{
    "entity_type": "page",
    "name": "Broker Mathematics: formulas, worked examples, pitfalls",
    "url": "https://continentalclub.ae/dld-broker-exam-practice/study-guide/broker-math/",
    "language": "en",
    "description": "Mathematics in the DLD exam and in practice consists of two dozen recurring types of problems. Almost all mistakes occur not because of arithmetic, but…",
    "published_at": "2026-10-27T22:05:43+00:00",
    "updated_at": "2026-10-27T22:05:43+00:00",
    "publisher": {
        "name": "Continental Club Property LLC",
        "orn": "31933",
        "url": "https://continentalclub.ae/"
    },
    "faq": [],
    "markdown": "https://continentalclub.ae/dld-broker-exam-practice/study-guide/broker-math.md",
    "content_md": "A study guide for the DLD broker exam. Not official DLD material; DLD does not publish the exam format — details are based on our brokers' experience. Updated: 13 Oct 2026. [All guides](/dld-broker-exam-practice/study-guide/) · [Glossary](/dubai-real-estate-glossary/)\n\n**In brief:** Mathematics in the DLD exam and in practice consists of two dozen recurring types of problems. Almost all mistakes occur not because of arithmetic, but because of the condition: the wrong percentage base (sale or listing price), the wrong units (m² or ft²), the wrong period (year, quarter, week), or the wrong sign in an adjustment. Below, for each type: formula, AED worked example, and pitfall. Exam conventions: 1 m² = 10.764 ft² (in exam problems they round to 10.76 — look at the answer options), year = 12 months = 52 weeks, percentages are simple, commission is calculated from the price stated in the contract.\n\nWhat is calculated within the agency for the client (assignment estimate, 4% DLD) is explained in detail in Assignment estimate: formula, 5 scenarios, top mistakes beginners make and 4% DLD: what price it is calculated from, reassessment, why underreporting is not possible; here they are provided in a condensed exam format.\n\n## 1. Areas and unit conversion\n\n**Formulas.** Area of a rectangle = length × width (in the same unit!). ft² = m² × 10.764; m² = ft² / 10.764. Price per ft² = price per m² / 10.764 (the price per unit changes *inversely* to the area).\n\n- Plot 60 × 120 ft = 7,200 ft².\n- 250 m² = 250 × 10.764 = 2,691 ft² (in an exam problem with 10.76 — 2,690).\n- Price of 12,917 AED per m² = 12,917 / 10.764 ≈ 1,200 AED per ft².\n\n**Pitfall.** The price per m² is converted into the price per ft² by *division*, not multiplication. Second, the plot is stated in feet while the price is per m²: first convert everything to one unit. Perimeter instead of area is another classic mistake.\n\n## 2. Land plot: area and price\n\n**Formula.** Price = length × width × rate per unit of area.\n\nExample. Plot 140 × 75 feet, rate 130 AED per ft²: 140 × 75 = 10,500 ft²; 10,500 × 130 = 1,365,000 AED.\n\n**Pitfall.** An extra “×100” or “×10” multiplier in the answer options — check the order of magnitude. Confused units (m instead of feet) change the answer by 10 times.\n\n## 3. Commission: amount and rate\n\n**Formulas.** Commission = price × rate; rate = commission / price; invoice with VAT = price × rate × 1.05.\n\nExample. Sold for 5,450,000 AED, commission 4% → 218,000 AED. Conversely: commission of 275,000 from 5,000,000 → 5.5%.\n\nThe market rate is 2% from each side; 5% VAT on agent services is added on top ⚠️ to be confirmed: “2% + VAT” is guidance from portals, see the broker agreement (Form A/B/F) for the actual condition.\n\n**Pitfall — base.