REM101: Real Estate Math Made Easy Exam Prep
with Detailed Rationales
Course Code: REM101
Course Name: Real Estate Math Made Easy
Topic: Amortization, Commission, and Tax Calculations
Academic Year: 2026/2027
Calculation
Primary Formula Core Input Variables
Domain
Amortization Payment = (Loan Amount / 1,000) × Loan Principal, Factor
Factor Factor Rate
Commission Net Share = Gross Sales Price × Total Sales Price, Multi-tier
Split Rate × Broker % × Agent % Splits
Property Tax Annual Tax = Assessed Value × (Mills / Assessed Valuation,
(Mills) 1,000) Millage Total
Gross Price = (Net Desired + Fixed Target Proceeds, Fee
Net to Seller
Costs) / (100% - Commission %) Percentages
Acres = (Width (ft) × Depth (ft)) / Linear Foot
Acreage Area
43,560 Dimensions
Section 1: Mid-Level Real Estate Core Competencies
• Question 1: A buyer purchases a rental property for $350,000 with an 80%
Loan-to-Value (LTV) ratio mortgage. The lender charges a 1.5% loan
origination fee and 2.5 discount points. What is the total amount of
upfront loan fees paid by the borrower at closing?
, o A) $14,000
o B) $11,200
o C) $10,500
o D) $7,000
o CORRECT ANSWER: B) $11,200
o RATIONALE: First, calculate the total loan amount using the
Mortgage Calculator principles: $350,000 × 0.80 = $280,000. Next,
combine the fee percentages because both are derived from the loan
amount: 1.5% (origination) + 2.5% (discount points) = 4.0% total.
Finally, multiply the loan amount by this combined percentage:
$280,000 × 0.04 = $11,200. Choice A uses the purchase price instead
of the loan amount, which is incorrect.
• Question 2: A residential property has an assessed value equal to 70% of its
market value. If the market value is $420,000 and the local municipality
levies an annual tax rate of 34 mills, what is the semi-annual property tax
liability?
o A) $9,996
o B) $4,998
o C) $4,998
o D) $2,499
o CORRECT ANSWER: C) $4,998
o RATIONALE: First, determine the assessed value of the property:
$420,000 × 0.70 = $294,000. Convert mills to a decimal format by
dividing by 1,000 (,000 = 0.034). Calculate the annual property
tax by multiplying the assessed value by the decimal tax rate:
$294,000 × 0.034 = $9,996. Because the question explicitly asks for
the semi-annual tax, divide this annual total by 2: $9, = $4,998.
• Question 3: An agent lists a home for $600,000 with a total commission
structure of 5.5%. The listing brokerage splits the commission 50/50 with
the cooperating buyer's brokerage. If the listing agent has a 75/25 split
, with their own firm (agent receives 75%), how much does the listing agent
earn?
o A) $33,000
o B) $16,500
o C) $12,375
o D) $4,125
o CORRECT ANSWER: C) $12,375
o RATIONALE: Calculate the gross transaction commission:
$600,000 × 0.055 = $33,000. Since the co-brokerage split is equal, the
listing firm receives half: $33,000 × 0.50 = $16,500. The listing agent
earns 75% of that firm's allocation: $16,500 × 0.75 = $12,375. Choice
A is the full gross commission, choice B is the firm's total share, and
choice D is the firm's retained share.
• Question 4: A seller wants to clear exactly $285,000 from the sale of their
suburban home after paying a 6% brokerage commission and $5,400 in
fixed closing costs. What is the minimum gross sales price required to
meet this objective?
o A) $307,524
o B) $302,400
o C) $308,936
o D) $290,400
o CORRECT ANSWER: C) $308,936
o RATIONALE: Apply the classic real estate net-to-seller formula:
Gross Sales Price = (Net Desired + Fixed Costs) / (100% -
Commission Rate). Add the target net to the fixed expenses: $285,000
+ $5,400 = $290,400. Divide this value by the remaining percentage
base: 100% - 6% = 94% (or 0.94). Thus, $290,.94 =
$308,936.17, which rounds down to $308,936. Other choices
incorrectly add 6% straight to the values.
, • Question 5: A commercial tract of raw land is formatted as a rectangle
measuring 450 feet wide by 871.2 feet deep. If the parcel sells for $18,000
per acre, what is the final purchase price?
o A) $162,000
o B) $162,000
o C) $392,040
o D) $9,000
o CORRECT ANSWER: B) $162,000
o RATIONALE: First, calculate the total area in square feet: 450 ft ×
871.2 ft = 392,040 sq ft. Convert this footprint to acres using the
standard real estate conversion factor found on NAR: 392,040 /
43,560 square feet per acre = 9 acres. Multiply the total acreage by the
per-acre market valuation rate: 9 acres × $18,000 = $162,000. Choice
C represents the total square footage.
