Real Estate Math Made Simple
Math questions make up 10-15% of the real estate exam and are often where candidates lose valuable points. The good news? You only need to master a handful of formulas to answer most math questions correctly.
Essential Real Estate Math Formulas
The T-Bar Method
Most real estate math problems can be solved using the T-Bar formula:
Part
─────────────
Total × Rate
Key relationships:
- Part = Total × Rate
- Rate = Part ÷ Total
- Total = Part ÷ Rate
Commission Calculations
Formula
Commission = Sales Price × Commission Rate
Example 1: Finding Commission Amount
A house sells for $350,000 with a 6% commission. What is the total commission?
Solution: Commission = $350,000 × 0.06 = $21,000
Example 2: Finding Sales Price
An agent earned $12,000 on a sale with a 5% commission. What was the sales price?
Solution: Sales Price = $12,000 ÷ 0.05 = $240,000
Example 3: Commission Splits
A property sells for $400,000 at 6% commission. The listing broker receives 60% and the selling broker 40%. The listing agent gets 50% of their broker's share. What does the listing agent earn?
Solution:
- Total commission: $400,000 × 0.06 = $24,000
- Listing broker's share: $24,000 × 0.60 = $14,400
- Listing agent's share: $14,400 × 0.50 = $7,200
Property Tax Calculations
Formula
Annual Tax = Assessed Value × Tax Rate
Example 4: Finding Annual Tax
Property assessed at $200,000 with a tax rate of 25 mills. What is the annual tax?
Solution:
- 25 mills = 25/1000 = 0.025
- Tax = $200,000 × 0.025 = $5,000
Mill Rate Conversion
- 1 mill = $1 per $1,000 of assessed value
- 1 mill = 0.001 (1/1000)
- 10 mills = 1%
Example 5: Converting Mill Rates
What is 35 mills expressed as a percentage and decimal?
Solution:
- Decimal: 35 ÷ 1,000 = 0.035
- Percentage: 0.035 × 100 = 3.5%
Loan and Interest Calculations
Formula
Annual Interest = Loan Amount × Interest Rate Monthly Interest = Annual Interest ÷ 12
Example 6: Finding Monthly Interest
A $300,000 loan at 6% annual interest. What is the first month's interest?
Solution:
- Annual interest: $300,000 × 0.06 = $18,000
- Monthly interest: $18,000 ÷ 12 = $1,500
Example 7: Finding Loan Amount
Monthly interest is $875 on a loan at 7% annual interest. What is the loan amount?
Solution:
- Annual interest: $875 × 12 = $10,500
- Loan amount: $10,500 ÷ 0.07 = $150,000
Loan-to-Value (LTV) Ratio
Formula
LTV = Loan Amount ÷ Property Value × 100
Example 8: Finding LTV
A buyer puts $50,000 down on a $250,000 home. What is the LTV?
Solution:
- Loan amount: $250,000 - $50,000 = $200,000
- LTV: $200,000 ÷ $250,000 = 0.80 = 80%
Example 9: Finding Required Down Payment
A lender requires 80% LTV on a $400,000 purchase. What down payment is needed?
Solution:
- Maximum loan: $400,000 × 0.80 = $320,000
- Down payment: $400,000 - $320,000 = $80,000
Proration Calculations
Property Tax Proration
Taxes are typically prorated based on who owns the property on the closing date.
Example 10: Seller Prepaid Taxes
Annual taxes of $3,600 were prepaid. Closing is September 15. How much does the buyer owe the seller?
Solution (using 30-day months, 360-day year):
- Daily tax: $3,600 ÷ 360 = $10/day
- Seller owned: Jan 1 - Sept 15 = 255 days
- Buyer owes for: Sept 16 - Dec 31 = 105 days
- Buyer owes seller: 105 × $10 = $1,050
Example 11: Unpaid Taxes
Annual taxes of $4,800 are unpaid. Closing is March 20. How much does the seller owe?
Solution:
- Daily tax: $4,800 ÷ 360 = $13.33/day
- Seller owned Jan 1 - March 20 = 80 days
- Seller owes: 80 × $13.33 = $1,066.40
Rent Proration
Example 12: Prorating Rent
Tenant pays $1,500/month rent in advance. Closing is on the 10th. How much rent credit does buyer receive?
Solution:
- Daily rent: $1,500 ÷ 30 = $50/day
- Buyer owns 20 days (11th-30th)
- Buyer credit: 20 × $50 = $1,000
Area and Volume Calculations
Area Formulas
| Shape | Formula |
|---|---|
| Rectangle | Length × Width |
| Triangle | ½ × Base × Height |
| Circle | π × Radius² (π ≈ 3.14) |
| Trapezoid | ½ × (Base₁ + Base₂) × Height |
Example 13: Finding Lot Area
A rectangular lot is 150 feet × 200 feet. How many square feet?
Solution: Area = 150 × 200 = 30,000 sq ft
Example 14: Converting to Acres
How many acres is a 43,560 sq ft lot?
Solution: Acres = 43,560 ÷ 43,560 = 1 acre
(Note: 1 acre = 43,560 square feet)
Example 15: Calculating Building Cost
A 2,000 sq ft home costs $150 per sq ft to build. What is the total cost?
Solution: Cost = 2,000 × $150 = $300,000
Appreciation and Depreciation
Appreciation Formula
New Value = Original Value × (1 + Rate)
Example 16: Appreciation
A home worth $300,000 appreciates 5% per year. What is it worth after 1 year?
Solution: New value = $300,000 × 1.05 = $315,000
Depreciation Formula
New Value = Original Value × (1 - Rate)
Example 17: Depreciation
A building valued at $400,000 depreciates 3% annually. What is it worth after 1 year?
Solution: New value = $400,000 × 0.97 = $388,000
Capitalization Rate
Formula
Cap Rate = Net Operating Income ÷ Property Value
Example 18: Finding Cap Rate
A property generates $50,000 NOI and is valued at $625,000. What is the cap rate?
Solution: Cap Rate = $50,000 ÷ $625,000 = 0.08 = 8%
Example 19: Finding Property Value
An investor wants an 8% cap rate on a property with $40,000 NOI. What should they pay?
Solution: Value = $40,000 ÷ 0.08 = $500,000
Quick Reference Chart
| Calculation | Formula |
|---|---|
| Commission | Sales Price × Rate |
| Annual Tax | Assessed Value × Tax Rate |
| Monthly Interest | (Loan × Rate) ÷ 12 |
| LTV | Loan ÷ Value × 100 |
| Cap Rate | NOI ÷ Value |
| Area (Rectangle) | L × W |
| Acres | Sq Ft ÷ 43,560 |
Calculator Tips
- Know your calculator - Practice before exam day
- Write down given information - Avoid confusion
- Show your work - Helps catch errors
- Check reasonableness - Does the answer make sense?
- Don't skip math questions - They're often easier than they look!