** Listing 2,000,000, sold for 1,800,000, rate 2%: commission from the sale price is 36,000, from the listing price 40,000. Read “of the sale price” / “of the listed price”. If not stated, calculate from the sale price.\n\n## 4. Commission from the sale price and from the listing price at a discount\n\nIf the discount from the listing is known: sale = listing × (1 − discount). Example: listing 1,400,000, sold at a 10% discount → 1,260,000; commission of 6% from the sale = 75,600, while 6% from the listing = 84,000. The difference in the condition is one word, while the answer options differ.\n\n## 5. Division of commission between brokers\n\n### In the ratio a : b\n\nShare = commission × a / (a + b); “how much more” = commission × (a − b) / (a + b).\n\nExample. Sale for 900,000, commission 5% = 45,000, divided 3 : 2. The first receives 3/5 = 27,000, the second 2/5 = 18,000. How much more the first receives is 9,000, i.e. 1/5 of the commission.\n\n### In percentages (60/40, 70/30)\n\nShare = commission × percentage; difference = commission × (p₁ − p₂).\n\nExample. 990,000 × 6% = 59,400. Broker B with 60% receives 35,640, broker A with 40% — 23,760, difference 11,880.\n\n### Three-way split (50/30/20)\n\nExample. 2,400,000 × 5% = 120,000. Shares: 60,000 / 36,000 / 24,000. How much less the third received than the second: 10% of 120,000 = 12,000.\n\n**Pitfalls.** Confusing who is “first” in the ratio; dividing by a instead of (a + b); calculating “how much more” as a share rather than the difference in shares; in wording such as “A made more than B”, reading who is actually greater.\n\n## 6. Reverse calculation: seller’s net amount and commission rate\n\n**Formulas.** Net = price × (1 − r). Required price for the desired net amount: price = Net / (1 − r). Rate: r = (price − Net) / price.\n\nExample. The seller wants to receive 1,470,000 net with a 2% commission. Price = 1,470,000 / 0.98 = 1,500,000. Check: 1,500,000 × 0.98 = 1,470,000.\n\nExample (rate). Listing 1,700,000, sold for 95% of the listing = 1,615,000. Net amount 1,501,948. Commission 1,615,000 − 1,501,948 = 113,052; rate = 113,052 / 1,615,000 = 7%. (In this exam problem, the system marked a different answer as correct — arithmetic does not have to match the key, see [DLD Broker Exam: How It Works and How to Prepare](/dld-broker-exam-practice/study-guide/exam-format/).)\n\n**Pitfall.** “Price × 1.02” and “Net / 1.02” are incorrect: commission is charged on the final price, not the net amount. The expression “Sale price × (1 − 0.055)” is the net amount with a 5.5% commission.\n\n## 7. Service charge\n\n**Formulas.** Chargeable area = unit area + 25% of balcony area; year = chargeable area × rate per ft²; quarter = year / 4; month = year / 12. For more details about the charge itself — service charge.\n\nExample. Unit 1,500 ft², balcony 200 ft², rate 15 AED per ft², balcony counted at 25%. Chargeable area: 1,500 + 0.25 × 200 = 1,550 ft². Year: 1,550 × 15 = 23,250 AED. Quarter: 5,812.5 AED.\n\n**Pitfalls.** The balcony is counted not at 100%, but at 25% (exam problem rule; in reality it depends on the project declaration ⚠️ to be confirmed). Area in m² is first converted to ft². Year and quarter are adjacent in the answer options — answer for the period asked. The rate per ft² is approved by RERA (Mollak) annually; the typical market range is 12–20 AED, higher in Downtown and on Palm ⚠️ to be confirmed by project.\n\n## 8. Yield and monthly income\n\n**Formulas.** Income = investment × rate; monthly = annual / 12; gross yield = annual rent / price; net yield = (rent − expenses) / price; GRM = price / annual rent. See also ROI.