Real estate math practice test, with every formula worked

Real estate math is about 7 of the 80 national questions on both vendors' outlines, and it is the most learnable part of the exam: every problem is one of a dozen formulas. Learn commission, proration, loan-to-value, amortisation, area, capitalisation rate and transfer tax, write the formula before the numbers, and these become the surest points on the test.

7
math questions in 80, both outlines: 12
formulas cover them: 43,560
square feet in an acre: Free
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Last checked 13 November 2026 · Counts as reported from the Pearson VUE and PSI national outlines; formulas and worked examples by LifeScore

Free drills: 12 original real estate exam-style questions each, at the national portion's pace, then every answer worked. New numbers every time. No sign-up.

12
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18 min
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every answer explained

By the LifeScore Editorial Team · Updated 13 November 2026 · How we check facts · How this is scored

What math is on the real estate exam?

Percentages applied to a base (commission, loan-to-value, points, cap rate), areas and acres, prorations by the day, and one month of a loan's amortisation. The table below has every formula with a worked line.

The formulas real estate math questions use, each with a worked line
Calculation	Formula	Worked line
Commission	Sale price × commission rate	$350,000 × 6% = $21,000
Commission split	Total commission × each side's share, then × the agent's split with the broker	$21,000 × 50% × 60% = $6,300
Loan-to-value (LTV)	Loan amount ÷ the lower of price or appraised value	$270,000 ÷ $300,000 = 90%
One month's interest	Loan balance × annual rate ÷ 12	$200,000 × 6% ÷ 12 = $1,000
Principal in a payment	Payment − that month's interest	$1,199.10 − $1,000 = $199.10
Discount points	Each point = 1% of the loan amount	2 points on $250,000 = $5,000
Area	Length × width; 1 acre = 43,560 square feet; 1 square yard = 9 square feet	330 ft × 132 ft = 43,560 sq ft = 1 acre
Capitalisation rate	Value = net operating income ÷ cap rate	$48,000 ÷ 8% = $600,000
Transfer tax	Price ÷ the taxed unit (often $500 or $1,000), rounded up if the rule says so, × the rate	$300,000 ÷ $500 × $1 = $600
Proration (365-day year)	Annual amount ÷ 365 × the days owed	$3,650 ÷ 365 × 120 = $1,200
Net to seller	Price − commission − other seller costs − loan payoff	$400,000 − $24,000 − $3,000 − $250,000 = $123,000
Straight-line depreciation	Building cost ÷ useful life = yearly depreciation	$275,000 ÷ 27.5 = $10,000 a year

Most of them are the same shape: part = whole × rate. A commission is the price times the rate; a loan is the value times the loan-to-value ratio; a point is 1% of the loan; a value is the income divided by the cap rate. Know which number is the whole and the rest is arithmetic.

Most states let you bring a basic calculator, or give you one on screen; check your handbook. Either way, estimate first so a slipped decimal stands out.

How do you work out commission and loan-to-value questions?

Commission is the sale price times the rate, then split by side and by the agent's share. Loan-to-value is the loan divided by the lower of the price and the appraisal.

Real Estate Exam-style question 1 · Commission split
A home sells for $380,000 with a 5.5% commission, shared equally between the listing and selling brokerages. The selling agent receives 70% of her brokerage's share. How much does the selling agent receive?
1. A$7,315
2. B$10,450
3. C$14,630
4. D$5,225
Worked answer
A: $7,315. Total commission is $380,000 × 5.5% = $20,900. The selling brokerage gets half, $10,450, and the agent gets 70% of that, $7,315.
1. Total: $380,000 × 0.055 = $20,900.
2. Selling side: $20,900 × 50% = $10,450.
3. Agent: $10,450 × 70% = $7,315.
The trap: Stopping at $10,450, the brokerage's share. The question asks for the agent's cut of it.
Real Estate Exam-style question 2 · Loan-to-value
A buyer agrees to pay $250,000 for a home that appraises at $240,000. The lender will lend 80% of value. What is the largest loan the buyer can get?
1. A$192,000
2. B$200,000
3. C$208,000
4. D$48,000
Worked answer
A: $192,000. Lenders apply the loan-to-value ratio to the lower of the price and the appraised value. 80% of $240,000 is $192,000.
1. The lower of price ($250,000) and appraisal ($240,000): $240,000.
2. $240,000 × 80% = $192,000.
The trap: Using the contract price: 80% of $250,000 is $200,000, which the lender will not lend on a $240,000 appraisal.

