is $350,000. The mill rate is 10. What is the quarterly tax amount?

Answer 34

adjust the mill rate: 0.010

350,000 x 0.010 = 3,500

3500 / 4 = $875

Question 35

The state charges a transfer tax of $2 per $500. What will be the transfer tax if a property sells for $150,000?

Answer 35

500 / 2 = 250

150,000 / 250 = $600

Question 36

The interest rate on a $120,000 loan is 6%. What is the monthly interest payment?

Answer 36

120,000 x 0.06 = 7200

7200 / 12months = $600

Question 37

A borrower’s monthly mortgage payment is $1400, their quarterly tax bill is $600, and their 6month insurance bill is $600. What is the PITI?

Answer 37

convert quarterly tax bill to monthly:
600 x 4 = 2400 / 12 = 200

convert insurance bill to monthly:
600 x 2 = 1200 / 12 = 100

Add:
1400 + 200 + 100 = $1700/month