\n\nExample 1 (monthly). Investment 1,260,000, yield 12.5% per annum: 1,260,000 × 0.125 / 12 = 13,125 AED per month.\n\nExample 2 (yield). Price 1,500,000, rent 105,000 per year: gross yield = 7%. If expenses are 15,000: net yield = 90,000 / 1,500,000 = 6%. GRM = 1,500,000 / 105,000 ≈ 14.3.\n\n**Pitfall.** Annual income instead of monthly income (forgot /12); gross instead of net; confusing yield and GRM (the *lower* the GRM, the more profitable the property).\n\n## 9. Capitalization\n\n**Formulas.** Cap rate = NOI / value; value = NOI / cap rate; NOI = income − operating expenses (excluding mortgage).\n\nExample. NOI 150,000 per year, cap rate 7.5%: value = 150,000 / 0.075 = 2,000,000 AED.\n\n**Pitfall.** Value is *divided* by the rate, not multiplied; mortgage payments are not included in NOI.\n\n## 10. Rent with different frequencies and expenses\n\n**Formula.** Annual income = Σ (rate × number of units × number of periods per year) − expenses. There are 12 months and 52 weeks.\n\nExample. Out of five units, three are rented at 4,500 AED per month, two — at 1,700 AED per week; expenses 27,220 per year. 3 × 4,500 × 12 = 162,000; 2 × 1,700 × 52 = 176,800; 162,000 + 176,800 − 27,220 = 311,580 AED.\n\n**Pitfall.** A year has 52 weeks, not 4 × 12 = 48; expenses are deducted once.\n\n## 11. Free month of rent\n\n**Formulas.** Amount payable = monthly rate × (months in the contract − free months). Effective discount = free months / contract term.\n\nExample. Rent 8,000 AED per month, contract for 13 months, one month free: the Tenant pays 12 × 8,000 = 96,000. Effective discount = 1/13 = 7.69%; effective rate = 96,000 / 13 ≈ 7,385 AED per month. If the month is free within a 12-month contract, the discount is 1/12 = 8.33%.\n\n**Pitfall.** Brokers call it a “1-month discount” and calculate 1/12. Always divide by the *total term* of the contract, including the free month.\n\n## 12. Percentage rent for a retail outlet\n\n**Formula.** Rent = area × rate per unit + share × (turnover − threshold). The percentage is paid only on the excess over the threshold.\n\nExample. Shop 60 × 120 ft = 7,200 ft², rate 100 AED per ft² and 4.5% of turnover above 400,000; turnover 2,000,000. Base: 720,000. Percentage: 4.5% × (2,000,000 − 400,000) = 72,000. Total per year 792,000; for 3 years 2,376,000 AED.\n\n**Pitfall.** Calculating the percentage from total turnover instead of the excess; forgetting to multiply by the number of years.\n\n## 13. Appreciation and depreciation\n\n**Formulas.** New price = price × (1 ± d). Reverse calculation of the original price after a decrease of d: original = current / (1 − d). After an increase of d: original = current / (1 + d). Increase per year (simple) = total increase / number of years.\n\nExample 1. House sold for 1,330,000 after depreciation of 15%: original price = 1,330,000 / 0.85 ≈ 1,564,706 AED.\n\nExample 2. Sold for 1,380,000 after a decrease of 8%: original = 1,380,000 / 0.92 = 1,500,000 AED.\n\nExample 3. Price 1,000,000, increase of 10% over 5 years = 100,000; per year (simple) 100,000 / 5 = 20,000 AED.\n\n**Pitfall.** After a decrease of 8%, divide by 0.92, not multiply by 1.08.\n\n## 14. CMA: comparable adjustments\n\n**Rule.** Adjust the *comparable* to the subject property: subtract what the comparable has in excess, add what the comparable does not have but the subject property has.\n\nExample 1. A comparable sold for 2,000,000, but it has one more bedroom (value 50,000) and one more bathroom (20,000) than the subject property. Adjusted value = 2,000,000 − 70,000 = 1,930,000 AED.