Appreciation, Depreciation, Profit, Loss and Equity Math

Start every problem by naming the quantity requested. A property can appreciate while the owner's equity falls if secured debt rises. A seller can have substantial equity but receive less cash after liens and selling costs. A tax gain uses amount realized and adjusted basis, not a shortcut based only on purchase price and sale price.

What are the core formulas?

Use the simple profit formula only when the problem defines those figures as the complete relationship. A real tax gain, accounting profit or seller's net proceeds may require adjusted basis, selling expenses, liabilities and other facts.

Official source map

The New York State Department of State 77-hour curriculum lists appreciation and depreciation under Real Estate Mathematics. It also treats depreciation in valuation, equity in finance and adjusted basis, depreciation, capital gain and capital loss in Income Tax Issues in Real Estate Transactions.

The Department of State salesperson page says the multiple-choice examination is based on that curriculum and allows 1 1/2 hours. It does not publish an official math-question count or subject distribution.

For federal tax terminology, the Internal Revenue Service Publication 544 explains that gain generally occurs when amount realized exceeds adjusted basis and loss occurs when adjusted basis exceeds amount realized. The IRS basis overview explains that basis is generally cost but can be increased or decreased by specified items.

For consumer finance, the Consumer Financial Protection Bureau home-equity guide defines home equity as current value minus existing mortgages. These sources define different concepts; do not merge them into one formula.

How do you calculate appreciation?

Example 1: Appreciation amount and new value

A property has an original value of $480,000 and appreciates 7.5%.

Appreciation = $480,000 × 0.075 = $36,000

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

The appreciation amount is $36,000. The appreciated value is $516,000. Answer the quantity requested.

Shortcut

The multiplier includes the original value and the increase:

$480,000 × 1.075 = $516,000

Use the two-step method while learning because it makes the appreciation amount visible.

How do you calculate depreciation in a value problem?

Example 2: Decrease and remaining value

A property valued at $625,000 loses 12% of its value.

Depreciation amount = $625,000 × 0.12 = $75,000

New value = $625,000 - $75,000 = $550,000

The decrease is $75,000. The remaining value is $550,000.

The shortcut multiplier is 0.88 because 1.00 minus 0.12 equals 0.88:

$625,000 × 0.88 = $550,000

Is value depreciation the same as tax depreciation?

No. In valuation, depreciation can mean a loss in value from physical deterioration, functional obsolescence or external obsolescence. In federal income tax, depreciation is a deduction governed by tax rules for qualifying property.

The IRS residential rental property guide explains basis, adjusted basis and depreciation for rental property. A simple exam-preparation problem that says “the property depreciated 10% in value” is not asking for a federal tax deduction unless the facts clearly make tax depreciation the issue.

How do you find the percentage increase or decrease?

Use the original amount as the ordinary percentage-change base:

Percentage change = Absolute change ÷ Original value

Example 3: Percentage increase

A value rises from $540,000 to $594,000.

Change = $594,000 - $540,000 = $54,000

$54,000 ÷ $540,000 = 0.10 = 10%

The increase is 10%.

Example 4: Percentage decrease

A value falls from $800,000 to $740,000.

Change = $800,000 - $740,000 = $60,000

$60,000 ÷ $800,000 = 0.075 = 7.5%

The decrease is 7.5%.

Do not divide by the ending value unless the question specifically asks what portion of the ending value the change represents.

How do you recover the original value?

Work backward by dividing the ending value by the multiplier.

Example 5: Original value before appreciation

A property is worth $552,000 after appreciating 15%.

Original value × 1.15 = $552,000

Original value = $552,000 ÷ 1.15 = $480,000

Example 6: Original value before depreciation

A property is worth $432,000 after a 10% decrease. A 10% decrease leaves a 0.90 multiplier.

Original value = $432,000 ÷ 0.90 = $480,000

Do not divide the ending value by the change rate. Divide by the percentage that the ending value represents.

How do you calculate simple profit or loss?

Read what the problem includes. A basic arithmetic exercise may define profit as sale price minus original cost.

