New York Real Estate Exam Math Formulas: One Map

This map puts those formulas in one place. The Department of State doesn't publish how many math questions appear on the exam, so learn every family below.

Official source map

The New York Department of State's 77-hour curriculum defines the subject scope and identifies calculation topics across the course. New York Tax Department materials supply current assessment, equalization, transfer-tax and mortgage-recording-tax structures. The formulas themselves are standard arithmetic. Tax rates, lending standards and closing conventions can change or vary by location, so the problem's stated facts, or the current official source, always control.

The master formula triangle

Many percentage questions use one relationship:

Part = Rate × Whole

Cover the value you need:

Use the formula only after converting a percentage to a decimal.

• 6% = 0.06
• 4.5% = 0.045
• 0.75% = 0.0075
• 125% = 1.25

The reasonableness check

If the decimal rate is below 1, the part should normally be smaller than the whole. If a 5% commission comes out larger than the sale price, the decimal or division step is wrong.

Formula map at a glance

The words in the problem determine which figure belongs in each slot. The formula does not repair mismatched units or an incorrect definition.

Reading is the first step

Try another problem before looking at the solution.

Use the free mixed math practice here, or try Math Coach in the Pass New York app for worked problems and hints. The free app includes two answer checks per topic. Full access removes that limit.

Try free math practiceExplore the free app

Commissions

Total commission

Commission = sale price × commission rate

Example: A property sells for $625,000 and the problem states a 4.5% commission.

$625,000 × 0.045 = $28,125

The total commission is $28,125.

Brokerage and salesperson splits

A multi-step problem may divide the commission between brokerages and then divide one brokerage's share with its salesperson.

Example:

1. Total commission: $28,125
2. Cooperating brokerage receives 50%: $28,125 × 0.50 = $14,062.50
3. Salesperson receives 70% of that brokerage share: $14,062.50 × 0.70 = $9,843.75

The salesperson's split applies to the brokerage's share, not the sale price, unless the facts say otherwise. Follow the money one step at a time.

No standard commission rate

Commission rates are negotiable. A math question will give you the rate or enough facts to calculate it, so never bring in a familiar percentage from outside.

Simple interest

For a simple-interest problem:

Interest = Principal × Rate × Time

Time must be expressed as part of a year.

Example: Find 45 days of interest on $320,000 at 6% using a 360-day year.

$320,000 × 0.06 × 45/360 = $2,400

If the problem instead says to use a 365-day year:

$320,000 × 0.06 × 45/365 = $2,367.12

The arithmetic changed because the stated convention changed. Never switch between 360 and 365 without a fact telling you which to use.

Principal, rate and time must align

• principal is the amount on which interest is calculated
• rate is annual unless the problem says otherwise
• time must match that annual rate

Six months is 6/12 or 0.5 year. Three months is 3/12 or 0.25 year.

Appreciation and depreciation

Appreciation amount

Increase = original value × appreciation rate

New value = original value + increase

Example: A $480,000 property appreciates 7.5%.

Increase = $480,000 × 0.075 = $36,000

New value = $480,000 + $36,000 = $516,000

The shortcut is:

New value = original value × 1.075

Loss in value

Decrease = original value × depreciation rate

New value = original value minus decrease

A 12% decline leaves 88% of the original value, so the shortcut multiplier is 0.88.

Percentage change

Percentage change = change ÷ original value

The denominator is the starting value, not the ending value.

Discount points

One point equals 1% of the loan amount.

Cost of points = loan amount × points percentage

Example: Two points on a $360,000 loan:

$360,000 × 0.02 = $7,200

Points are calculated from the loan amount, not the purchase price, unless the two figures happen to be the same.

If a problem asks how many points a fee represents:

Points as a decimal = fee ÷ loan amount

Multiply the decimal by 100 to state the number of points.

