South Dakota Real Estate Math
Practice Questions & Answers (2026)
Real estate math questions appear on every South Dakota real estate exam and test a focused set of calculations: commission splits, prorations (property tax, rent, interest), loan-to-value ratios, appreciation and depreciation, and area calculations. The South Dakota Real Estate Commission does not provide a calculator — but the math is designed to be workable without one if you know the right formulas. South Dakota candidates consistently lose points on proration questions because they apply the wrong day-count convention (360-day vs. 365-day year) or miscalculate the seller's vs. buyer's share. Work through every problem in this section until you can solve each type without hesitation.
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South Dakota Real Estate Math — Practice Questions & Answers
137 questions on Real Estate Math from the South Dakota real estate question bank. First 10 are free — sign up to unlock all 137.
Q1. A property sells for $285,000. The total commission rate is 6%. The listing agent and selling agent split the commission equally. How much does each agent's brokerage receive?
Explanation
Total commission = $285,000 × 0.06 = $17,100. Each brokerage receives half: $17,100 ÷ 2 = $8,550.
Q2. A buyer purchases a home for $320,000 and makes a 10% down payment. What is the loan amount?
Explanation
Down payment = $320,000 × 0.10 = $32,000. Loan amount = $320,000 − $32,000 = $288,000.
Q3. A lot measures 150 feet wide by 200 feet deep. What is the area of the lot in acres? (1 acre = 43,560 sq ft)
Explanation
Area = 150 ft × 200 ft = 30,000 sq ft. Acres = 30,000 ÷ 43,560 ≈ 0.69 acres.
Q4. A property has a net operating income (NOI) of $24,000 per year. If the capitalization rate is 8%, what is the estimated value of the property?
Explanation
Value = NOI ÷ Cap Rate = $24,000 ÷ 0.08 = $300,000. This is the income approach to value formula: Value = NOI / Cap Rate.
Q5. A South Dakota property sells for $275,000. The buyer puts 20% down. What is the loan amount?
Explanation
Down payment = $275,000 × 0.20 = $55,000. Loan amount = $275,000 − $55,000 = $220,000.
Q6. A broker charges a 6% commission on the sale of a $350,000 property. The listing broker splits the commission 50/50 with the buyer's broker. How much does each broker receive?
Explanation
Total commission = $350,000 × 0.06 = $21,000. Each broker receives $21,000 ÷ 2 = $10,500.
Q7. A South Dakota rental property generates $1,800/month rent. Operating expenses are $800/month. What is the annual NOI?
Explanation
Monthly NOI = $1,800 − $800 = $1,000. Annual NOI = $1,000 × 12 = $12,000.
Q8. A property in Sioux Falls is assessed at $180,000. The tax rate is $15 per $1,000 of assessed value. What are the annual property taxes?
Explanation
Property taxes = ($180,000 ÷ $1,000) × $15 = 180 × $15 = $2,700.
Q9. A rectangular agricultural parcel in South Dakota measures 1/2 mile by 1/4 mile. How many acres does it contain? (1 section = 640 acres)
Explanation
1/2 mile × 1/4 mile = 1/8 section. 640 acres × 1/8 = 80 acres.
Q10. A South Dakota home buyer's gross monthly income is $6,000. Using a 28% front-end ratio, what is the maximum monthly PITI payment the lender will allow?
Explanation
Maximum PITI = $6,000 × 0.28 = $1,680 per month.
Q11. A South Dakota property was purchased for $200,000 and sold for $240,000. What is the percentage of appreciation?
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