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Real Estate Salesperson Exam (National Portion) Real Estate Math Summary

Checked 10/30/26

Real Estate Math: key points

  • 1 acre = 43,560 square feet.
  • One discount point = 1% of the loan amount.
Importance
★★★★★ (5 / 5)
Weight
About 7 of 7 Real Estate Math Calculations questions (100%)

Area and acreage, commission splits, LTV, points, property tax, net to seller, prorations, PITI, cap rate, and return on investment.

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Real Estate Math: 10 sample questions

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Question 1. A rectangular lot is 150 feet by 290.4 feet. How many acres is it?

  1. ① 4.4 acres
  2. ② 1 acre
  3. ③ 0.5 acre
  4. ④ 2 acres
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Answer: ② 1 acre

Key point: Acres = square feet ÷ 43,560

  1. Area = 150 × 290.4 = 43,560 square feet.
  2. Acres = 43,560 ÷ 43,560 = 1 acre.
  3. Remember: 1 acre = 43,560 square feet.

Wrong choices

  • 2 acres: 2 acres would be 87,120 square feet.
  • 0.5 acre: 0.5 acre would be 21,780 square feet.
  • 4.4 acres: This divides by 10,000 instead of 43,560.
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Question 2. A home sells for $300,000. The commission rate is 6%. What is the total commission?

  1. ① $50,000
  2. ② $18,000
  3. ③ $1,800
  4. ④ $180,000
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Answer: ② $18,000

Key point: Commission = price × rate

  1. Commission = Sale price × Rate.
  2. $300,000 × 0.06 = $18,000.
  3. Check: $18,000 ÷ $300,000 = 0.06.

Wrong choices

  • $1,800: This moves the decimal one place too far.
  • $180,000: This uses 60% instead of 6%.
  • $50,000: This divides the price by 6 instead of multiplying by 6%.
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Question 3. A salesperson's broker receives a 6% commission on a $250,000 sale. The salesperson gets 60% of the broker's share. How much does the salesperson earn?

  1. ① $9,000
  2. ② $15,000
  3. ③ $9,600
  4. ④ $6,000
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Answer: ① $9,000

Key point: Total commission × agent's split

  1. Total commission = $250,000 × 0.06 = $15,000.
  2. Salesperson's share = $15,000 × 0.60 = $9,000.
  3. Check: broker keeps $15,000 − $9,000 = $6,000 (40%).

Wrong choices

  • $15,000: $15,000 is the whole commission before the split.
  • $6,000: $6,000 is the broker's 40% share.
  • $9,600: This uses the wrong split amount.
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Question 4. A buyer is getting a loan with an 80% loan-to-value ratio on a $350,000 home. What is the loan amount?

  1. ① $300,000
  2. ② $280,000
  3. ③ $70,000
  4. ④ $350,000
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Answer: ② $280,000

Key point: Loan = value × LTV

  1. Loan = Price (or appraised value, if lower) × LTV.
  2. $350,000 × 0.80 = $280,000.
  3. Down payment = $350,000 − $280,000 = $70,000.

Wrong choices

  • $70,000: $70,000 is the 20% down payment.
  • $350,000: That is the full price, a 100% LTV.
  • $300,000: This is not 80% of $350,000.
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Question 5. A lender charges 2 discount points on a $200,000 loan. How much do the points cost?

  1. ① $2,000
  2. ② $40,000
  3. ③ $400
  4. ④ $4,000
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Answer: ④ $4,000

Key point: 1 point = 1% of the loan amount

  1. One discount point = 1% of the loan amount (not the price).
  2. 2 points = 2% × $200,000 = $4,000.

Wrong choices

  • $400: This uses 0.2% instead of 2%.
  • $40,000: This uses 20% instead of 2%.
  • $2,000: This treats 2 points as 1%.
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Question 6. A home's assessed value is $180,000. The tax rate is 25 mills. What is the annual property tax?

