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Real estate math for the NJ exam, worked out

Every formula the PSI outline names, a worked example for each, the trap that costs people the point, and 9 calculators to check your work. Learn it by hand here, because you cannot bring a calculator in.

Start with the formulas Take the math drill
math questions, about 7% of the national part
5 or 6
formula types named in the PSI outline
9
calculators you can bring. Scratch paper is provided at test centers
0
to pass overall. Use worked examples to practice each method
70%

The short version: real estate calculations are 7% of the national content on the PSI New Jersey exam, roughly 5 or 6 questions. The outline names seller net proceeds, buyer funds at closing, prorations, transfer fees, PITI, equity, rate of return and cap rate, loan-to-value, and discount points and loan origination fees. The math is arithmetic. What loses points is the setup, so each formula below comes with the mistake to avoid.

How to solve any math question in 4 steps

  1. 1Find the questionUnderline what they want: the agent's share, the buyer's cash, the value. Plenty of wrong answers come from solving for the wrong thing.
  2. 2Write the formulaBefore any numbers. It keeps the order straight when the question piles on details.
  3. 3Plug and work itRound only at the end. Keep units consistent: monthly with monthly, acres with acres.
  4. 4Sanity checkAgent pay is less than the total commission. LTV is a percentage under 100. If it looks odd, it is.

Every formula, with a worked example

Try each example on paper before you open the solution. That is exactly the skill the exam tests.

Closing

Seller net proceeds

Named in the PSI outline

The PSI outline lists it by name. It pulls commission, the loan payoff and the NJ transfer fee into one problem.

Seller net
Price − commission − loan payoff − transfer fee − other seller costs
Price needed for a target net
(Desired net + costs) ÷ (1 − commission rate)

Try it

A $380,000 sale. Commission is 5%, the mortgage payoff is $214,500, the NJ Realty Transfer Fee is $3,023 and other seller costs are $1,200. What does the seller walk away with?

Show the solutionWork it first
  1. 1Commission: $380,000 × 0.05 = $19,000
  2. 2Total deductions: $19,000 + $214,500 + $3,023 + $1,200 = $237,723
  3. 3Net: $380,000 − $237,723 = $142,277
  4. Answer: $142,277

The trap: For a target net, do not multiply by 1.06. A seller who wants $300,000 after $6,000 of costs and a 6% commission needs ($300,000 + $6,000) ÷ 0.94 = about $325,532, not $324,360.

Buyer funds needed at closing

Named in the PSI outline

Listed in the PSI outline. The skill is knowing what the buyer has already paid and what counts as a credit.

Cash to close
Down payment + buyer closing costs − deposit already paid − credits from seller

Try it

A buyer purchases for $400,000 with an 80% loan. Closing costs are $9,500, the buyer already put down a $10,000 deposit, and the seller gives a $3,000 credit. How much does the buyer bring to closing?

Show the solutionWork it first
  1. 1Loan: $400,000 × 0.80 = $320,000, so the down payment is $80,000
  2. 2Add closing costs: $80,000 + $9,500 = $89,500
  3. 3Subtract the deposit and credit: $89,500 − $10,000 − $3,000 = $76,500
  4. Answer: $76,500

The trap: Forgetting the earnest money deposit. It was paid weeks ago and is already in the broker's trust account, so it reduces what the buyer brings.

Prorations

Named in the PSI outline

On the PSI list and the most error-prone math on the exam. Taxes, rent and interest all work the same way: find the daily amount, multiply by the days owed, then decide who gets the credit.

Daily amount
Annual amount ÷ 365 (or 360), or monthly amount ÷ days in the month
Proration
Daily amount × days owed

Try it

Annual property taxes are $7,300 and have not been paid. The seller owned the home for 120 days of the tax year. Using a 365-day year, what is the proration?

Show the solutionWork it first
  1. 1Daily: $7,300 ÷ 365 = $20 per day
  2. 2Seller's share: $20 × 120 = $2,400
  3. 3Unpaid tax the buyer will pay later, so debit the seller and credit the buyer $2,400
  4. Answer: $2,400, credited to the buyer

The trap: Getting the math right and the direction wrong. If the seller already paid an expense, the seller gets credited for the days after closing. If it is unpaid, the buyer gets credited for the seller's days. Rent the seller collected in advance is a credit to the buyer.

Read whether the question uses a 360-day or 365-day year and who owns the day of closing. Both change the answer, and the question always tells you. New Jersey property taxes are paid in quarterly installments, so tax questions often involve a partly paid quarter.

NJ Realty Transfer Fee

Named in the PSI outline

Transfer fees are on the PSI list, and New Jersey's is unusual: the seller pays it, it is charged per $500 in bands, and the whole schedule jumps once the price passes $350,000.

Up to $350,000
$2.00 per $500 to $150,000, $3.35 to $200,000, $3.90 to $350,000
Over $350,000 (whole price)
$2.90, $4.25, $4.80 to $550,000, $5.30 to $850,000, $5.80 to $1M, $6.05 above
Over $1M, deeds recorded from July 10, 2025
Plus a graduated percent fee of 1% to 3.5% of the full price

Try it

What is the standard Realty Transfer Fee on a $300,000 sale?