The trap in each is stopping one step short or using the wrong base. A split question asks for one person's cut, often after two splits; an LTV question almost always has a price and an appraisal that differ, and the lender uses the lower.

How do you do proration on the real estate exam?

Find the daily amount (annual ÷ 365, or ÷ 360 if the question says a banker's year), count the days the seller owned the property or the days left, and decide who owes whom from whether the bill was paid in advance or in arrears.

Real Estate Exam-style question 1 · Proration
Annual property taxes of $4,380 are paid in arrears and nothing has been paid for the current year. Closing is on April 10, and the seller owns the day of closing. Using a 365-day year, how is the tax prorated?
1. A$1,200 credit to the buyer
2. B$1,200 credit to the seller
3. C$3,180 credit to the buyer
4. D$1,188 credit to the buyer
Worked answer
A: $1,200 credit to the buyer. Taxes paid in arrears mean the buyer will pay the whole year's bill later, so the seller owes the buyer for the days the seller owned the home. January 1 to April 10 is 31 + 28 + 31 + 10 = 100 days. $4,380 ÷ 365 = $12 a day, × 100 = $1,200, a debit to the seller and a credit to the buyer.
1. Daily rate: $4,380 ÷ 365 = $12.
2. Seller's days, closing day included: 31 + 28 + 31 + 10 = 100.
3. Seller owes $12 × 100 = $1,200, credited to the buyer.
The trap: Crediting the seller. In arrears means unpaid, so the seller has used days the buyer will pay for; the credit goes to the buyer.

Paid in arrears (not yet paid): the seller owes the buyer for the seller's days. Debit seller, credit buyer.
Paid in advance (already paid): the buyer owes the seller for the days left. Debit buyer, credit seller.
Who owns the closing day changes the count by one. Read the question; our questions say so every time.
A 365-day year uses the real days in each month; a 360-day (banker's) year treats every month as 30 days.

Math with new numbers every time

Four math drills of 12 and seven math questions in each of six full mocks, every one worked step by step.

The Real Estate Exam Pass Pack gives you 6 full mocks on the real clock, 36 drills of 12 questions for the sections that cost you points, and a predictor that turns your mocks into the odds of reaching your target. One payment, no subscription, and your free score stays free.

Prep courses for these tests usually cost $19 to $129. The Real Estate Exam Pass Pack is US$39 (£29), once.

See the Real Estate Exam Pass Pack How our questions are built and checked

6
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topic drills: 1
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How do you calculate interest and principal on a mortgage payment?

One month's interest is the loan balance times the annual rate divided by 12. The principal paid is the payment minus that interest, and the new balance is the old balance minus the principal.

Real Estate Exam-style question 1 · Amortisation
A $300,000 fully amortized loan at 6% annual interest has a principal-and-interest payment of $1,798.65 a month. How much of the first payment reduces the principal?
1. A$298.65
2. B$1,500.00
3. C$1,798.65
4. D$1,201.35
Worked answer
A: $298.65. The first month's interest is $300,000 × 6% ÷ 12 = $1,500. The rest of the payment, $1,798.65 − $1,500 = $298.65, goes to principal.
1. Interest for the month: $300,000 × 0.06 ÷ 12 = $1,500.
2. Principal: $1,798.65 − $1,500 = $298.65.
The trap: Answering $1,500, the interest. The principal is what is left after the interest is paid.

The exam gives you the payment; you will not need to build it from the amortisation formula. What it tests is that interest is charged on the balance, so the interest falls and the principal rises every month on a fully amortized loan.

Discount points are 1% of the loan amount each, not of the price. On a $300,000 loan, 1.5 points is $4,500, whatever the home sold for.

How do you solve area, cap rate and transfer tax problems?

For area, multiply the sides and convert with 43,560 square feet to the acre or 9 square feet to the square yard. For cap rate, value = net operating income ÷ rate. For transfer tax, divide the price by the taxed unit, round up if the rule says "or fraction thereof", and multiply by the rate.

