GablePrep

Real estate math formulas

51 problem types with the formula and a worked example for each. Every example is computed by program and re-checked, so the arithmetic is right.

Practice with a free quiz Read the cheat-sheet guide

Conventions used on exams: prorations usually use a 360-day year with 30-day months unless the question says otherwise; 1 acre = 43,560 sq ft; 1 sq yd = 9 sq ft; 1 cu yd = 27 cu ft; 1 section = 640 acres. The question always tells you which convention to use — read it.

Commission & Splits

Commission on a sale — Commission = Sale price × Commission rate

Example. A home sells for $200,000. The listing agreement provides for a 5.5% commission. What is the total commission?

  1. Convert 5.5% to a decimal: 0.055
  2. $200,000 × 0.055 = $11,000
  3. Answer: $11,000
Find the sale price from the commission — Sale price = Commission ÷ Commission rate

Example. A broker earned a 5% commission of $25,000 on a sale. What was the sale price?

  1. Convert 5% to a decimal: 0.05
  2. $25,000 ÷ 0.05 = $500,000
  3. Answer: $500,000
Find the commission rate — Rate = Commission ÷ Sale price × 100

Example. A property sold for $350,000 and the commission paid was $19,250. What commission rate was charged?

  1. $19,250 ÷ $350,000 = 0.055
  2. 0.055 × 100 = 5.5%
  3. Answer: 5.5%
Agent share of a split commission — Agent share = Price × Rate × Side share (50%) × Agent split

Example. A home sells for $550,000 with a 7% total commission, split equally between the listing broker and the selling broker. The listing broker pays the listing agent 80% of the listing side. How much does the listing agent receive?

  1. Total commission: $550,000 × 0.07 = $38,500
  2. Listing side (50%): $19,250
  3. Agent split: $19,250 × 0.8 = $15,400
  4. Answer: $15,400
Commission on a lease — Commission = Monthly rent × 12 × Years × Rate

Example. A broker negotiates a 2-year lease at $3,300 per month and is paid 6% of the total rent over the full term. What is the commission?

  1. Total rent: $3,300 × 12 × 2 = $79,200
  2. $79,200 × 0.06 = $4,752
  3. Answer: $4,752
Seller net proceeds — Net = Price − Commission − Payoff − Other costs

Example. A seller accepts $280,000 for a home. The seller pays a 5% commission, a mortgage payoff of $75,000, and other closing costs of $4,000. How much does the seller net?

  1. Commission: $280,000 × 0.05 = $14,000
  2. $280,000 − $14,000 − $75,000 − $4,000 = $187,000
  3. Answer: $187,000
List price needed to net a target — Price = Desired net ÷ (1 − Commission rate)

Example. A seller wants to net exactly $305,500 after paying a 6% commission (no other costs). At what price must the home sell?

  1. Seller keeps 94% of the price
  2. $305,500 ÷ 0.94 = $325,000
  3. Answer: $325,000

Loans & Interest

Loan amount from LTV — Loan = Value × LTV

Example. A buyer purchases a home for $500,000 with a 95% loan-to-value ratio on the purchase price. What is the loan amount?

  1. $500,000 × 0.95 = $475,000
  2. Answer: $475,000
Down payment from LTV — Down payment = Price − Loan

Example. A lender will finance 85% of a $380,000 purchase price. How much cash down payment is required?

  1. Loan: $380,000 × 0.85 = $323,000
  2. $380,000 − $323,000 = $57,000
  3. Answer: $57,000
LTV uses the lower of price or appraisal — LTV = Loan ÷ Lower of (price, appraised value)

Example. A buyer agrees to pay $215,000 for a home that appraises at $200,000. The lender makes a $160,000 loan. What is the loan-to-value ratio (lenders use the lower of price or appraised value)?

  1. Lower value: $200,000
  2. $160,000 ÷ $200,000 = 0.8 = 80%
  3. Answer: 80%
Cost of discount points — Points cost = Loan × Points ÷ 100

Example. A borrower takes a $210,000 loan and pays 1 discount points. One point equals 1% of the loan. What do the points cost?

  1. $210,000 × 0.01 = $2,100
  2. Answer: $2,100
Simple interest — Interest = Principal × Rate × Time

Example. What is the total simple interest on a $25,000 loan at 7% per year for 5 years?

  1. $25,000 × 0.07 × 5 = $8,750
  2. Answer: $8,750
Interest portion of the first payment — Monthly interest = Balance × Annual rate ÷ 12

Example. A borrower has a $204,000 mortgage balance at 7% annual interest, paid monthly. How much of the next payment is interest?

  1. Annual interest: $204,000 × 0.07 = $14,280
  2. $14,280 ÷ 12 = $1,190
  3. Answer: $1,190
Principal portion of a payment — Principal portion = Payment − (Balance × Rate ÷ 12)

Example. A loan has a balance of $300,000 at 5% interest. The monthly principal-and-interest payment is $1,400. How much of this payment reduces the principal?

  1. Interest: $300,000 × 0.05 ÷ 12 = $1,250
  2. $1,400 − $1,250 = $150
  3. Answer: $150
Payment from a loan factor — Payment = (Loan ÷ 1,000) × Factor

Example. A lender's payment factor for the borrower's rate and term is 5.99 per $1,000 borrowed. What is the monthly principal-and-interest payment on a $290,000 loan?