Show the solutionWork it first
  1. 1First $150,000: 300 units × $2.00 = $600
  2. 2Next $50,000: 100 units × $3.35 = $335
  3. 3Last $100,000: 200 units × $3.90 = $780
  4. 4Total: $600 + $335 + $780 = $1,715
  5. Answer: $1,715, paid by the seller

The trap: On a $485,000 sale, using the low schedule for the first $350,000. Above $350,000 the higher schedule applies to the entire price, which gives $4,031. And the graduated fee on big sales applies to the full price, not the amount over $1 million: a $2.2 million sale pays 2% × $2,200,000 = $44,000.

Finance

Loan-to-value and PMI

Named in the PSI outline

On the PSI list. LTV decides how much a buyer can borrow and whether private mortgage insurance applies.

LTV
Loan amount ÷ the lower of sale price or appraised value

Try it

A buyer agrees to pay $450,000, the appraisal comes in at $440,000 and the loan is $360,000. What is the LTV, and is PMI likely on a conventional loan?

Show the solutionWork it first
  1. 1Use the lower value: $440,000
  2. 2LTV: $360,000 ÷ $440,000 = 81.8%
  3. 3Above 80%, so PMI is likely
  4. Answer: 81.8%, PMI likely

The trap: Dividing by the $450,000 price gives 80% and the wrong conclusion. Lenders use the lower of the two values.

On conventional loans, PMI can be cancelled at the borrower's request once the balance reaches 80% of the original value and ends automatically at 78%.

Discount points and origination fees

Named in the PSI outline

The PSI outline lists both. They are the same math: a percentage of the loan amount.

Discount points
Loan amount × (number of points × 1%)
Origination fee
Loan amount × fee %

Try it

A $320,000 loan carries 1.5 discount points and a 1% origination fee. What do they cost together?

Show the solutionWork it first
  1. 1Total percentage: 1.5% + 1% = 2.5%
  2. 2Cost: $320,000 × 0.025 = $8,000
  3. Answer: $8,000

The trap: Taking points on the sale price instead of the loan. One point is 1% of the loan amount, always.

PITI and the monthly payment

Named in the PSI outline

PITI is on the PSI list. Exam questions give you a payment factor or the principal and interest, then ask you to add the monthly taxes and insurance.

Principal and interest
(Loan ÷ 1,000) × payment factor
PITI
P&I + annual taxes ÷ 12 + annual insurance ÷ 12

Try it

A $300,000 loan has a payment factor of $6.65 per $1,000. Annual taxes are $8,400 and insurance is $1,500. What is the monthly PITI?

Show the solutionWork it first
  1. 1P&I: 300 × $6.65 = $1,995
  2. 2Taxes: $8,400 ÷ 12 = $700
  3. 3Insurance: $1,500 ÷ 12 = $125
  4. 4PITI: $1,995 + $700 + $125 = $2,820
  5. Answer: $2,820 a month

The trap: Adding the annual tax bill to a monthly payment. Convert taxes and insurance to monthly before you add.

Valuation and investment

Equity and appreciation

Named in the PSI outline

Equity is on the PSI list, and appreciation questions use the same percent change math.

Equity
Market value − loan balance
Percent change
(New value − original value) ÷ original value

Try it

An owner bought for $300,000. The home is now worth $345,000 and the loan balance is $210,000. What is the appreciation rate and the equity?

Show the solutionWork it first
  1. 1Change: $345,000 − $300,000 = $45,000
  2. 2Appreciation: $45,000 ÷ $300,000 = 15%
  3. 3Equity: $345,000 − $210,000 = $135,000
  4. Answer: 15% appreciation, $135,000 equity

The trap: Dividing by the new value. Percent change is always measured from the starting value. And growth compounds: 5% a year for two years on $300,000 is $330,750, not $330,000.

Cap rate, rate of return and IRV

Named in the PSI outline

Rate of return and cap rate are on the PSI list. Every version is the same triangle: Income = Rate × Value.

Net operating income
Gross income − vacancy and credit loss − operating expenses
IRV
Value = NOI ÷ cap rate · Rate = NOI ÷ value · NOI = value × rate

Try it

A building earns $120,000 a year in gross rent. Vacancy is 5% and operating expenses are $36,000. At a 6.5% cap rate, what is it worth?

Show the solutionWork it first
  1. 1Vacancy: $120,000 × 0.05 = $6,000
  2. 2NOI: $120,000 − $6,000 − $36,000 = $78,000
  3. 3Value: $78,000 ÷ 0.065 = $1,200,000
  4. Answer: $1,200,000

The trap: Subtracting the mortgage payment. Debt service is not an operating expense, so it never comes out of NOI.

Depreciation

Common on the exam

Shows up in the cost approach and investment questions. Only the building depreciates, never the land.

Straight-line
Building cost ÷ useful life = annual depreciation
Tax recovery periods
27.5 years residential rental, 39 years nonresidential

Try it

An investor buys a rental for $500,000. The land is worth $100,000. Using a 27.5-year life, what is the annual depreciation?