\n\nExample 2. The comparable has no parking space (worth 30,000), while the subject property has one: 1,500,000 + 30,000 = 1,530,000 AED.\n\n**Pitfall.** The sign. Ask yourself: “is the comparable better or worse than my subject property?” Better — subtract, worse — add.\n\n## 15. Mortgage: LTV, down payment, discount points\n\n**Formulas.** Loan = price × LTV; down payment = price × (1 − LTV); one discount point = 1% of the *loan*. See Mortgages in the UAE: Central Bank rules and what they change in a transaction and mortgage.\n\nExample 1. Price 4,500,000, LTV 80% (expat, first home, up to 5 million): loan 3,600,000, down payment 900,000.\n\nExample 2. Price 6,000,000, expat, first home, above 5 million — LTV 70%: loan 4,200,000, down payment 1,800,000.\n\nExample 3. Property 184,000, LTV 75%, closing includes 2.5 points: loan 138,000; 2.5% × 138,000 = 3,450 AED.\n\nLTV rates according to Mortgages in the UAE: Central Bank rules and what they change in a transaction: an expat’s first home is 80% up to 5 million and 70% above; off-plan 50% for all; sources differ for a second home — ⚠️ to be confirmed (60% according to Mortgages in the UAE: Central Bank rules and what they change in a transaction or 65% and 50% according to new publications).\n\n**Pitfall.** Points are calculated from the loan, not the price; the threshold is 5 million; LTV is different for property under construction.\n\n## 16. Simple interest, annuity, and DBR\n\n**Simple interest.** I = P × r × t, where t is in years. Loan 600,000 at 5% for 3 months: 600,000 × 0.05 × 3/12 = 7,500 AED. The pitfall is leaving t in months.\n\n**Annuity payment.** PMT = P × r / (1 − (1 + r)⁻ⁿ), r is the monthly rate, n is the number of months. Loan 1,000,000, 4.5% per annum, 25 years: r = 0.045/12, n = 300; payment ≈ 5,558 AED per month. It is usually not needed for the exam, but in practice it is convenient to show to the client.\n\n**DBR.** Permitted payments on all loans = 50% of gross income. Income 40,000: limit 20,000; already pays 8,000 — 12,000 AED remains for a new mortgage.\n\n## 17. Inheritance shares and joint ownership\n\n### Inheritance\n\nShare = area × weight / sum of weights. In exam problems, a son receives a share 2 times larger than a daughter. The condition may be incomplete (the number of children is not stated) — then a standard assumption is made.\n\nExample. Plot 129,120 ft² = 12,000 m² (when converting with 10.76). Heirs: two sons (weight 2 each) and two daughters (weight 1). Sum of weights 6. A son receives 2/6 × 12,000 = 4,000 m², a daughter — 2,000 m². For calculations involving a real family, the law and will are determined separately (see Multiple Owners, Gifting, and Inheritance of Property in Dubai).\n\n### Joint ownership by shares\n\nOwner’s share in money = price × their share. Property sold for 3,000,000; shares 60/40: 1,800,000 and 1,200,000. If an owner with a 25% share sells only their share when the entire property is valued at 2,400,000, their part = 600,000 AED.\n\n**Pitfall.** Shares are fractional (60/40, 1/3) — add them as a check: the sum of shares must be 100%.\n\n## 18. DLD 4% fees and other buyer’s additional costs\n\n**Formulas.** DLD = 4% of the price (for an assignment — of the higher of the sale price and Original Price, see 4% DLD: what price it is calculated from, reassessment, why underreporting is not possible). Trustee and administrative fee amounts are fixed.\n\nExample. Price 2,350,000: DLD = 94,000 AED. The condition “DLD by cheque” at a price of 1,750,000 — 70,000 AED.