Math is usually a small share of the real estate license exam, but candidates often lose points there that they could have kept. The questions are predictable: the same few formulas come up again and again, in slightly different wording. If you know each formula and practice turning a word problem into it, these can be some of the easiest points on the test.
Below are the formulas that show up most often, each with a worked example. Every number in this post has been checked.
Key takeaways
- Most exam math is one of eight types: commission, splits, proration, LTV, PITI and qualifying, area, cap rate, and appreciation.
- Many formulas are one relationship written three ways: Part = Whole × Rate.
- Proration conventions (365 vs. 360 days, who "owns" closing day) vary by state and by exam. Read the question for its instruction.
- Always check whether a question wants a monthly or annual figure, and square feet or acres.
- Calculator rules vary by state and testing vendor. Check your candidate handbook for what is provided or allowed.
The one formula behind most of the others
A huge share of exam math is a version of:
Part = Whole × Rate
- Commission = Sale price × Commission rate
- Interest = Loan amount × Interest rate
- NOI = Value × Cap rate
If you know any two, you can solve for the third. Rate = Part ÷ Whole. Whole = Part ÷ Rate. Many students draw a "T" with Part on top and Whole and Rate below. Cover the one you need and the diagram shows you whether to multiply or divide.
1. Commission
Formula: Commission = Sale price × Commission rate
Example: A home sells for $425,000 with a 5.5% total commission.
- $425,000 × 0.055 = $23,375
Commissions are negotiable, and the exam will give you the rate. Don't assume a "standard" rate.
Working backward to a sale price
Sellers sometimes say how much they want to walk away with. To find the price needed to net a certain amount after commission:
Formula: Sale price = Desired net ÷ (1 − Commission rate)
Example: A seller wants to net $300,000 after a 6% commission (ignore other costs).
- $300,000 ÷ (1 − 0.06) = $300,000 ÷ 0.94 = $319,148.94
A common trap is adding 6% to $300,000 ($318,000). That is too low, because the commission is figured on the higher sale price, not on the net.
2. Commission splits
Commissions usually get split more than once: between the listing and buyer brokerages, then between each brokerage and its agent.
Example: Continuing with the $23,375 commission, the two brokerages split it 50/50, and the listing agent is on a 70/30 split with her broker.
- Listing brokerage share: $23,375 × 0.50 = $11,687.50
- Listing agent's share: $11,687.50 × 0.70 = $8,181.25
- Listing broker keeps: $11,687.50 × 0.30 = $3,506.25
Work through splits one layer at a time. Exam questions often include an extra layer, such as a referral fee taken off the top, to see whether you apply each percentage to the right base. You can check your work with the commission calculator.
3. Proration
Proration divides ongoing costs (property taxes, HOA dues, rent, prepaid interest) between buyer and seller as of the closing date.
Steps:
- Find the daily (or monthly) amount.
- Count the days that belong to the party who owes.
- Multiply.
Example (365-day year): Annual property taxes are $6,570, paid in arrears. Closing is June 15, and the seller is responsible through the day of closing. How much does the seller owe the buyer?
- Daily rate: $6,570 ÷ 365 = $18.00
- Days Jan 1 through Jun 15: 31 + 28 + 31 + 30 + 31 + 15 = 166 days
- Seller's share: 166 × $18.00 = $2,988.00
Because the taxes are paid in arrears, the buyer will pay the whole bill later. The seller's $2,988 shows up as a debit to the seller and a credit to the buyer.
Same example, 360-day "banker's year" (12 months of 30 days):
- Daily rate: $6,570 ÷ 360 = $18.25
- Days: 5 full months × 30 + 15 = 165 days
- Seller's share: 165 × $18.25 = $3,011.25
The two methods give different answers. Which one to use, and whether the buyer or seller owns the day of closing, depends on local custom and on the question. Most exam questions tell you which method to use, so read for it. The proration calculator lets you compare both methods.
4. Loan-to-value (LTV)
Formula: LTV = Loan amount ÷ Property value
Lenders base value on the lower of the purchase price or the appraised value.
Example: A buyer agrees to pay $350,000. The home appraises at $340,000. The lender will lend $306,000.
- Lower value: $340,000
- LTV: $306,000 ÷ $340,000 = 90%
The trap is dividing by the $350,000 contract price, which gives about 87.4%.
