How Much Math Is on the Exam
Less than candidates fear, and more than the outline suggests. The national portion of the salesperson exam has a dedicated Real Estate Math Calculations area worth 8.75% — seven scored questions of 80 — but calculation also appears inside the appraisal, financing and practice areas: a cap-rate question is filed under Property Value and Appraisal, a commission split under Real Estate Practice. On the combined 150-question California exam, expect roughly ten to fifteen questions that need arithmetic. None needs more than a four-function calculator, which the test centre provides on screen.
Every formula the exam uses is below, each with a worked example and the wrong answer the distractors are built from (usually the same numbers combined the other way round). Practise them on our free real estate practice questions, where every calculation explanation shows the working.
The Constants to Memorise
| Fact | Value |
|---|---|
| Acre | 43,560 square feet |
| Section (government survey) | 1 square mile = 640 acres; a township is 36 sections |
| Mile | 5,280 feet |
| One discount point | 1% of the loan amount, not the price |
| Interest in a payment | Annual interest = balance × rate; monthly = annual ÷ 12 |
| Proration year | The question says: a 360-day "banker's" year (30-day months) or a 365-day calendar year |
| Mill | $1 per $1,000 of assessed value (0.001) |
| California documentary transfer tax | $1.10 per $1,000 of price ($0.55 per $500), before any city tax |
| Math on the national exam | 8.75% = 7 scored questions, plus calculations inside other areas |
Commissions and Splits
Total commission = sale price × rate. Then split it as the question says, in order.
Example: a home sells for $425,000 with a 6% commission, split 60/40 between listing and selling brokers, and the listing broker pays their salesperson 70% of the broker's share. Total: $425,000 × 0.06 = $25,500. Listing broker: $25,500 × 0.60 = $15,300. Salesperson: $15,300 × 0.70 = $10,710. Trap answers: $25,500 (forgot the split), $15,300 (stopped a step early), $17,850 (took 70% of the whole commission).
Reverse it when the question gives the commission and asks the price: a $13,500 commission at 4.5% means a price of $13,500 ÷ 0.045 = $300,000.
Loans: LTV, Down Payment, Points, Interest and PITI
Loan-to-value and down payment
Loan = price × LTV; down payment = price − loan. A $340,000 purchase with an 80% LTV: loan $272,000, down payment $68,000. If the appraisal comes in lower than the price, the lender uses the lower of price and appraised value — a $340,000 contract appraised at $330,000 at 80% LTV gives a $264,000 loan and the buyer finds the extra $10,000.
Discount points
Points × 1% × loan amount. Two points on a $272,000 loan: 0.02 × $272,000 = $5,440. The trap: 0.02 × $340,000 = $6,800 uses the price.
Interest
Annual interest = principal × rate; first month's interest = annual ÷ 12. A $250,000 loan at 6.6%: $16,500 a year, $1,375 in the first month. If the total monthly payment is $1,597, the first month's principal reduction is $1,597 − $1,375 = $222, and the balance after one payment is $249,778. The exam rarely asks past the second month; if it does, compute the second month's interest on the new balance.
Simple interest for a term
$150,000 at 7% for two years: $150,000 × 0.07 × 2 = $21,000.
PITI and escrow
Monthly taxes and insurance = (annual tax + annual premium) ÷ 12. $3,600 tax and $1,200 insurance: $4,800 ÷ 12 = $400, added to principal and interest to make the full payment.
Qualifying ratios
A front-end ratio of 28% on a $6,000 monthly income allows a housing payment of $1,680; a back-end ratio of 36% allows $2,160 for housing plus other debt. If the buyer already pays $600 in car and card payments, the housing payment cannot exceed $1,560 — the smaller of the two limits wins.
Appraisal: Cap Rate, NOI, GRM and the Cost Approach
Net operating income
NOI = effective gross income − operating expenses, where effective gross income is gross rent minus vacancy and collection loss. Debt service is not an operating expense. Gross rent $120,000, vacancy 5%, expenses $36,000: EGI $114,000, NOI $78,000.
Capitalisation rate
Value = NOI ÷ cap rate; cap rate = NOI ÷ value. NOI $78,000 at an 8% cap: $78,000 ÷ 0.08 = $975,000. The direction to remember: a higher cap rate gives a lower value for the same income — the investor demands more return, so pays less.
Gross rent multiplier
GRM = sale price ÷ monthly rent; value = GRM × subject's monthly rent. Comparables sold for $240,000 renting at $2,000 a month give a GRM of 120; a subject renting at $2,400 is worth 120 × $2,400 = $288,000. Use the subject's rent, not the comparable's — the classic trap. A gross income multiplier works the same way with annual figures.
Cost approach
Value = land value + replacement (or reproduction) cost − accrued depreciation. Land $250,000, replacement cost $180,000, depreciation $30,000: $400,000. Adding the depreciation instead of subtracting it ($460,000) is the distractor. Straight-line depreciation: a building with a 50-year economic life is 20 years old, so it has lost 20 ÷ 50 = 40% of its value.
Sales comparison adjustments
Adjust the comparable, never the subject: if the comparable has something the subject lacks, subtract; if the subject has something the comparable lacks, add. A comparable sold at $295,000 with a $15,000 pool the subject does not have is adjusted to $280,000. With several adjusted comparables, the indicated value is their reconciled figure — usually the mean when the question gives nothing else: ($320,000 + $345,000 + $360,000) ÷ 3 = $341,667.