Example 7: Simplified profit

A problem says a property was purchased for $410,000 and later sold for $470,000, with no other costs or adjustments to consider.

Profit = $470,000 - $410,000 = $60,000

The simplified profit is $60,000.

Example 8: Simplified loss

A problem says an asset cost $525,000 and was sold for $490,000, with no other figures to consider.

Loss = $525,000 - $490,000 = $35,000

The simplified loss is $35,000.

The wording “no other costs or adjustments” matters. It prevents the simple exercise from being mistaken for a full transaction or tax calculation.

Why is tax gain not the same as simple profit?

The IRS compares amount realized with adjusted basis. Publication 544 explains that amount realized includes money plus the fair market value of property or services received, subject to the applicable rules. Adjusted basis starts with cost or another basis and changes for specified additions and deductions.

Example 9: Simplified tax-style relationship

An educational problem supplies:

• amount realized: $610,000
• adjusted basis: $455,000

Realized gain = $610,000 - $455,000 = $155,000

This arithmetic does not determine how much gain is recognized, excluded, taxable or deductible. Those outcomes depend on federal tax rules and the taxpayer's facts.

Do not call sale price minus mortgage balance a tax gain. The mortgage balance is relevant to debt and cash flow, not a substitute for adjusted basis.

How do you calculate equity?

For basic exam math:

Equity = Current value - Total debt secured by the property

Example 10: One mortgage

A property is worth $650,000 and has a $390,000 mortgage balance.

Equity = $650,000 - $390,000 = $260,000

Example 11: More than one secured debt

A property is worth $720,000. It has a $410,000 first mortgage and a $35,000 home-equity loan.

Total secured debt = $410,000 + $35,000 = $445,000

Equity = $720,000 - $445,000 = $275,000

Include each debt the problem says is secured by the property. Do not add unrelated unsecured debt to this basic formula.

Can equity change without appreciation?

Yes. Paying down secured debt can increase equity even if property value stays flat.

Example 12

A property remains worth $500,000. The mortgage balance falls from $360,000 to $340,000.

Earlier equity = $500,000 - $360,000 = $140,000

Later equity = $500,000 - $340,000 = $160,000

Equity increased $20,000 because debt decreased, not because value appreciated.

Equity can also fall if debt rises or value falls.

Is equity the same as seller cash at closing?

No. Equity is a value-minus-debt estimate. Seller cash at closing can also reflect commissions, transfer taxes, attorney fees, lien payoffs, credits, adjustments and other transaction amounts.

Example 13: Simplified seller cash

A problem provides:

• sale price: $700,000
• mortgage payoff: $420,000
• stated selling costs: $42,000

Simplified cash before other adjustments = $700,000 - $420,000 - $42,000 = $238,000

If current value and sale price are both treated as $700,000, basic equity before selling costs is $280,000. The $42,000 cost explains why simplified cash is lower.

Avoid using this shortcut for a real closing without a complete settlement statement and professional advice.

Can a property appreciate while a seller has a loss?

Yes, depending on what “loss” measures. Value may rise from the original purchase price, while transaction costs or adjusted-basis facts produce a different economic or tax result. A property may also appreciate while equity declines if secured borrowing increases faster than value.

Example 14: Appreciation with lower equity

A property rises from $500,000 to $540,000. During the same period, secured debt rises from $300,000 to $370,000.

Earlier equity = $500,000 - $300,000 = $200,000

Later equity = $540,000 - $370,000 = $170,000

The property appreciated $40,000, but equity fell $30,000 because secured debt rose $70,000.

What are the common traps?

Confusing appreciation amount with new value

A 6% increase on $500,000 is $30,000; the new value is $530,000.

Using ending value as the percentage-change denominator

Ordinary percentage change uses the starting value.

Treating depreciation as one concept

Valuation depreciation, a percentage loss in a math problem and federal tax depreciation have different meanings.

Subtracting a mortgage to find profit

Mortgage balance does not replace cost or adjusted basis. It belongs in equity and payoff calculations.

Calling equity cash

Equity does not account for every closing cost or adjustment.

Ignoring additional liens

Basic equity uses total debt secured by the property, not only the first mortgage when other secured loans are stated.

