- Official section
- National XI.I: Appreciation and Depreciation
- Broker weight
- A supporting percentage and valuation skill
- Expected scored items
- The current PSI outline tests value change through valuation and calculation concepts rather than a separate scored appreciation category
Value-change and basis math guide
Appreciation and depreciation without mixing definitions
The word depreciation does three jobs in real estate. It can describe a drop in market value, accrued loss in the appraisal cost approach, or tax cost recovery that adjusts basis. Label the job first. The arithmetic may look familiar, but the input, purpose, and legal consequence are not interchangeable.
Last updated: August 1, 2026
What calculation do you need to make?
Short answer: Value change equals new value minus original value. Percentage change equals value change divided by original value. One-period appreciated value equals original value times one plus the decimal rate; one-period depreciated value equals original value times one minus the decimal rate. Compound value after n periods equals original value times one plus the periodic rate raised to n. Adjusted basis generally starts with applicable basis, adds capitalized improvements and other increases, and subtracts depreciation allowed or allowable and other reductions. Realized gain equals amount realized minus adjusted basis in a simplified sale problem. Appraisal age-life depreciation equals effective age divided by economic life times improvement cost new, with land valued separately.
The current PSI broker outline does not identify tax-return preparation as a separate calculation family. Basis and tax depreciation are included here only to prevent common exam-word confusion and to solve expressly simplified facts. Federal basis, gain, exclusion, depreciation, recapture, casualty, gift, inheritance, conversion, exchange, and business-use rules are detailed and change over time. IRS basis rules can require a reduction for depreciation allowed or allowable, so omitting an unclaimed deduction is not automatically correct. Actual appraisal depreciation also requires market evidence, appropriate cost, and professional judgment. Use the definition and method stated in the problem. This is exam preparation, not tax, appraisal, legal, or investment advice. Sources were checked through August 1, 2026.
How do you solve appreciation, depreciation, and basis questions?
- Box the requested result and label the meaning of depreciation: market change, appraisal loss, or tax cost recovery.
- For value change, identify original value, new value, rate, number of periods, and whether the method is simple or compound.
- Use change divided by original value for a rate and one plus or minus the decimal rate for a one-period value.
- For basis, create a ledger with original basis, additions, depreciation, reimbursements, and every stated adjustment.
- Calculate amount realized separately from adjusted basis before finding a simplified realized gain or loss.
- For age-life depreciation, use effective age divided by economic life and apply it only to improvement cost new.
- Add land after subtracting supported improvement depreciation in the cost approach.
- Keep full precision, reverse-check the formula, and label the result as value, adjusted basis, realized gain, or appraisal indication rather than overstating it.
- Unknown
- Dollar value change
- Formula
- New value - original value
- Exam safeguard
- Preserve negative sign
- Unknown
- Percentage change
- Formula
- Dollar change / original value x 100
- Exam safeguard
- Original is denominator
- Unknown
- One-period appreciated value
- Formula
- Original x (1 + rate)
- Exam safeguard
- Rate in decimal form
- Unknown
- One-period depreciated value
- Formula
- Original x (1 - rate)
- Exam safeguard
- Do not subtract percentage points
- Unknown
- Compound future value
- Formula
- Original x (1 + rate) to period power
- Exam safeguard
- Update base each period
- Unknown
- Adjusted basis
- Formula
- Basis + increases - decreases
- Exam safeguard
- Use stated tax facts
- Unknown
- Realized gain
- Formula
- Amount realized - adjusted basis
- Exam safeguard
- Not automatically taxable gain
- Unknown
- Age-life ratio
- Formula
- Effective age / economic life
- Exam safeguard
- Use market ages
- Unknown
- Appraisal depreciation
- Formula
- Age-life ratio x improvement cost new
- Exam safeguard
- Do not apply to land
- Unknown
- Cost indication
- Formula
- Land + cost new - depreciation
- Exam safeguard
- Add stated site items if given
Can you follow the calculation from facts to answer?
Calculate one-period appreciation
Scenario: A property worth $320,000 appreciates 7.5% during the stated period. Find the dollar increase and new value.
- Appreciation amount is $320,000 x 0.075 = $24,000.
- New value is $320,000 + $24,000 = $344,000.
- The same result comes from $320,000 x 1.075.
