Real estate math (calculations) Practice Questions
105 questions on real estate math (calculations), each with an explanation. This area covers property area, valuation, commission, loan costs, settlement costs, investment, management calculations.
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A building cost $900,000 with $150,000 attributable to land. Using straight-line depreciation over a 39-year recovery period, the annual depreciation deduction is:
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10 sample real estate math (calculations) questions, answered
Every question above with its correct answer and the reasoning behind it. Read the explanations for the ones you answered correctly too. A lucky guess and knowing the rule look identical on a score report. These are sample questions from our larger bank.
1. A building cost $900,000 with $150,000 attributable to land. Using straight-line depreciation over a 39-year recovery period, the annual depreciation deduction is:
Why: $900,000 − $150,000 = $750,000 depreciable basis, because land is never depreciated. $750,000 ÷ 39 = $19,230.77 per year.
2. A tenant leases 2,400 square feet at $23 per square foot per year, plus a $0.85 per square foot monthly common-area charge. Total annual rent is:
Why: Base rent is 2,400 × $23 = $55,200. Common area is 2,400 × $0.85 × 12 = $24,480. Total $79,680. Treating the common-area charge as annual rather than monthly gives $57,240.
3. A seller wants to net $250,000 after paying a 6% commission and $3,500 in closing costs. What must the property sell for, to the nearest dollar?
Why: The seller must cover net plus costs from 94% of the price: ($250,000 + $3,500) ÷ 0.94 = $269,681. Adding 6% to $253,500 instead gives $268,710 and is the classic error — commission is a percentage of the SALE price, not of the net.
4. An ARM rate is 5%, with a 1.5-percentage-point periodic increase cap. Its uncapped new rate is 7.25%. Ignoring other limits, what rate applies?
Why: The periodic cap limits this increase to 1.5 points. Adding that to 5% gives 6.5%, below the uncapped 7.25% result.
5. A zoning rule permits floor area equal to 1.5 times a 20,000-square-foot lot. What maximum floor area does that ratio allow?
Why: Multiply the lot area by the stated floor-area ratio: 20,000 times 1.5 equals 30,000 square feet. Other development limits are excluded here.
6. A buyer puts 15% down on a $384,000 home. Two years later the home is worth $415,000 and the loan balance is $318,600. Equity has grown by:
Why: Starting equity was $384,000 × 0.15 = $57,600. Current equity is $415,000 − $318,600 = $96,400. Growth is $96,400 − $57,600 = $38,800. The $96,400 option is total equity, not the growth.
7. An ARM has a 3% index, a 2.25% margin and no binding cap at adjustment. What is its fully indexed rate?
Why: The fully indexed rate is index plus margin: 3% plus 2.25% equals 5.25%. Any applicable caps would need separate consideration.
8. A building earns $180,000 potential gross income, loses 6% to vacancy and receives $4,000 other income. What is effective gross income?
Why: Vacancy is $10,800. Subtract it from $180,000 and add $4,000 other income to obtain effective gross income of $173,200.
9. A residential rental cost $565,000, of which $115,000 is land. Using a 27.5-year recovery period, the annual straight-line depreciation is:
Why: $565,000 − $115,000 = $450,000 depreciable basis, since land is never depreciated. $450,000 ÷ 27.5 = $16,363.64. Using the full purchase price gives $20,545.45.
10. A property returns $31,500 annually and sold for $450,000. If a comparable property returns $28,000, what should it sell for at the same rate?
Why: The rate is $31,500 ÷ $450,000 = 7%. Applying it: $28,000 ÷ 0.07 = $400,000. Multiplying $28,000 by 7% instead gives $1,960 and inverts the relationship.
Where this weighting comes from
Weightings come directly from the test provider’s published examination content outline for the national portion of the salesperson exam. PSI publishes percentages only; Pearson VUE publishes scored-item counts only. PSI and Pearson VUE use different content taxonomies, so their weightings are not interchangeable and should not be averaged. Check which provider administers your state’s exam, and confirm against the current candidate handbook before you study. Outlines are revised periodically and older versions stay in circulation online. View the PSI outline.