Real Estate Exam-style question 1 · Area and acres
A rectangular tract is 660 feet by 330 feet. Land nearby sells for $12,000 an acre. What is the tract worth?
1. A$60,000
2. B$54,450
3. C$12,000
4. D$2,613,600
Show the worked answer
A: $60,000. 660 × 330 = 217,800 square feet. An acre is 43,560 square feet, so the tract is 217,800 ÷ 43,560 = 5 acres, worth 5 × $12,000 = $60,000.
1. Area: 660 × 330 = 217,800 sq ft.
2. Acres: 217,800 ÷ 43,560 = 5.
3. Value: 5 × $12,000 = $60,000.
The trap: Multiplying square feet by the price per acre. Convert to acres first.
Real Estate Exam-style question 2 · Capitalisation rate
A small apartment building has potential gross income of $96,000, a 5% vacancy and collection loss, and operating expenses of $31,200. At a 7.5% capitalisation rate, what is it worth?
1. A$800,000
2. B$1,216,000
3. C$1,280,000
4. D$450,000
Worked answer
A: $800,000. Net operating income is gross income less vacancy and operating expenses: $96,000 × 95% = $91,200, minus $31,200 = $60,000. Value = $60,000 ÷ 7.5% = $800,000.
1. Effective gross income: $96,000 × 0.95 = $91,200.
2. NOI: $91,200 − $31,200 = $60,000.
3. Value: $60,000 ÷ 0.075 = $800,000.
The trap: Capitalising the gross income ($1,280,000) or forgetting the expenses ($1,216,000). Only net operating income is capitalised.
Real Estate Exam-style question 3 · Transfer tax
A state charges a transfer tax of $1.00 for each $500 of the sale price or fraction thereof. A home sells for $325,250. What is the tax?
1. A$651
2. B$650
3. C$650.50
4. D$325.25
Show the worked answer
A: $651. $325,250 ÷ $500 = 650.5 units. "Or fraction thereof" means a part unit counts as a whole one, so 651 units × $1.00 = $651.
1. Units: $325,250 ÷ $500 = 650.5.
2. Round up a fraction: 651.
3. Tax: 651 × $1.00 = $651.
The trap: Rounding down or keeping the half. "Or fraction thereof" always rounds up.

Transfer tax rates and units differ by state and county, so a national question gives you the rate. Learn the method, not a number. Your state's own transfer tax rate, if it has one, belongs to the state portion and your state's own law.

How do you adjust comparables in the sales comparison approach?

Adjust the comparable, never the subject. If the comparable has something the subject lacks, subtract its value; if it lacks something the subject has, add it.

Real Estate Exam-style question 1 · Sales comparison
A comparable home sold for $412,000. It has a pool worth $20,000 that the subject lacks, and the subject has an extra bathroom worth $8,000 that the comparable lacks. What is the comparable's adjusted price?
1. A$400,000
2. B$424,000
3. C$384,000
4. D$440,000
Worked answer
A: $400,000. Adjust the comparable to look like the subject. Take away what the comparable has and the subject does not (the pool, −$20,000), and add what the subject has and the comparable does not (the bathroom, +$8,000): $412,000 − $20,000 + $8,000 = $400,000.
1. Comparable better (pool): subtract $20,000.
2. Comparable worse (no extra bath): add $8,000.
3. $412,000 − $20,000 + $8,000 = $400,000.
The trap: Adjusting the subject instead, which flips both signs and gives $424,000.

A common memory aid: CBS, comparable better, subtract; CPA, comparable poorer, add. The valuation drill on this page mixes adjustment questions with the three approaches to value and the kinds of depreciation.

How do I get better at real estate math?

Write the formula in words, then the numbers, then estimate the answer before you calculate. Do a drill a day until every formula in the table is automatic.

Our math drills use new numbers every time, so you cannot learn the answers, only the method. Each one is worked line by line, and each wrong option is the result of a real mistake: the brokerage's share where the agent's was asked, the price where the appraisal applies, rounding down where the rule rounds up.

Then take the full real estate exam practice test: its 7 math questions sit among 73 others on a 120-minute clock, the way they will on exam day. The real estate license exam guide explains the rest of the national portion, and real estate exam passing score has each state's pass line.

Frequently asked questions

How many math questions are on the real estate exam?

About 7 of the 80 scored national questions on both Pearson VUE's and PSI's outlines, as prep sites report them. Some math also appears inside financing and valuation questions.

Can I use a calculator?

Most states allow a basic, silent, non-programmable calculator or provide one on screen. Check your state's candidate handbook.

Do I use 360 or 365 days for proration?

Whatever the question says. If it does not say, check the handbook for your state; our questions always state the year and who owns the closing day.

What is the hardest real estate math?

For most people, prorations, because you have to decide who owes whom as well as do the arithmetic. Paid in arrears credits the buyer; paid in advance credits the seller.

Make the math your surest points

Six full real estate exam-style mocks, four math drills and four drills for every other area, every answer worked, for one payment.