Answer: The increase is $24,000 and the new value is $344,000.
Reverse an appreciated value
Scenario: A property is worth $367,500 after one 5% increase. What was its original value?
- The one-period growth factor is 1.05.
- $367,500 / 1.05 = $350,000.
- Check: $350,000 x 1.05 = $367,500.
Answer: The original value was $350,000.
Compound appreciation for two years
Scenario: A $300,000 property appreciates 4% per year for two years, compounded annually. What is its value?
- The annual growth factor is 1.04.
- $300,000 x 1.04 x 1.04 = $324,480.
- Using $300,000 x 8% would produce $324,000 and miss the second year's growth on prior appreciation.
Answer: The compounded value after two years is $324,480.
Build adjusted basis and realized gain
Scenario: A simplified problem gives $300,000 original basis, $50,000 capital improvements, $30,000 allowed or allowable depreciation, a $450,000 sale price, and $25,000 selling expenses.
- Adjusted basis is $300,000 + $50,000 - $30,000 = $320,000.
- Amount realized is $450,000 - $25,000 = $425,000.
- Realized gain is $425,000 - $320,000 = $105,000.
Answer: The simplified adjusted basis is $320,000 and realized gain is $105,000.
Calculate age-life depreciation
Scenario: An improvement has effective age of 10 years, total economic life of 50 years, and replacement cost new of $600,000.
- Age-life ratio is 10 / 50 = 20%.
- Accrued depreciation is $600,000 x 0.20 = $120,000.
- Depreciated improvement value is $600,000 - $120,000 = $480,000.
Answer: Estimated depreciation is $120,000 and improvement value is $480,000.
Complete a cost-approach indication
Scenario: Land is worth $150,000, improvement cost new is $600,000, and supported accrued depreciation is $120,000. No separate site-improvement amount is stated.
- Depreciated improvement value is $600,000 - $120,000 = $480,000.
- Land is not included in the improvement depreciation base.
- Cost indication is $150,000 + $480,000 = $630,000.
Answer: The simplified cost-approach indication is $630,000.
Which math errors cost the most points?
- Trap
- Divide value change by the new value.
- Correction
- Percentage change uses original value as the denominator.
- Trap
- Add 5 to original value for 5% appreciation.
- Correction
- Convert 5% to 0.05 and multiply it by the original value.
- Trap
- Multiply an annual rate by years when the problem says compounded.
- Correction
- Apply the growth factor to each updated period value.
- Trap
- Subtract market depreciation from tax basis automatically.
- Correction
- Tax basis adjustments follow tax rules, not a market-value decline percentage.
- Trap
- Call tax depreciation physical deterioration.
- Correction
- Tax depreciation is cost recovery; physical deterioration is an appraisal value-loss category.
- Trap
- Depreciate land for federal income tax.
- Correction
- Allocate basis and depreciate only qualifying depreciable property under the stated tax method.
- Trap
- Treat every repair as a basis increase.
- Correction
- Use the facts and applicable capitalization rule; ordinary repairs and capital improvements are not automatic synonyms.
- Trap
- Use seller net proceeds as realized gain.
- Correction
- Gain compares amount realized with adjusted basis, not closing cash with mortgage payoff.
- Trap
- Call realized gain taxable gain without more facts.
- Correction
- Recognition, exclusion, recapture, and other tax rules can change the taxable result.
- Trap
- Use actual age automatically in age-life depreciation.
- Correction
- The formula uses effective age when that is the supported appraisal input.
- Trap
- Apply improvement depreciation to land value.
- Correction
- Depreciate cost new of improvements and value land separately.
- Trap
- Treat one formula output as a complete appraisal or tax return.
- Correction
- Both professional valuation and tax treatment require additional facts, standards, and judgment.
Can you solve these original problems?
These questions are original study items aligned to the published outline. They are not copied, recalled, or predicted PSI questions.
1. A $400,000 property appreciates 6% during one stated period. What is its new value?
- $424,000
- $406,000
- $376,000
- $640,000
Show answer and explanation
Answer: $424,000
$400,000 x 1.06 = $424,000.
2. A property rises from $300,000 to $345,000. What is the appreciation rate?
- 15%
- 13.04%
- 45%
- 1.5%
Show answer and explanation
Answer: 15%
The $45,000 change divided by the $300,000 original value equals 15%.