Show the solutionWork it first
  1. 1Building only: $500,000 − $100,000 = $400,000
  2. 2Annual: $400,000 ÷ 27.5 = $14,545.45
  3. Answer: About $14,545 a year

The trap: Depreciating the full purchase price. Land does not wear out, so take it out first.

Commission, tax and area

Commission and splits

Common on the exam

Not named in the PSI list, but it shows up constantly because it tests whether you can follow a chain of percentages in the right order.

Total commission
Sale price × commission rate
Agent's share
Total × brokerage side % × agent split %

Try it

A home sells for $425,000 at a 5% commission. The listing brokerage gets 50% of it, and the listing agent keeps 60% of the brokerage's share. What does the agent earn?

Show the solutionWork it first
  1. 1Total: $425,000 × 0.05 = $21,250
  2. 2Listing side: $21,250 × 0.50 = $10,625
  3. 3Agent: $10,625 × 0.60 = $6,375
  4. Answer: $6,375

The trap: Applying the agent's 60% to the full $21,250 gives $12,750. That wrong answer is almost always one of the choices.

Property tax

Common on the exam

Not named in the PSI list, but tax bills feed straight into prorations and PITI. New Jersey expresses tax rates per $100 of assessed value.

Annual tax
Assessed value × tax rate
Rate per $100
(Assessed value ÷ 100) × rate
Mills
1 mill = $0.001, so 28.5 mills = 0.0285

Try it

A home is assessed at $350,000 and the tax rate is $2.85 per $100. What is the annual tax?

Show the solutionWork it first
  1. 1Units of $100: $350,000 ÷ 100 = 3,500
  2. 2Tax: 3,500 × $2.85 = $9,975
  3. Answer: $9,975 a year

The trap: Multiplying the assessed value by 2.85 directly. Check whether the rate is per $100, per $1,000 or in mills before you multiply.

Area and acreage

Common on the exam

Not on the PSI list by name, but land pricing questions depend on it and it is free points if you know the conversions.

Rectangle
Length × width
Triangle
½ × base × height
Acres
Square feet ÷ 43,560

Try it

A lot measures 330 feet by 264 feet and sells for $18,000 an acre. What is the price?

Show the solutionWork it first
  1. 1Area: 330 × 264 = 87,120 sq ft
  2. 2Acres: 87,120 ÷ 43,560 = 2
  3. 3Price: 2 × $18,000 = $36,000
  4. Answer: $36,000

The trap: Pricing square feet as if they were acres, or forgetting to halve a triangle.

Check your work: 9 free calculators

Each one shows its steps and the trap, so you see where a wrong answer would come from. Use them to check practice problems, not instead of working them.

Commission split

Salesperson earns

$8,610

Total commission (5%)
$20,500
Brokerage side (60%)
$12,300
Agent split (70%)
$8,610

Exam trap. Applying the agent split to the full commission gives $14,350. It is usually one of the answer choices.

New Jersey only

NJ Realty Transfer Fee calculator

Estimate for an ordinary, nonexempt residential sale recorded under current rules. Other property classes and exemptions can change the result. Rates per $500 from the NJ Division of Taxation. Over $350,000, the higher schedule applies to the whole price. Partial exemptions are claimed on an Affidavit of Consideration. For exam practice, not a legal or tax quote.

Total paid by the seller

$4,031

$0 to $150,000 at $2.90 per $500
$870
$150,000 to $200,000 at $4.25 per $500
$425
$200,000 to $485,000 at $4.80 per $500
$2,736

Exam fact. The seller pays the transfer fee. For deeds recorded on or after July 10, 2025, covered property transfers over $1 million also carry a seller-paid graduated fee of 1% to 3.5% of the full price, which replaced the buyer-paid mansion tax.

Numbers to know cold

The exam rarely gives you these. Write them on your scratch paper in the first minute.

Printable formula sheet
Real estate math conversions
1 acre43,560 square feet
1 square yard9 square feet
1 mile5,280 feet
1 section640 acres (1 square mile)
1 point1% of the loan amount
1 mill$0.001 (one tenth of a cent)
Year365 days, or 360 (12 months of 30) if the question says so
Monthly from annualDivide by 12

The math drill: 30 exam-style questions

Work each one on paper first. Every answer comes with the steps, and your score counts toward the real estate math topic in the study guide.

  • Commission splits and seller net
  • Prorations and transfer fees
  • LTV, points and PITI
  • Cap rate, area and tax
1 of 30

A $410,000 home sells at 5%. The listing brokerage keeps 60% and pays its salesperson 70% of that. What does the salesperson earn?

Math Coach, in the app

It reads your mistake, not just your score.

Pick a wrong answer and the coach shows which step went wrong, like splitting before the brokerage side or using the higher value for LTV, then gives you more problems with that exact pattern. Launching soon; the worked examples and calculators on this page are free now.

Get the app

Real estate math FAQ

Sources

Real estate calculations are 7% of the national content in the PSI outline, which works out to roughly 5 or 6 questions. Math also appears inside financing and valuation questions, so expect a few more that need a quick calculation.

Get comfortable with the steps. Then practice them.

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