Real Estate Exam Math Practice: 20 Problems You Must Master
Math questions account for 10-15% of most real estate exams. Many students fear math, but with practice, these problems become easy points. Here are 20 must-know problems with step-by-step solutions.
Tip: Bookmark our Math Formulas Cheat Sheet for quick reference while practicing.
Commission Problems
Problem 1: Basic Commission
A property sells for $425,000 with a 6% total commission. The listing and buyer's brokerages split the commission 50/50. The listing agent has a 70/30 split with their brokerage. How much does the listing agent earn?
Solution:- Total commission: $425,000 × 0.06 = $25,500
- Listing brokerage share: $25,500 × 0.50 = $12,750
- Listing agent share: $12,750 × 0.70 = $8,925
Problem 2: Finding the Sale Price
An agent earned $9,450 in commission. The commission rate was 6%, and the agent had a 60/40 split with their broker. What was the sale price?
Solution:- Agent received 60% of the commission: $9,450 ÷ 0.60 = $15,750 (total commission)
- Total commission was 6% of sale price: $15,750 ÷ 0.06 = $262,500
Problem 3: Net to Seller
A seller wants to net $300,000 after paying a 5% commission. What must the sale price be?
Solution:- If commission is 5%, seller keeps 95%
- $300,000 ÷ 0.95 = $315,789.47
- (NOT $300,000 × 1.05 = $315,000 — this is a common trap!)
Mortgage & Loan Problems
Problem 4: Loan-to-Value (LTV)
A buyer purchases a home for $380,000 with a down payment of $76,000. What is the LTV ratio? Will PMI be required?
Solution:- Loan amount: $380,000 - $76,000 = $304,000
- LTV: $304,000 ÷ $380,000 = 0.80 = 80%
- PMI required? No — PMI is required when LTV exceeds 80%
Problem 5: Down Payment Percentage
A buyer takes out a $285,000 loan on a $300,000 property. What is the down payment percentage?
Solution:- Down payment: $300,000 - $285,000 = $15,000
- Percentage: $15,000 ÷ $300,000 = 0.05 = 5%
Problem 6: Discount Points
A buyer is taking a $250,000 loan and paying 2 discount points. How much do the points cost?
Solution:- 1 point = 1% of loan amount
- 2 points = 2% × $250,000 = $5,000
Problem 7: Total Interest
A buyer has a $200,000 mortgage at $1,200/month for 30 years. How much total interest will they pay?
Solution:- Total payments: $1,200 × 360 months = $432,000
- Total interest: $432,000 - $200,000 = $232,000
Proration Problems
Problem 8: Property Tax Proration
Annual property taxes are $4,380. The seller has paid taxes for the full year. Closing is on September 15. Using a 365-day year, how much does the buyer owe the seller?
Solution:- Daily rate: $4,380 ÷ 365 = $12.00/day
- Seller owns Jan 1 - Sep 14 = 257 days
- Buyer owes for Sep 15 - Dec 31 = 108 days
- Buyer owes seller: 108 × $12.00 = $1,296.00
Problem 9: Rent Proration
Monthly rent is $2,400. The property closes on March 20. The seller has already collected March rent. How much does the seller owe the buyer?
Solution:- Daily rate: $2,400 ÷ 31 days (March) = $77.42/day
- Buyer's portion: March 20-31 = 12 days
- Seller owes buyer: 12 × $77.42 = $929.03
Investment Analysis Problems
Problem 10: Cap Rate
A property generates $36,000 in annual gross rent, has $12,000 in operating expenses, and is valued at $400,000. What is the cap rate?
Solution:- NOI: $36,000 - $12,000 = $24,000
- Cap rate: $24,000 ÷ $400,000 = 0.06 = 6%
Problem 11: Property Value from Cap Rate
An investor wants an 8% cap rate. The property generates $32,000 NOI. What is the maximum they should pay?
Solution:- Value = NOI ÷ Cap rate
- $32,000 ÷ 0.08 = $400,000
Problem 12: Gross Rent Multiplier
A property is listed at $360,000 with monthly rent of $3,000. What is the GRM?
Solution:- Annual gross rent: $3,000 × 12 = $36,000
- GRM: $360,000 ÷ $36,000 = 10
Problem 13: Cash-on-Cash Return
An investor puts $80,000 down, generates $24,000 annual rent, has $14,000 in expenses (including mortgage), and gets $10,000 net cash flow. What is the cash-on-cash return?
Solution:- Cash-on-cash: $10,000 ÷ $80,000 = 0.125 = 12.5%
Area & Property Problems
Problem 14: Lot Size in Acres
A rectangular lot measures 200 feet by 300 feet. How many acres is it?
Solution:- Area: 200 × 300 = 60,000 sq ft
- Acres: 60,000 ÷ 43,560 = 1.377 acres
Problem 15: Price Per Square Foot
A 2,400 sq ft home sells for $456,000. What is the price per square foot?
Solution:- $456,000 ÷ 2,400 = $190/sq ft
Problem 16: Irregular Lot
A lot is shaped like an L. The main rectangle is 150 ft × 100 ft. The extension is 50 ft × 60 ft. What is the total area?
Solution:- Main rectangle: 150 × 100 = 15,000 sq ft
- Extension: 50 × 60 = 3,000 sq ft
- Total: 15,000 + 3,000 = 18,000 sq ft
Depreciation & Tax Problems
Problem 17: Straight-Line Depreciation
A residential rental property was purchased for $275,000. The land is valued at $50,000. What is the annual depreciation?
Solution:- Building value: $275,000 - $50,000 = $225,000
- Residential depreciation: 27.5 years
- Annual depreciation: $225,000 ÷ 27.5 = $8,181.82/year
Problem 18: Property Tax
A property has a market value of $350,000. The assessment rate is 80%. The tax rate is 32 mills. What is the annual property tax?
Solution:- Assessed value: $350,000 × 0.80 = $280,000
- Tax rate: 32 mills = 32 ÷ 1,000 = 0.032
- Annual tax: $280,000 × 0.032 = $8,960
Problem 19: Transfer Tax
A property sells for $500,000. The state charges a transfer tax of $2.00 per $500 of sale price. What is the transfer tax?
Solution:- Number of $500 units: $500,000 ÷ $500 = 1,000
- Transfer tax: 1,000 × $2.00 = $2,000
Problem 20: Assessed Value from Tax
A property owner pays $6,300 in annual taxes. The tax rate is 42 mills. What is the assessed value?
Solution:- Tax rate: 42 mills = 0.042
- Assessed value: $6,300 ÷ 0.042 = $150,000
Key Math Tips for Exam Day
- Always convert percentages to decimals before calculating
- Read carefully — "net to seller" problems are tricky
- NOI never includes mortgage payments — this is the #1 trap
- 1 acre = 43,560 sq ft — memorize this
- 1 mill = $1 per $1,000 of assessed value
- Residential depreciation = 27.5 years, commercial = 39 years
- Check if the problem uses a 360-day or 365-day year
Practice More
These 20 problems cover the most common exam math topics. For more practice:
- Math Formulas Cheat Sheet — all formulas in one place
- Commission Calculator — practice with different scenarios
- Mortgage Calculator — explore loan calculations
- Math Drill — timed math practice