3. Original basis is $250,000, capital improvements are $40,000, and stated basis reductions are $25,000. What is adjusted basis?
- $265,000
- $315,000
- $225,000
- $290,000
Show answer and explanation
Answer: $265,000
$250,000 + $40,000 - $25,000 = $265,000.
4. An improvement has effective age 12 years and economic life 60 years. What is the simplified age-life ratio?
- 20%
- 5%
- 72%
- 48%
Show answer and explanation
Answer: 20%
12 / 60 = 0.20, or 20%.
5. Which item is valued separately rather than included in the improvement depreciation base?
- Land
- Building roof
- Heating system
- Interior finish
Show answer and explanation
Answer: Land
The cost approach deducts accrued depreciation from improvement cost and adds land value separately.
Which numbers and formulas are easy to confuse?
- Terms
- Appreciation amount vs. appreciation rate
- Difference
- Appreciation amount is the dollar increase. Appreciation rate is that increase divided by original value.
- Question cue
- Dollar change versus relative change.
- Terms
- Simple appreciation vs. compound appreciation
- Difference
- Simple change repeatedly uses original value. Compound change updates the value base after each period.
- Question cue
- Fixed base versus growing base.
- Terms
- Market depreciation vs. tax depreciation
- Difference
- Market depreciation describes a value decline. Tax depreciation is statutory cost recovery for qualifying property and reduces basis.
- Question cue
- Economic value movement versus tax deduction.
- Terms
- Appraisal depreciation vs. tax depreciation
- Difference
- Appraisal depreciation measures loss from cost new from all causes. Tax depreciation follows tax basis, method, recovery period, and convention.
- Question cue
- Cost-approach loss versus statutory recovery.
- Terms
- Cost basis vs. market value
- Difference
- Basis is a tax and accounting reference amount. Market value is a market opinion as of an effective date.
- Question cue
- Tax ledger amount versus market conclusion.
- Terms
- Adjusted basis vs. loan balance
- Difference
- Adjusted basis reflects basis adjustments. Loan balance is secured debt and can rise or fall independently.
- Question cue
- Tax reference versus financing balance.
- Terms
- Amount realized vs. sale price
- Difference
- Sale price is gross consideration. Amount realized reflects the federal sale formula, including stated selling expenses and other required items.
- Question cue
- Gross sale amount versus disposition amount.
- Terms
- Realized gain vs. taxable gain
- Difference
- Realized gain is amount realized minus adjusted basis. Taxable gain depends on recognition, exclusion, recapture, and other applicable rules.
- Question cue
- Calculated economics versus reported tax consequence.
- Terms
- Effective age vs. actual age
- Difference
- Actual age is chronological. Effective age reflects observed condition, utility, and market perception for the appraisal analysis.
- Question cue
- Years since built versus market-age estimate.
- Terms
- Land value vs. improvement depreciation
- Difference
- Land is valued separately in the cost approach. Accrued depreciation is deducted from improvement cost new.
- Question cue
- Separate site value versus building loss.
What does the outline expect you to calculate?
- Topic
- Dollar value change
- What to know
- Original value, new value, increase, decrease, appreciation amount, depreciation amount, market change, sale price, current value, subtraction, positive result, and negative result
- Best exam move
- Subtract original value from new value and preserve the sign before calculating a percentage.
- Topic
- Percentage value change
- What to know
- Dollar change, original value, base, denominator, percentage, decimal, appreciation rate, depreciation rate, gain, loss, and relative change
- Best exam move
- Divide the change by original value, not by the new value.
- Topic
- One-period appreciation
- What to know
- Original value, appreciation rate, decimal, increase amount, one plus rate, new value, multiplication, one year, one period, and check
- Best exam move
- Multiply original value by one plus the decimal rate or calculate and add the increase.
- Topic
- One-period depreciation
- What to know
- Original value, decline rate, decimal, decrease amount, one minus rate, remaining value, multiplication, one year, and percentage loss
- Best exam move
- Multiply original value by one minus the rate when the problem asks for value after one stated decline.
- Topic
- Reverse original value
- What to know
- Current value, appreciated value, depreciated value, growth factor, decline factor, unknown original, division, reverse formula, and multiplication check
- Best exam move
- Divide current value by one plus appreciation rate or one minus depreciation rate for one period.