Area, perimeter and land conversion

Rectangle

Area = length × width

An 80-foot by 125-foot lot contains:

80 × 125 = 10,000 square feet

Triangle

Area = base × perpendicular height ÷ 2

A triangle with a 60-foot base and 100-foot perpendicular height contains:

60 × 100 ÷ 2 = 3,000 square feet

Trapezoid

Area = (parallel side 1 + parallel side 2) × perpendicular height ÷ 2

Use the two parallel sides, not whichever sides happen to be listed first.

Irregular lots

Split the drawing into rectangles, triangles or trapezoids. Calculate each area and add them. If part is cut out, subtract that part.

Perimeter

Perimeter = sum of the outside boundary lengths

Area is measured in square units. Perimeter is measured in linear units. A question asking for fencing wants perimeter, not area.

Acres and hectares

1 acre = 43,560 square feet

Acres = square feet ÷ 43,560

The 10,000-square-foot lot above contains:

10,000 ÷ 43,560 = about 0.23 acre

One hectare is 10,000 square meters, or about 2.471 acres. Use the conversion supplied by the question if it specifies rounding.

Price per square foot

Price per square foot = price ÷ square feet

Example: A home sells for $720,000 and contains 1,800 square feet.

$720,000 ÷ 1,800 = $400 per square foot

To estimate a price from a unit rate:

Estimated price = price per square foot × subject square feet

Confirm that the area measurements are comparable. Gross building area, living area, usable area and rentable area are not automatically interchangeable.

Mortgage and qualifying formulas

Loan-to-value ratio

LTV = loan amount ÷ value basis

Example: A $380,000 loan is made against a $475,000 value basis.

$380,000 ÷ $475,000 = 0.80 = 80% LTV

The question may use purchase price, appraised value or another defined basis. Use the figure the lender or problem identifies.

Loan amount

Loan amount = value basis × LTV rate

Down payment

Down payment = purchase price minus loan amount

Down-payment percentage is:

Down payment ÷ purchase price

Monthly income

If annual income is given:

Gross monthly income = annual gross income ÷ 12

Use gross income, not take-home pay, when the problem calls for gross income.

Housing and total-debt ratios

Housing ratio = monthly housing expense ÷ gross monthly income

Total debt ratio = total monthly debt obligations ÷ gross monthly income

The lender defines which expenses and debts are included. Qualification thresholds differ by loan program and underwriting facts, so use the ratios stated in the problem rather than memorizing one universal approval standard.

Property tax and assessment formulas

New York municipalities may assess at a stated percentage of market value. The Tax Department explains that the level of assessment is the percentage of full value used by the assessing unit, subject to special class rules in New York City and Nassau County.

Assessed value

Assessed value = market value × level of assessment

Example: Market value is $650,000 and the level of assessment is 40%.

$650,000 × 0.40 = $260,000 assessed value

Taxable assessed value

Taxable assessed value = assessed value minus applicable exemptions

Only subtract an exemption if the problem provides it and says it applies.

Property tax

Property tax = taxable assessed value × tax rate

If the rate is stated as $32 per $1,000:

$260,000 ÷ $1,000 × $32 = $8,320

Tax rate from a levy

Tax rate = tax levy ÷ total taxable assessed value

If the levy is $24 million and the total taxable assessed value is $3 billion:

$24,000,000 ÷ $3,000,000,000 = 0.008

That is 0.8%, or $8 per $1,000.

Equalization rate

The state formula is:

Equalization rate = total assessed value ÷ total market value

An equalization rate is a municipal measure, not the tax rate on one parcel. Keep those ideas separate.

Transfer tax and mortgage recording tax

The current curriculum names real property transfer tax and mortgage recording tax as rate problems. These taxes are not one statewide percentage that fits every transaction.

New York State real estate transfer tax

The Tax Department currently states a basic rate of $2 for each $500, or fractional part, of consideration when the taxable consideration exceeds $500. Additional taxes can apply based on price, property type and New York City location.

For a basic-rate example with $750,000 of consideration:

$750,000 ÷ $500 × $2 = $3,000

For a real closing, use the current official schedule. An exemption, the 1% mansion tax on residential sales of $1 million or more, or New York City's additional taxes can change the result.