  1. ① $450
  2. ② $4,500
  3. ③ $7,200
  4. ④ $45,000
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Answer: ② $4,500

Key point: 1 mill = $1 per $1,000 = 0.001

  1. 25 mills = 25 ÷ 1,000 = 0.025.
  2. Tax = $180,000 × 0.025 = $4,500.
  3. Check: $180,000 ÷ 1,000 × 25 = $4,500.

Wrong choices

  • $450: This uses 2.5 mills by mistake.
  • $45,000: This uses 25% instead of 25 mills.
  • $7,200: This does not use the mill rate correctly.
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Question 7. A seller wants to net $190,000 after paying a 5% commission. Ignoring other costs, what is the lowest sale price that will do this?

  1. ① $200,000
  2. ② $199,500
  3. ③ $209,000
  4. ④ $180,500
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Answer: ① $200,000

Key point: Price needed = desired net ÷ (1 − commission rate)

  1. The seller keeps 100% − 5% = 95% of the price.
  2. Price = $190,000 ÷ 0.95 = $200,000.
  3. Check: $200,000 − 5% ($10,000) = $190,000.

Wrong choices

  • $199,500: This adds 5% of $190,000 instead of dividing by 0.95.
  • $180,500: This subtracts 5% instead of adding it back.
  • $209,000: This adds 10% instead of 5%.
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Question 8. Annual property taxes of $3,650 are paid in arrears. Closing is on April 10, and the seller owns the day of closing. Using a 365-day year, what is the seller's share?

  1. ① $990 debit to the seller
  2. ② $2,650 debit to the seller
  3. ③ $1,000 credit to the seller
  4. ④ $1,000 debit to the seller
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Answer: ④ $1,000 debit to the seller

Key point: Arrears taxes → seller's days are a debit to seller, credit to buyer

  1. Daily tax = $3,650 ÷ 365 = $10 per day.
  2. Seller's days: Jan 31 + Feb 28 + Mar 31 + Apr 10 = 100 days.
  3. Seller's share = 100 × $10 = $1,000.
  4. The taxes have not been paid yet (arrears), so the seller owes this amount: debit seller, credit buyer.

Wrong choices

  • $1,000 credit to the seller: Taxes paid in arrears are owed by the seller, so they are a debit to the seller.
  • $2,650 debit to the seller: $2,650 is the buyer's share of the year.
  • $990 debit to the seller: This leaves out the day of closing.
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Question 9. A property earns $60,000 in effective gross income. Operating expenses are $15,000 and annual mortgage payments are $20,000. Using an 8% cap rate, what is the value?

  1. ① $750,000
  2. ② $562,500
  3. ③ $45,000
  4. ④ $312,500
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Answer: ② $562,500

Key point: NOI excludes mortgage payments; value = NOI ÷ cap rate

  1. NOI = $60,000 − $15,000 = $45,000 (mortgage payments are not subtracted).
  2. Value = $45,000 ÷ 0.08 = $562,500.
  3. Check: $562,500 × 0.08 = $45,000.

Wrong choices

  • $312,500: This subtracts the mortgage payments, which are not operating expenses.
  • $750,000: This uses gross income instead of NOI.
  • $45,000: $45,000 is the NOI, not the value.
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Question 10. An investor bought a property for $200,000 and sold it for $250,000. What was the percentage of profit based on the purchase price?

  1. ① 80%
  2. ② 50%
  3. ③ 25%
  4. ④ 20%
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Answer: ③ 25%

Key point: Percent change = (new − old) ÷ old

  1. Profit = $250,000 − $200,000 = $50,000.
  2. Percent = $50,000 ÷ $200,000 = 0.25 = 25%.

Wrong choices

  • 20%: 20% is the profit divided by the sale price, not the purchase price.
  • 50%: This does not divide by the purchase price correctly.
  • 80%: 80% is the purchase price as a percent of the sale price.

Test yourself.

Real Estate Math: 5 questions →Real Estate Math Calculations: 5 questions →

Written by AI · Not yet reviewed by staff