\n\nUnder ECR 30/2013, DLD is divided equally, 2% + 2% (buyer and seller), unless the parties agree otherwise — in the exam, follow the condition of the problem. Land for 5 million with a 2% + 2% split — 100,000 from each side.\n\nFee table as at 13.10.2026 (source — verification of dubai_fees_2026, most figures from secondary sources):\n\n| Fee | Rate | Status |\n| --- | --- | --- |\n| DLD for transfer | 4% | confirmed secondarily, by several sources |\n| Trustee, ready property | 2,100 (up to 500,000) and 4,200 (from 500,000) AED with VAT | ⚠️ to be confirmed |\n| Trustee, off-plan (Oqood) | 3,675 and 5,250 AED with VAT | ⚠️ to be confirmed (only the amount of 5,250 is indirectly confirmed) |\n| Title Deed (ready) | 580 AED; DLD states 250 in the mortgage section | ⚠️ to be confirmed, sources differ |\n| Admin fee | structure unclear | ⚠️ to be confirmed |\n| Mortgage registration | 0.25% of the loan (confirmed by DLD) + fixed fees | percentage confirmed; fixed amounts ⚠️ to be confirmed |\n| Bank valuation | 2,500–3,500 AED | ⚠️ to be confirmed |\n| Developer NOC | 500–5,000 AED + VAT | ⚠️ to be confirmed |\n| Agent commission | 2% + 5% VAT | ⚠️ to be confirmed according to the agreement |\n| Ejari | approximately 177.75 AED online | ⚠️ to be confirmed |\n| Early mortgage settlement | the lower of 1% of the balance and 10,000 AED | according to Bayut data, not the primary source ⚠️ to be confirmed |\n\nDo not quote a figure from this table to the client without marking it “indicative” and checking it as at the transaction date.\n\n## 19. Assignment estimate (briefly)\n\nThe full explanation is in Assignment estimate: formula, 5 scenarios, top mistakes beginners make, here are the formulas needed for the exam. Definitions: Original Price (OP), Sale Price (SP), Paid — paid, Overdue, Future — future payments, Penalties.\n\n- Check: Paid + Overdue + Future = OP.\n- To the seller before commission: SP − (Overdue + Future) = Paid + (SP − OP).\n- Net to the seller: this amount − Penalties − seller’s commission.\n- Buyer at the transaction: SP − Future + DLD 4% + buyer’s commission. Future is not included in this amount — the buyer pays it to the developer later.\n\nExample. OP 2,000,000, Paid 1,000,000, Overdue 100,000, Future 900,000, SP 2,100,000, Penalties 20,000, commission 2% from each side = 42,000, DLD 4% × 2,100,000 = 84,000. To the seller before commission 1,100,000; net 1,100,000 − 20,000 − 42,000 = 1,038,000. Buyer at the transaction 2,100,000 − 900,000 + 84,000 + 42,000 = 1,326,000 AED.\n\n**Pitfall — DLD base at a discount.** SP = 1,300,000 (below OP 2,000,000), Overdue 100,000, Paid 1,000,000, Future 900,000. DLD is paid from the higher price — from OP: 4% × 2,000,000 = 80,000, not 52,000. Buyer: 1,300,000 − 900,000 + 80,000 + 26,000 = 506,000 AED (if DLD is calculated from SP, the result is 478,000 — incorrect). Seller: 1,300,000 − 1,000,000 = 300,000 before commission, 274,000 after commission of 26,000.\n\n## 20. Transaction when the seller has a mortgage\n\nThe procedure and documents are in Mortgages in the UAE: Central Bank rules and what they change in a transaction. Simple calculation: SP − seller’s outstanding bank debt (from the Liability Letter) − seller’s commission = what the seller receives.\n\nExample. SP 2,500,000, seller’s outstanding mortgage 1,200,000, seller’s commission 2% = 50,000. To the seller’s bank — 1,200,000; to the seller — 2,500,000 − 1,200,000 − 50,000 = 1,250,000 (the seller pays the commission to the agency separately). DLD 4% = 100,000 is paid by the buyer.