North Dakota Real Estate Math Practice: Formulas and Problems

# North Dakota Real Estate Math Practice: Formulas and Problems

Real estate math questions appear on both the national and state sections of the North Dakota PSI exam. Most candidates find these questions straightforward once they memorize the key formulas and practice applying them under time pressure.

Essential Formulas

Commission Calculation Commission = Sale Price x Commission Rate

Example: A home sells for $285,000 with a 6% commission. Total commission = 285,000 x 0.06 = $17,100. If the listing and selling sides split equally, each receives $8,550.

Loan-to-Value Ratio (LTV) LTV = Loan Amount / Appraised Value x 100

Example: Loan of $190,000 on a $220,000 home. LTV = 190,000 / 220,000 = 86.4%

Property Tax Proration Annual Tax / 365 = Daily Rate. Daily Rate x Days Seller Owned = Seller's Share.

Example: Annual taxes are $3,285. Closing is June 1 (seller owned 151 days). Daily rate = 3,285 / 365 = $9.00/day. Seller owes 151 x $9 = $1,359.

Gross Rent Multiplier (GRM) GRM = Sale Price / Gross Annual Rent

Example: Property sells for $180,000, collects $18,000 annual rent. GRM = 180,000 / 18,000 = 10

Capitalization Rate Cap Rate = Net Operating Income / Value x 100

Example: NOI = $24,000, property value = $300,000. Cap Rate = 24,000 / 300,000 = 8%

Mortgage Interest (First Month) Monthly Interest = Loan Balance x Annual Rate / 12

Example: $200,000 loan at 7% annual rate. First month interest = 200,000 x 0.07 / 12 = $1,166.67

Practice Problems

Problem 1: A salesperson earns 60% of the 5.5% commission on a $320,000 sale. What does she earn?

Total commission = 320,000 x 0.055 = $17,600. Salesperson share = 17,600 x 0.60 = $10,560

Problem 2: Annual property taxes are $4,380. Closing is August 15. Using a 360-day banker's year, how much does the seller owe?

Daily rate = 4,380 / 360 = $12.17. Days owned through Aug 15 = 226 days (30-day months). Seller owes 226 x $12.17 = $2,750.42

Problem 3: A property generates $2,400/month net operating income. An investor wants a 9% cap rate. What is the maximum price she should pay?

Annual NOI = 2,400 x 12 = $28,800. Value = NOI / Cap Rate = 28,800 / 0.09 = $320,000

Tips for Exam Day

Read each math question twice before calculating. North Dakota's exam does not penalize for guessing, so attempt every question. Bring a basic calculator — PSI provides one on-screen. Practice these formulas until the process is automatic, not just memorized.