Mortgage recording tax

Mortgage recording tax varies by jurisdiction and mortgage facts. The Tax Department publishes components per $100 of mortgage debt and a current rate table. A solvable practice problem needs to provide the applicable rate or enough facts to identify it.

Generic formula:

Mortgage recording tax = taxable mortgage debt ÷ $100 × stated rate per $100

One county's total is not a statewide rate.

Prorations, credits and debits

Proration divides a periodic expense or income between parties according to time and responsibility.

Basic process

1. identify the full period amount
2. choose the stated day-count or month convention
3. calculate the per-day or per-month amount
4. count the responsible days or months
5. decide who paid and who owes
6. assign the debit and credit

Daily formula

Proration = annual amount ÷ days in year × responsible days

Example: An annual item is $7,200, the problem uses a 360-day year and one party owes 20 days.

$7,200 ÷ 360 × 20 = $400

The amount is $400. Whether it is a buyer debit and seller credit, or the reverse, depends on whether the item was prepaid or accrued and on who owns the relevant days.

Who owns the day of closing?

Questions may state that the buyer owns the day of closing, that the seller owns it, or that a 30-day month and 360-day year apply. Follow the stated convention.

Valuation formulas

Sales comparison adjustments

Adjust the comparable, not the subject.

• If the comparable is inferior, add to the comparable's price.
• If the comparable is superior, subtract from the comparable's price.

Memory line:

Comparable inferior, add. Comparable superior, subtract.

Cost approach

Value = replacement or reproduction cost new minus depreciation plus land value

Example:

$500,000 cost new minus $80,000 depreciation plus $200,000 land = $620,000

Land is generally valued separately and is not treated as a depreciating building component in this formula.

Income capitalization

Value = net operating income ÷ capitalization rate

This formula belongs to income-producing property and reappears in the investment section below.

Investment-property formulas

Effective gross income

EGI = potential gross income minus vacancy and collection loss

If the problem lists other income separately from potential rent, add it after the vacancy deduction.

Net operating income

NOI = effective gross income minus operating expenses

Debt service, income taxes and book depreciation are not operating expenses in the standard NOI calculation.

Capitalization rate

Cap rate = NOI ÷ value

Value = NOI ÷ cap rate

Example: Annual NOI is $96,000 and the market capitalization rate is 8%.

$96,000 ÷ 0.08 = $1,200,000 indicated value

Gross rent multiplier

GRM = sale price ÷ gross rent

Match the time periods. If sale price is divided by monthly rent, compare the result only with a monthly GRM. If annual rent is used, the multiplier is an annual measure.

Example:

$1,200,000 ÷ $12,000 monthly gross rent = 100 monthly GRM

Cash flow before taxes

Cash flow before taxes = NOI minus debt service

Cash-on-cash return

Cash-on-cash return = annual before-tax cash flow ÷ cash invested

If cash flow is $30,000 and cash invested is $300,000:

$30,000 ÷ $300,000 = 10%

Cap rate and cash-on-cash return are easy to mix up. Cap rate relates NOI to property value and ignores financing. Cash-on-cash return relates cash flow after debt service to the investor's cash.

Basis and gain formulas

Tax questions can use a simplified sequence when all inputs are supplied.

Adjusted basis = original basis plus permitted capital additions minus permitted basis reductions

Gain = amount realized minus adjusted basis

Not every repair is a capital improvement, not every closing cost adds to basis, and not every gain is taxable. Federal tax rules, property use, depreciation and exclusions change the result. Use only the facts and categories the question provides.

A seven-step method for every math question

1. Write what the question asks for

Dollar amount, rate, area, length, days, value or ratio?

2. List the facts with units

Write “$320,000 loan,” “6% per year” and “45 days,” not just three loose numbers.

3. Convert percentages

Move the decimal two places left before multiplication or division.