Applying equal rates to different bases

A 20% decrease followed by a 20% increase does not return to the original amount because the second rate applies to a smaller base.

Original practice set

1. A $440,000 property appreciates 8%. Find the appreciation amount and new value.
2. A $750,000 property loses 6% of its value. Find the decrease and remaining value.
3. A value rises from $620,000 to $682,000. Find the percentage increase.
4. A property is worth $585,000 after appreciating 17%. Find the original value.
5. A simplified problem gives proceeds of $530,000 and stated cost of $475,000. Find profit.
6. Amount realized is $690,000 and adjusted basis is $520,000. Find realized gain.
7. Current value is $810,000, the first mortgage is $480,000 and a home-equity loan is $45,000. Find equity.
8. A property stays worth $600,000 while secured debt falls from $420,000 to $390,000. Find the equity increase.

Practice solutions

1. $440,000 × 0.08 = $35,200 appreciation; new value is $475,200.
2. $750,000 × 0.06 = $45,000 decrease; remaining value is $705,000.
3. Change is $62,000; $62,000 ÷ $620,000 = 0.10, or 10%.
4. $585,000 ÷ 1.17 = $500,000.
5. $530,000 - $475,000 = $55,000 simplified profit.
6. $690,000 - $520,000 = $170,000 realized gain in the stated relationship.
7. Secured debt is $525,000; $810,000 - $525,000 = $285,000 equity.
8. Earlier equity is $180,000; later equity is $210,000; increase is $30,000.

Frequently asked questions

What is appreciation in real estate math?

Appreciation is an increase in value. Multiply original value by the rate to find the increase, then add it to the original value.

What is depreciation in a value problem?

It is the amount of value lost under the problem's facts. Multiply original value by the loss rate, then subtract the result.

Is appraisal depreciation the same as tax depreciation?

No. Valuation depreciation addresses loss in value. Federal tax depreciation is a deduction governed by tax law for qualifying property.

What is the formula for percentage change?

Subtract to find the change, then divide by the original amount.

What is the basic equity formula?

Current property value minus all debt secured by the property.

Is equity the same as profit?

No. Equity compares current value with secured debt. Profit or gain compares proceeds or amount realized with the relevant cost or adjusted basis under the problem.

Is equity the amount a seller receives at closing?

Not necessarily. Closing cash can be reduced or increased by payoffs, costs, taxes, credits and adjustments.

Does a mortgage reduce tax gain?

Avoid using mortgage balance as a substitute for adjusted basis. Federal gain generally compares amount realized with adjusted basis, subject to applicable tax rules.

Does New York publish how many appreciation questions appear?

The public salesperson page identifies the curriculum basis and testing time but does not publish a math-question count or subject distribution.

What to do next

Review Part, Rate and Whole if reverse-percentage problems are difficult. Use the math formula map to connect value change and equity with finance, tax and investment calculations. Then work through the Real Estate Mathematics study guide.

Sources and verification notes

This article was checked on August 27, 2026. It separates valuation math, basic equity, simplified profit and federal tax terminology. Original examples do not determine a taxpayer's recognized gain, exclusion, deduction or liability.

1. New York State Department of State, Real Estate Salesperson 77-Hour Curriculum. Appreciation, depreciation, valuation, equity, adjusted basis and gain or loss objectives.
2. New York State Department of State, Become a Real Estate Salesperson. Exam format, curriculum basis, time and calculator rules.
3. Internal Revenue Service, Publication 544, Sales and Other Dispositions of Assets. Amount realized, adjusted basis and realized gain or loss.
4. Internal Revenue Service, Topic 703, Basis of Assets. Cost basis and adjustments that can increase or decrease basis.
5. Internal Revenue Service, Publication 527, Residential Rental Property. Rental-property basis, adjusted basis and tax depreciation context.
6. Consumer Financial Protection Bureau, Using Home Equity to Meet Financial Needs. Basic current-value-minus-mortgages equity relationship and consumer context.

This article provides educational exam preparation, not valuation, tax, accounting, lending or legal advice. It uses original practice rather than state-exam questions.