\n\nIf the buyer takes a mortgage with LTV 80%: loan 2,000,000; down payment 500,000; plus DLD 100,000 and mortgage registration 0.25% × 2,000,000 = 5,000 AED (plus fixed fees ⚠️ to be confirmed) and agency commission. From the bank’s 2,000,000 and the buyer’s 500,000, cheques are prepared: 1,200,000 to the seller’s bank, the balance to the seller.\n\n**Pitfall.** If the bank values the property below the transaction price, the loan is calculated from the lower amount, and the buyer pays the difference themselves.\n\n## General pitfalls: checklist before answering\n\n1. Percentage base: sale price or listing price.\n2. Share or difference in shares; who is “first” in the ratio.\n3. Units: m² and ft²; price per m² and per ft².\n4. Period: year, quarter, month, week (52).\n5. Sign of the CMA adjustment and direction of the reverse calculation (÷ (1 − d), not × (1 + d)).\n6. Thresholds: turnover of 400,000, 5 million for LTV.\n7. Who pays: DLD under the law is 2% + 2%, under the problem condition — as stated.\n8. Ignore an extraneous number in the condition.\n\n## See also\n\n- Assignment estimate: formula, 5 scenarios, top mistakes beginners make\n- 4% DLD: what price it is calculated from, reassessment, why underreporting is not possible\n- Mortgages in the UAE: Central Bank rules and what they change in a transaction\n- Multiple Owners, Gifting, and Inheritance of Property in Dubai\n- [DLD Broker Exam: How It Works and How to Prepare](/dld-broker-exam-practice/study-guide/exam-format/)\n\n## Test yourself\n\n**1. Listing 2,000,000 AED, sold for 1,800,000, commission 2% of the sale price. What is the commission?**\n\nA) 40,000 B) 36,000 C) 38,000 D) 41,400\n\n**Answer**\n\nB. 1,800,000 × 2% = 36,000. Option A is a pitfall (commission from the listing).\n\n**2. Commission 900,000 × 5% = 45,000 is divided between two brokers 3 : 2. How much more does the first receive?**\n\nA) 27,000 B) 18,000 C) 9,000 D) 4,500\n\n**Answer**\n\nC. The first receives 27,000, the second 18,000, difference 9,000 (1/5 of the commission). Option A is the first’s share, not the difference.\n\n**3. House sold for 1,380,000 after a price decrease of 8%. What was the original price?**\n\nA) 1,490,400 B) 1,500,000 C) 1,269,600 D) 1,600,000\n\n**Answer**\n\nB. 1,380,000 / 0.92 = 1,500,000. Option A is a pitfall (× 1.08).\n\n**4. Unit 1,500 ft², balcony 200 ft² (counted at 25%), rate 15 AED per ft². Quarterly service charge?**\n\nA) 23,250 B) 5,812.5 C) 6,375 D) 25,500\n\n**Answer**\n\nB. Area 1,500 + 50 = 1,550 ft²; year 23,250; quarter 23,250 / 4 = 5,812.5. Option A is annual, C is a calculation with the balcony at 100% for the quarter.\n\n**5. Assignment: SP 1,300,000, OP 2,000,000, Future 900,000, DLD 4%, buyer’s commission 2% of SP. How much does the buyer pay at the transaction?**\n\nA) 478,000 B) 506,000 C) 1,406,000 D) 400,000\n\n**Answer**\n\nB. DLD is calculated from the higher price, i.e. OP: 80,000. Total 1,300,000 − 900,000 + 80,000 + 26,000 = 506,000. Option A is DLD from SP.\n\nPreparing for the DLD exam? [Free practice test: 30 questions, 60 minutes](/dld-broker-exam-practice/) · [How to become a broker in Dubai](/articles/become-real-estate-broker-dubai/) · [Broker Academy](/academy/)",
    "attribution": "Continental Club Property",
    "translations": {
        "ru": {
            "url": "https://continentalclub.ae/ru/trenazher-ekzamena-dld/uchebnik/matematika-brokera/",
            "md": "https://continentalclub.ae/ru/trenazher-ekzamena-dld/uchebnik/matematika-brokera.md",
            "json": "https://continentalclub.ae/ru/trenazher-ekzamena-dld/uchebnik/matematika-brokera.json"
        }
    }
}