• Question 6: A property is sold for $320,000. The buyer puts 15% down and
finances the balance. If the lender charges an annual interest rate of 6.5%
and the monthly P&I payment factor is $6.32 per $1,000 of the loan amount,
what is the monthly P&I payment?
o A) $2,022.40
o B) $1,719.04
o C) $1,520.00
o D) $2,100.25
o CORRECT ANSWER: B) $1,719.04
o RATIONALE: First, find the loan amount by removing the 15%
down payment component ($320,000 × 0.85 = $272,000). Next,
divide this loan value by $1,000 to identify the mathematical factor
base ($272,,000 = 272). Finally, multiply this factor by the
monthly amortization scalar: 272 × $6.32 = $1,719.04. Choice A uses
the absolute purchase price incorrectly.
with Detailed Rationales
Course Code: REM101
Course Name: Real Estate Math Made Easy
Topic: Amortization, Commission, and Tax Calculations
Academic Year: 2026/2027
Calculation
Primary Formula Core Input Variables
Domain
Amortization Payment = (Loan Amount / 1,000) × Loan Principal, Factor
Factor Factor Rate
Commission Net Share = Gross Sales Price × Total Sales Price, Multi-tier
Split Rate × Broker % × Agent % Splits
Property Tax Annual Tax = Assessed Value × (Mills / Assessed Valuation,
(Mills) 1,000) Millage Total
Gross Price = (Net Desired + Fixed Target Proceeds, Fee
Net to Seller
Costs) / (100% - Commission %) Percentages
Acres = (Width (ft) × Depth (ft)) / Linear Foot
Acreage Area
43,560 Dimensions
Section 1: Mid-Level Real Estate Core Competencies
• Question 1: A buyer purchases a rental property for $350,000 with an 80%
Loan-to-Value (LTV) ratio mortgage. The lender charges a 1.5% loan
origination fee and 2.5 discount points. What is the total amount of
upfront loan fees paid by the borrower at closing?
, o A) $14,000
o B) $11,200
o C) $10,500
o D) $7,000
o CORRECT ANSWER: B) $11,200
o RATIONALE: First, calculate the total loan amount using the
Mortgage Calculator principles: $350,000 × 0.80 = $280,000. Next,
combine the fee percentages because both are derived from the loan
amount: 1.5% (origination) + 2.5% (discount points) = 4.0% total.
Finally, multiply the loan amount by this combined percentage:
$280,000 × 0.04 = $11,200. Choice A uses the purchase price instead
of the loan amount, which is incorrect.
• Question 2: A residential property has an assessed value equal to 70% of its
market value. If the market value is $420,000 and the local municipality
levies an annual tax rate of 34 mills, what is the semi-annual property tax
liability?
o A) $9,996
o B) $4,998
o C) $4,998
o D) $2,499
o CORRECT ANSWER: C) $4,998
o RATIONALE: First, determine the assessed value of the property:
$420,000 × 0.70 = $294,000. Convert mills to a decimal format by
dividing by 1,000 (,000 = 0.034). Calculate the annual property
tax by multiplying the assessed value by the decimal tax rate:
$294,000 × 0.034 = $9,996. Because the question explicitly asks for
the semi-annual tax, divide this annual total by 2: $9, = $4,998.
• Question 3: An agent lists a home for $600,000 with a total commission
structure of 5.5%. The listing brokerage splits the commission 50/50 with
the cooperating buyer's brokerage. If the listing agent has a 75/25 split
, with their own firm (agent receives 75%), how much does the listing agent
earn?
o A) $33,000
o B) $16,500
o C) $12,375
o D) $4,125
o CORRECT ANSWER: C) $12,375
o RATIONALE: Calculate the gross transaction commission:
$600,000 × 0.055 = $33,000. Since the co-brokerage split is equal, the
listing firm receives half: $33,000 × 0.50 = $16,500. The listing agent
earns 75% of that firm's allocation: $16,500 × 0.75 = $12,375. Choice
A is the full gross commission, choice B is the firm's total share, and
choice D is the firm's retained share.
• Question 4: A seller wants to clear exactly $285,000 from the sale of their
suburban home after paying a 6% brokerage commission and $5,400 in
fixed closing costs. What is the minimum gross sales price required to
meet this objective?
o A) $307,524
o B) $302,400
o C) $308,936
o D) $290,400
o CORRECT ANSWER: C) $308,936
o RATIONALE: Apply the classic real estate net-to-seller formula:
Gross Sales Price = (Net Desired + Fixed Costs) / (100% -
Commission Rate). Add the target net to the fixed expenses: $285,000
+ $5,400 = $290,400. Divide this value by the remaining percentage
base: 100% - 6% = 94% (or 0.94). Thus, $290,.94 =
$308,936.17, which rounds down to $308,936. Other choices
incorrectly add 6% straight to the values.
, • Question 5: A commercial tract of raw land is formatted as a rectangle
measuring 450 feet wide by 871.2 feet deep. If the parcel sells for $18,000
per acre, what is the final purchase price?
o A) $162,000
o B) $162,000
o C) $392,040
o D) $9,000
o CORRECT ANSWER: B) $162,000
o RATIONALE: First, calculate the total area in square feet: 450 ft ×
871.2 ft = 392,040 sq ft. Convert this footprint to acres using the
standard real estate conversion factor found on NAR: 392,040 /
43,560 square feet per acre = 9 acres. Multiply the total acreage by the
per-acre market valuation rate: 9 acres × $18,000 = $162,000. Choice
C represents the total square footage.
• Question 6: A property is sold for $320,000. The buyer puts 15% down and
finances the balance. If the lender charges an annual interest rate of 6.5%
and the monthly P&I payment factor is $6.32 per $1,000 of the loan amount,
what is the monthly P&I payment?
o A) $2,022.40
o B) $1,719.04
o C) $1,520.00
o D) $2,100.25
o CORRECT ANSWER: B) $1,719.04
o RATIONALE: First, find the loan amount by removing the 15%
down payment component ($320,000 × 0.85 = $272,000). Next,
divide this loan value by $1,000 to identify the mathematical factor
base ($272,,000 = 272). Finally, multiply this factor by the
monthly amortization scalar: 272 × $6.32 = $1,719.04. Choice A uses
the absolute purchase price incorrectly.