- Topic
- Simple multi-period change
- What to know
- Original base, annual rate, number of years, simple appreciation, same dollar increase, rate times periods, total change, and stated method
- Best exam move
- Use rate times periods only when the question specifies simple change on the original base.
- Topic
- Compound value change
- What to know
- Periodic rate, number of periods, exponent, updated base, compounding, future value, annual growth, appreciation, depreciation, calculator power, and sequence
- Best exam move
- Use original value times the growth factor raised to the number of periods.
- Topic
- Percentage points versus percent change
- What to know
- Rate movement, percentage point, basis point, relative percentage, old rate, new rate, value change, multiplier, and denominator
- Best exam move
- Describe a rate difference in percentage points only when comparing two percentages, not two property values.
- Topic
- Cost basis
- What to know
- Purchase cost, cash, assumed debt, acquisition cost, capitalized fee, recording fee, revenue stamp, legal fee, settlement item, allocation, land, building, and IRS rule
- Best exam move
- Use the basis facts expressly supplied rather than equating basis with down payment or loan balance.
- Topic
- Basis increases
- What to know
- Capital improvement, addition, roof replacement, paving, central air, rewiring, rehabilitation, local improvement assessment, title defense, zoning cost, and capitalization
- Best exam move
- Add only items the problem identifies as capitalized basis increases.
- Topic
- Basis decreases
- What to know
- Depreciation allowed or allowable, casualty deduction, insurance reimbursement, energy subsidy, credit, easement payment, postponed gain, rebate, partial disposition, and adjustment
- Best exam move
- Subtract the stated basis reductions once, even if the taxpayer failed to claim an allowable depreciation deduction.
- Topic
- Adjusted basis formula
- What to know
- Original basis, increases, decreases, capital improvements, depreciation, adjusted basis, sale date, gain calculation, loss calculation, and records
- Best exam move
- Build basis as a ledger before comparing it with amount realized.
- Topic
- Amount realized and gain
- What to know
- Selling price, selling expense, commission, transfer cost, amount realized, adjusted basis, realized gain, realized loss, recognized gain, taxable gain, and exclusion
- Best exam move
- Calculate amount realized first, then subtract adjusted basis; do not call the result taxable without the required tax facts.
- Topic
- Tax depreciation boundary
- What to know
- Income-producing use, business use, placed in service, depreciable basis, land allocation, building, recovery period, method, convention, Form 4562, allowed, and allowable
- Best exam move
- Use only the simplified depreciation method given and never depreciate the land allocation.
- Topic
- Appraisal depreciation
- What to know
- Loss in value from any cause, cost new, physical deterioration, functional obsolescence, external obsolescence, curable, incurable, improvement, cost approach, and effective date
- Best exam move
- Measure appraisal loss against improvement cost new rather than tax basis.
- Topic
- Age-life method
- What to know
- Effective age, total economic life, remaining economic life, ratio, cost new, accrued depreciation, improvement value, straight-line estimate, and market support
- Best exam move
- Divide effective age by economic life and apply the ratio to depreciable improvement cost new.
- Topic
- Cost-approach value
- What to know
- Land value, replacement cost, reproduction cost, improvement cost new, accrued depreciation, site improvements, entrepreneurial incentive, indicated value, and reconciliation
- Best exam move
- Subtract improvement depreciation from cost new, then add separately valued land and any stated site contribution.
- Topic
- Precision and conclusion boundary
- What to know
- Decimal rate, exponent, full precision, intermediate rounding, final rounding, estimated value, realized gain, taxable gain, appraisal indication, tax result, and verification
- Best exam move
- Reverse-check the arithmetic and label the result narrowly enough for the method actually used.
How should you drill this calculation?
- Session
- Session 1
- Focus
- Master value-change formulas
- Proof you are ready
- Solve 20 dollar-change, percentage-change, one-period future-value, and reverse-original-value problems.
- Session
- Session 2
- Focus
- Separate simple and compound change
- Proof you are ready
- Calculate 20 multi-period scenarios and explain why each uses a fixed or updated base.