5. PITI and qualifying ratios
PITI is a monthly housing payment: Principal, Interest, Taxes and Insurance.
Example: A $280,000, 30-year fixed loan at 6.5%. Annual property taxes are $4,800 and annual homeowners insurance is $1,500.
- Monthly principal and interest: $1,769.79 (from the standard amortization formula; exams usually give you this figure or a payment factor)
- Monthly taxes: $4,800 ÷ 12 = $400.00
- Monthly insurance: $1,500 ÷ 12 = $125.00
- PITI: $1,769.79 + $400 + $125 = $2,294.79
Qualifying with a housing ratio
If a lender's front-end (housing) ratio limit is 28% of gross monthly income:
- Income needed per month: $2,294.79 ÷ 0.28 = $8,195.68
- Income needed per year: about $98,348
Lenders and loan programs use different ratio limits. The exam will give you the ratio to use.
Discount points
One point is 1% of the loan amount, not the price.
- 2 points on a $280,000 loan: $280,000 × 0.02 = $5,600
6. Area and acreage
Conversions to memorize:
- 1 acre = 43,560 square feet
- 1 square yard = 9 square feet
- 1 mile = 5,280 feet
Rectangle: Area = Length × Width
Example: A lot is 330 feet by 264 feet and sells for $65,000 per acre.
- Area: 330 × 264 = 87,120 sq ft
- Acres: 87,120 ÷ 43,560 = 2 acres
- Price: 2 × $65,000 = $130,000
Triangle: Area = ½ × Base × Height
- A triangular parcel with a 150-foot base and 200-foot height: ½ × 150 × 200 = 15,000 sq ft, or about 0.34 acres
Square yards: A 30 ft × 24 ft room = 720 sq ft ÷ 9 = 80 square yards, which is how carpet is often priced.
For odd shapes, break the figure into rectangles and triangles, find each area, and add them.
7. Capitalization rate (income approach)
Formula: Value = Net operating income ÷ Cap rate
(Another version of Part = Whole × Rate: NOI = Value × Cap rate.)
Example: A small apartment building has potential gross income of $120,000. Vacancy and collection loss is 5%. Operating expenses are $38,000. Investors in the area expect an 8% cap rate.
- Effective gross income: $120,000 × 0.95 = $114,000
- NOI: $114,000 − $38,000 = $76,000
- Value: $76,000 ÷ 0.08 = $950,000
Two traps to avoid:
- Mortgage payments (debt service) are not operating expenses. Don't subtract them to get NOI.
- A higher cap rate means a lower value for the same NOI.
8. Appreciation and depreciation
Simple percentage change: (New value − Old value) ÷ Old value
Example: A home bought for $250,000 is now worth $310,000.
- ($310,000 − $250,000) ÷ $250,000 = 24% appreciation
Always divide by the original value. Dividing by the new value is a common wrong answer.
Compound appreciation: Value × (1 + rate)^years
- $300,000 growing 4% per year for 3 years: $300,000 × 1.04³ = $337,459.20
Simple appreciation ($300,000 + 3 × $12,000 = $336,000) gives a different answer, so read whether the question says "per year, compounded."
Straight-line depreciation (investment property): (Cost − Land value) ÷ Useful life
- Residential rental bought for $400,000 total, of which the land is worth $80,000, with a 27.5-year recovery period: ($400,000 − $80,000) ÷ 27.5 = $320,000 ÷ 27.5 = $11,636.36 per year
Land is never depreciated.
Test-day habits that prevent math mistakes
- Underline what is asked. Monthly or annual? Buyer or seller? Square feet or acres?
- Write down the formula before plugging in numbers.
- Estimate first. If 6% of $400,000 is about $24,000, an answer of $2,400 is wrong.
- Don't round until the end.
- Use the answer choices. If you are stuck, plug a choice back into the formula.
Practice until it's automatic
Reading worked examples helps, but the skill you need on test day is turning a wordy question into the right formula fast. Do a set of mixed math questions in a practice test, check splits with the commission calculator, compare proration methods with the proration calculator, and review terms like "debit," "credit," and "NOI" in the glossary. For timed, full-length exams built for your state, see REEX Prep plans.