4. Match time periods and measurements

Annual income cannot be compared with monthly debt until one is converted. Feet cannot be combined with yards without conversion.

5. Choose the formula

Use the relationship the words describe, not the formula whose numbers look familiar.

6. Calculate without early rounding

Keep full calculator precision through intermediate steps. Round the final answer as directed.

7. Check direction and scale

Should the answer be larger or smaller than the starting figure? Is it a dollar result or a percentage? Does a 2% charge look like roughly two dollars per hundred?

Common mistakes

“Five percent means multiply by five”

No. Five percent is 0.05.

“Points are based on sale price”

No. Points are percentages of the loan amount.

“Area and perimeter use the same units”

No. Area uses square units. Perimeter uses linear units.

“An acre is 40,000 square feet”

No. One acre is 43,560 square feet.

“Any debt ratio over a familiar number fails”

No. Underwriting standards vary. Use the threshold stated in the problem.

“Assessed value is always market value”

No. New York assessing units may use a level of assessment below full market value, with special class structures in New York City and Nassau County.

“A proration amount tells me the debit and credit”

No. The amount is only the first result. Payment timing and ownership of the period determine the accounting entries.

“NOI subtracts the mortgage payment”

No. Debt service is excluded from standard NOI and is subtracted later to find before-tax cash flow.

Frequently asked questions

What math is in the New York real estate salesperson curriculum?

Subject 10 names percentages, commissions, interest, appreciation, depreciation, points, area, irregular lots, perimeter, acres, hectares, price per square foot, basic mortgage qualifying and real-estate tax rates. Other subjects add closing prorations, valuation, property taxes and investment calculations.

What is the most useful real estate math formula?

Part = Rate × Whole. It can be rearranged to find commissions, percentages, tax amounts, loan ratios and many other results.

How many square feet are in an acre?

43,560 square feet.

Is one mortgage point 1% of the purchase price?

No. One point is 1% of the loan amount.

How do I calculate assessed value in New York?

For a basic exam problem, multiply market value by the stated level of assessment. New York City and Nassau County have special class structures, so use the facts supplied.

Should I use 360 or 365 days for interest and prorations?

Use the convention stated in the question. If the problem specifies a 360-day year, do not substitute 365.

What is the difference between cap rate and cash-on-cash return?

Cap rate is NOI divided by property value and does not reflect financing. Cash-on-cash return is annual before-tax cash flow divided by the investor's cash invested.

Do I need to memorize New York transfer and mortgage recording tax rates?

Know what each tax measures and how to apply a stated rate. Actual rates can depend on price, location and property or mortgage facts. Use current Tax Department schedules for real transactions.

When should I round a math answer?

Keep full precision through the intermediate calculations and round the final answer according to the question, commonly to the nearest cent, whole dollar or requested decimal place.

How can I avoid calculator mistakes?

Estimate first, enter the formula in one direction, label the answer with units and reverse-check when possible. For example, multiply a calculated rate by the whole to see whether it returns the original part.

What to do next

Open the Real Estate Mathematics study hub and practice one formula family at a time. Then use the math tools to check your setup and the free practice sampler to decide which formula a scenario requires before touching the calculator.

Sources and verification notes

Worked examples are original teaching examples. Stated tax rates and lender standards can change, and local or transaction facts may alter a real calculation.

1. New York State Department of State, Real Estate Salesperson 77-Hour Curriculum. Subject 10 math scope and calculation objectives across closing, finance, valuation, taxes and investment property.
2. New York State Department of Taxation and Finance, How Property Is Assessed. Market value, level of assessment and assessed-value relationship.
3. New York State Department of Taxation and Finance, Equalization Rates. Official equalization-rate formula and meaning.
4. New York State Department of Taxation and Finance, Real Estate Transfer Tax. Current state rate structure and additional-tax notes.
5. New York State Department of Taxation and Finance, Mortgage Recording Tax. Current components, local variation and rate-table source.

This article provides general educational guidance. It does not reproduce live examination content or provide tax, lending or legal advice.