- Session
- Session 3
- Focus
- Build basis ledgers
- Proof you are ready
- Classify 40 purchase costs, improvements, reimbursements, depreciation items, and other adjustments as basis increases, decreases, or neither.
- Session
- Session 4
- Focus
- Calculate gain carefully
- Proof you are ready
- Solve 15 amount-realized and adjusted-basis problems while keeping seller net, realized gain, and taxable gain separate.
- Session
- Session 5
- Focus
- Master appraisal depreciation
- Proof you are ready
- Classify physical, functional, and external loss, then solve 15 age-life and cost-approach calculations.
- Session
- Session 6
- Focus
- Complete a mixed change-and-basis set
- Proof you are ready
- Score at least 90% and justify each answer by depreciation meaning, original base, rate method, basis ledger, income period, land treatment, and conclusion boundary.
Do not count recognition as mastery. Close the notes and explain the rule, apply it to a new fact pattern, and identify why each distractor fails.
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From concept to decision
Drill this topic, then review the explanation
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Questions students ask about Appreciation, Depreciation, and Basis Formulas
What is the real estate appreciation formula?
Appreciation amount equals original value multiplied by the appreciation rate. New value equals original value plus the appreciation amount, or original value multiplied by one plus the decimal rate for one period. A $320,000 value appreciating 7.5% increases by $24,000 to $344,000.
How do you calculate the percentage change in property value?
Subtract original value from new value, divide the change by original value, and multiply by 100. The original value is the denominator. A rise from $300,000 to $330,000 is $30,000 divided by $300,000, or 10%.
How do you find original value after appreciation?
For one stated period, divide the new value by one plus the decimal appreciation rate. If a property is worth $367,500 after a 5% increase, original value was $367,500 divided by 1.05, or $350,000.
What is the difference between simple and compound appreciation?
Simple appreciation applies each period's rate to the original base. Compound appreciation applies each new period's rate to the prior period's updated value. Real estate exam questions should state or imply the method; do not multiply an annual rate by years when compounding is required.
What does depreciation mean in real estate appraisal?
Appraisal depreciation is loss in value from any cause measured against cost new in the cost approach. It includes physical deterioration, functional obsolescence, and external obsolescence. It is not the same as an income-tax deduction.
What is the age-life depreciation formula?
A simplified age-life ratio equals effective age divided by total economic life. Multiply that ratio by improvement cost new to estimate accrued depreciation, then subtract depreciation from improvement cost. Value land separately and add it afterward.
What is adjusted basis?
Adjusted basis begins with the property's applicable basis, commonly cost for a purchase, then reflects required additions and reductions. Capital improvements can increase basis, while depreciation allowed or allowable and other adjustments can reduce it. Gift, inheritance, conversion, exchange, and casualty facts can require different rules.
How do you calculate gain on a property sale?
A simplified federal formula is amount realized minus adjusted basis. IRS Publication 523 treats amount realized as selling price reduced by selling expenses in its home-sale worksheet. Taxable gain can differ from realized gain because exclusions, recognition rules, recapture, use, ownership, and other tax provisions apply.
Can land be depreciated for federal income tax?
Land is not depreciable for federal tax because it is not treated as wearing out or becoming obsolete in the same way as depreciable improvements. Allocate basis between land and depreciable property before using a tax depreciation method.
Are these official Illinois broker exam questions?
No. They are original calculations aligned to the PSI broker outline effective June 24, 2026. Current IRS 2025 publications released or updated in 2026, current Fannie Mae cost-approach guidance, and current appraisal standards were checked through August 1, 2026.
Primary sources
- PSI Illinois Candidate Information Booklet dated June 24, 2026
- IRS Publication 551, 2025 Basis of Assets
- IRS Publication 523, 2025 Selling Your Home
- IRS Publication 527, 2025 Residential Rental Property
- IRS Publication 946, current How To Depreciate Property resources
- Fannie Mae Selling Guide B4-1.3-10, current cost-approach guidance
- The Appraisal Foundation, current Uniform Standards of Professional Appraisal Practice
The current official outline controls the tested scope. Statutes, regulations, and official agency materials control when a general study rule and a jurisdiction-specific rule differ.
Editorial status
Checked against primary sources
The Pass Illinois editorial team last checked this guide on August 1, 2026. Every practice question is an original study item, and the source links above let you verify the rules that support the lesson.