Property Tax and Transfer Tax
Tax = assessed value × rate, where assessed value may be market value × an assessment ratio. Market value $250,000 at an 80% ratio is $200,000 assessed; at $3.25 per $100 the tax is $200,000 ÷ 100 × $3.25 = $6,500. With a mill rate of 18 mills: $200,000 × 0.018 = $3,600.
California's documentary transfer tax is $1.10 per $1,000 of the price: on $525,000 the county tax is 525 × $1.10 = $577.50, customarily paid by the seller (cities may add their own). Proposition 13 questions are conceptual rather than arithmetic — assessed value is capped at the purchase price plus at most 2% a year until a change of ownership.
Prorations at Closing
Prorations divide a yearly or monthly cost between seller and buyer at the closing date. Three decisions come from the question: the day count (360-day banker's year with 30-day months, or 365-day calendar year), whether the closing day belongs to the buyer or the seller, and whether the item was paid in advance or in arrears.
Example: annual property tax of $4,380 was paid in advance for the calendar year; closing is 1 April, buyer owns the closing day, 365-day year. The seller used 90 days (January to March) and is owed the rest: $4,380 ÷ 365 = $12 a day; the buyer's share is 275 days × $12 = $3,300, shown as a credit to the seller and a debit to the buyer.
Rent works the other way: rent is collected in advance, so at a mid-month closing the seller owes the buyer the unused days. $2,400 rent for a 30-day month, closing on the 11th with the buyer owning the closing day: the buyer is credited 20 days × $80 = $1,600.
Area, Acreage and Legal Descriptions
Rectangle = length × width; triangle = ½ × base × height. A lot of 120 ft × 85 ft is 10,200 sq ft; at $25 a square foot it is priced at $255,000. Convert to acres by dividing by 43,560: a 130,680 sq ft parcel is 3 acres.
Government survey questions are fraction chains: the NE¼ of the SW¼ of a section is ¼ × ¼ × 640 = 40 acres. Multiply the fractions, then multiply by 640. A parcel described as "the S½ of the NW¼" is 80 acres.
Appreciation, Depreciation and Seller's Net
New value = old value × (1 ± rate). A $380,000 home appreciating 3% is worth $391,400; a buyer who put 10% down ($38,000) with a $342,000 loan now has equity of $391,400 − $342,000 = $49,400. Over several years the rate compounds: 3% for two years is × 1.03 × 1.03, not × 1.06.
Working backwards is the other common form: a home sold for $312,000 after appreciating 4% was bought for $312,000 ÷ 1.04 = $300,000 — dividing, not subtracting 4%.
Seller's net: the price the seller needs to list at to clear a target after paying a commission is target ÷ (1 − rate). To net $282,000 after a 6% commission: $282,000 ÷ 0.94 = $300,000. Adding 6% to $282,000 ($298,920) is the trap.
Return on investment: a $500,000 property bought with $175,000 down that gains $20,000 in value and $8,000 in principal paydown in a year returned $28,000 on $175,000 of equity — 16%. Leverage is why the return on equity beats the 4% the property itself gained.
A Method for Exam Day
- Write the formula before touching the numbers. Most errors are the right numbers in the wrong slots.
- Label every figure — price, loan, NOI, rate — because the distractors are the same figures combined differently.
- Check the base. Points on the loan, not the price; GRM on the subject's rent; cap rate on NOI, not gross.
- Sanity-check the size. A monthly interest figure bigger than a yearly one, or a value lower than the NOI, means a slipped decimal.
- Do not round early. Carry cents to the end; round only the final answer to what the choices show.
Frequently Asked Questions
How many math questions are on the real estate exam?
The national salesperson outline gives Real Estate Math Calculations 8.75% — seven scored questions of 80 — and calculations also appear inside the appraisal, financing and practice areas. On California's 150-question combined exam, expect roughly ten to fifteen questions that need arithmetic.
Can I use a calculator on the real estate exam?
Test centres provide an on-screen four-function calculator. Personal calculators, phones and notes are not allowed in the room; you get scratch paper or a whiteboard.
What is the formula for cap rate?
Cap rate = net operating income ÷ value, and value = NOI ÷ cap rate. NOI is effective gross income minus operating expenses, before any loan payments.
How do I calculate a seller's net?
Divide the amount the seller wants to keep by one minus the commission rate. To net $282,000 after 6%, list at $282,000 ÷ 0.94 = $300,000. Adding the commission percentage to the net gives a price that is too low.
How many square feet are in an acre?
43,560. A section is one square mile, 640 acres; a quarter-quarter section is 40 acres.
Sources
- Pearson VUE National Real Estate Salesperson Content Outline (effective January 2025) — the Real Estate Math Calculations area (8.75%) and the calculation topics listed under Property Value and Appraisal, Financing and Settlement, and Real Estate Practice.
- California DRE Salesperson Examination Content — the 150-question, three-hour, 70% format and the Property Valuation and Financial Analysis area.
- California Revenue and Taxation Code §11911 for the documentary transfer tax rate; Proposition 13 (Cal. Const. art. XIII A) for the assessment cap.
- All worked examples are QuizCram's own; no exam items are reproduced.
