Real Estate Salesperson Exam (National Portion): Real Estate Math Concepts
Importance ★★★★★ · 100% (estimate)
Overview
This chapter collects the formulas used on the exam. All math questions ask you to apply or analyze, so practice until each step is automatic.
For area, multiply length by width; one acre is 43,560 square feet and a square yard is 9 square feet. Commission equals price times rate, and a split takes a percentage of that. The loan amount equals value times the loan-to-value ratio, and one discount point is 1% of the loan amount. Property tax equals assessed value times the tax rate; one mill is one tenth of a cent, or 0.001.
To find the price a seller needs to net a set amount, divide the net by one minus the commission rate. For prorations, find the daily amount and count the days each party owns, following the question's day count and who owns the closing day; taxes paid in arrears are a debit to the seller. PITI adds monthly principal and interest, taxes, and insurance. Value by income equals NOI divided by the cap rate.
Key concepts
Acre
A unit of land area equal to 43,560 square feet.
Memory tipMemorize 43,560
Discount point
One percent of the loan amount, paid to lower the interest rate or as a fee.
Memory tipPoints on the loan, not the price
Mill
One tenth of a cent, or $1 of tax per $1,000 of assessed value.
Memory tip25 mills = 0.025
Net to seller
Price needed = desired net ÷ (1 − commission rate).
Memory tipDivide, don't add
Proration
Splitting costs by days of ownership; taxes paid in arrears are a debit to the seller and a credit to the buyer.
Memory tipDaily amount × days
PITI
Monthly principal and interest plus one twelfth of annual taxes and insurance.
Memory tipDivide annual costs by 12
Often tested
- Commission = sale price × rate.
- Monthly interest = loan × annual rate ÷ 12.
- Percent change = (new − old) ÷ old.
3 sample questions
Verified practice questions from this unit.
Question 1. A rectangular lot is 150 feet by 290.4 feet. How many acres is it?
- ① 4.4 acres
- ② 1 acre
- ③ 0.5 acre
- ④ 2 acres
▼ Show answer and explanation▲ Hide answer and explanation
Answer: ② 1 acre
Key point: Acres = square feet ÷ 43,560
- Area = 150 × 290.4 = 43,560 square feet.
- Acres = 43,560 ÷ 43,560 = 1 acre.
- 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.
Question 2. A home sells for $300,000. The commission rate is 6%. What is the total commission?
- ① $50,000
- ② $18,000
- ③ $1,800
- ④ $180,000
▼ Show answer and explanation▲ Hide answer and explanation
Answer: ② $18,000
Key point: Commission = price × rate
- Commission = Sale price × Rate.
- $300,000 × 0.06 = $18,000.
- 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%.
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 $9,000
- ② $15,000
- ③ $9,600
- ④ $6,000
▼ Show answer and explanation▲ Hide answer and explanation
Answer: ① $9,000
Key point: Total commission × agent's split
- Total commission = $250,000 × 0.06 = $15,000.
- Salesperson's share = $15,000 × 0.60 = $9,000.
- 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.
AI-written · Verified · Written by AI. Only units that passed a separate AI check (re-reading facts and numbers) are published. Tell us if you find a mistake.