Real Estate Exam Math: Essential Formulas and Practice Problems 2026

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:

$\frac{\text{Part}}{\text{Total} \times \text{Rate}}$

Key relationships:

• $\text{Part} = \text{Total} \times \text{Rate}$
• $\text{Rate} = \frac{\text{Part}}{\text{Total}}$
• $\text{Total} = \frac{\text{Part}}{\text{Rate}}$

Commission Calculations

Formula

$\text{Commission} = \text{Sales Price} \times \text{Commission Rate}$

Example 1: Finding Commission Amount

A house sells for $350,000 with a 6% commission. What is the total commission?

Solution:

$\text{Commission} = \$350{,}000 \times 0.06 = \$21{,}000$

Example 2: Finding Sales Price

An agent earned $12,000 on a sale with a 5% commission. What was the sales price?

Solution:

$\text{Sales Price} = \frac{\$12{,}000}{0.05} = \$240{,}000$

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:

1. Total commission: $400,000 × 0.06 = $24,000
2. Listing broker's share: $24,000 × 0.60 = $14,400
3. Listing agent's share: $14,400 × 0.50 = $7,200

Property Tax Calculations

Formula

$\text{Annual Tax} = \text{Assessed Value} \times \text{Tax Rate}$

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 = $\frac{25}{1000} = 0.025$
• Tax: $200,000 × 0.025 = $5,000

Mill Rate Conversion

• 1 mill = $1 per $1,000 of assessed value
• 1 mill = $0.001$ (or $\frac{1}{1000}$)
• 10 mills = 1%

Example 5: Converting Mill Rates

What is 35 mills expressed as a percentage and decimal?

Solution:

• Decimal: $\frac{35}{1{,}000} = 0.035$
• Percentage: $0.035 \times 100 = 3.5%$

Loan and Interest Calculations

Formulas

$\text{Annual Interest} = \text{Loan Amount} \times \text{Interest Rate}$

$\text{Monthly Interest} = \frac{\text{Annual Interest}}{12}$

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

$\text{LTV} = \frac{\text{Loan Amount}}{\text{Property Value}} \times 100$

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 calculation:

$\text{LTV} = \frac{\$200{,}000}{\$250{,}000} \times 100 = 80\%$

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.

$\text{Daily Rate} = \frac{\text{Annual Amount}}{360}$

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

Example 13: Finding Lot Area

A rectangular lot is 150 feet × 200 feet. How many square feet?

Solution:

$\text{Area} = 150 \times 200 = 30{,}000 \text{ sq ft}$

Example 14: Converting to Acres

How many acres is a 43,560 sq ft lot?

Solution:

$\text{Acres} = \frac{43{,}560}{43{,}560} = 1 \text{ acre}$

(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:

$\text{Cost} = 2{,}000 \times \$150 = \$300{,}000$

Appreciation and Depreciation

Appreciation Formula

$\text{New Value} = \text{Original Value} \times (1 + \text{Rate})$

Example 16: Appreciation

A home worth $300,000 appreciates 5% per year. What is it worth after 1 year?

Solution:

$\text{New Value} = \$300{,}000 \times 1.05 = \$315{,}000$

Depreciation Formula

$\text{New Value} = \text{Original Value} \times (1 - \text{Rate})$

Example 17: Depreciation

A building valued at $400,000 depreciates 3% annually. What is it worth after 1 year?

Solution:

$\text{New Value} = \$400{,}000 \times 0.97 = \$388{,}000$

Capitalization Rate

Formula

$\text{Cap Rate} = \frac{\text{Net Operating Income (NOI)}}{\text{Property Value}}$

Example 18: Finding Cap Rate

A property generates $50,000 NOI and is valued at $625,000. What is the cap rate?

Solution:

$\text{Cap Rate} = \frac{\$50{,}000}{\$625{,}000} = 0.08 = 8\%$

Example 19: Finding Property Value

An investor wants an 8% cap rate on a property with $40,000 NOI. What should they pay?

Solution:

$\text{Value} = \frac{\$40{,}000}{0.08} = \$500{,}000$

Quick Reference Chart

Calculator Tips

1. Know your calculator - Practice before exam day
2. Write down given information - Avoid confusion
3. Show your work - Helps catch errors
4. Check reasonableness - Does the answer make sense?
5. Don't skip math questions - They're often easier than they look!