  1. $290,000 ÷ 1,000 = 290
  2. 290 × 5.99 = $1,737.10
  3. Answer: $1,737.10
Total monthly PITI — PITI = P&I + Taxes ÷ 12 + Insurance ÷ 12

Example. A buyer's principal-and-interest payment is $2,350 per month. Annual property taxes are $2,400 and annual homeowner's insurance is $1,200, both escrowed monthly. What is the total monthly PITI payment?

  1. Taxes: $2,400 ÷ 12 = $200
  2. Insurance: $1,200 ÷ 12 = $100
  3. $2,350 + $200 + $100 = $2,650
  4. Answer: $2,650
Monthly PMI cost — Monthly PMI = Loan × Annual rate ÷ 12

Example. A borrower with a $312,000 loan pays private mortgage insurance at an annual rate of 0.4% of the loan balance. What is the monthly PMI payment?

  1. Annual PMI: $312,000 × 0.004 = $1,248
  2. ÷ 12 = $104
  3. Answer: $104

Borrower Qualifying

Maximum housing payment (front-end ratio) — Max housing payment = Gross monthly income × 28%

Example. A lender limits the housing payment (PITI) to 28% of gross monthly income. A borrower earns $60,000 per year. What is the maximum monthly housing payment?

  1. Monthly income: $60,000 ÷ 12 = $5,000
  2. $5,000 × 0.28 = $1,400
  3. Answer: $1,400
Housing payment limit from total debt ratio — Max housing = Income × 36% − Other debts

Example. A lender caps total monthly debt at 36% of gross monthly income. A borrower earns $5,500 per month and has $550 in other monthly debt payments. What is the maximum monthly housing payment under this ratio?

  1. $5,500 × 0.36 = $1,980
  2. $1,980 − $550 = $1,430
  3. Answer: $1,430

Area, Volume & Land

Carpet cost per square yard — Square yards = Square feet ÷ 9

Example. A room measures 18 feet by 15 feet. Carpet costs $21 per square yard installed. What is the total cost to carpet the room?

  1. Area: 18 × 15 = 270 sq ft
  2. 270 ÷ 9 = 30 sq yd
  3. 30 × $21 = $630
  4. Answer: $630
Area of a triangular lot — Area of a triangle = ½ × Base × Height

Example. A triangular lot has a base of 90 feet and a height of 90 feet. What is its area?

  1. ½ × 90 × 90 = 4,050 sq ft
  2. Answer: 4,050 sq ft
Acres to square feet — Square feet = Acres × 43,560

Example. How many square feet are in 0.5 acres? (1 acre = 43,560 square feet)

  1. 0.5 × 43,560 = 21,780 sq ft
  2. Answer: 21,780 sq ft
Price of a rectangular parcel per acre — Acres = Area ÷ 43,560; Value = Acres × Price per acre

Example. A rectangular parcel is 660 feet by 660 feet. Land in the area sells for $5,000 per acre. What is the parcel worth? (1 acre = 43,560 sq ft)

  1. Area: 660 × 660 = 435,600 sq ft
  2. 435,600 ÷ 43,560 = 10 acres
  3. 10 × $5,000 = $50,000
  4. Answer: $50,000
Irregular lot area — Area = Large rectangle − Cut-out rectangle

Example. An L-shaped lot is a 140-foot by 190-foot rectangle with a 50-foot by 20-foot rectangle cut out of one corner. What is the lot's area?

  1. 140 × 190 = 26,600 sq ft
  2. 50 × 20 = 1,000 sq ft
  3. 26,600 − 1,000 = 25,600 sq ft
  4. Answer: 25,600 sq ft
Cubic yards of concrete — Volume (cu ft) = L × W × Thickness (ft); Cubic yards = Cubic feet ÷ 27

Example. A concrete slab is 27 feet long, 12 feet wide, and 12 inches thick. How many cubic yards of concrete are needed? (27 cubic feet = 1 cubic yard)

  1. Thickness: 12 ÷ 12 = 1 ft
  2. Volume: 27 × 12 × 1 = 324 cu ft
  3. 324 ÷ 27 = 12 cu yd
  4. Answer: 12 cu yd
Acres in a section fraction — Acres = 640 × each fraction in the description

Example. How many acres are in the NW 1/4 of the S 1/2 of the N 1/2 of a standard section? (A section is 640 acres.)

  1. Multiply the fractions: 0.25 × 0.5 × 0.5 = 0.0625
  2. 640 × 0.0625 = 40 acres
  3. Answer: 40 acres
Front-foot value — Value = Front feet × Price per front foot (depth is not used)

Example. Lots in a commercial district sell for $900 per front foot. A lot has 80 feet of street frontage and is 100 feet deep. What is its value?

  1. 80 × $900 = $72,000
  2. Answer: $72,000

Investment & Income

Value from NOI and cap rate — Value = NOI ÷ Cap rate

Example. An income property produces a net operating income of $92,000 per year. Similar properties sell at a 8% capitalization rate. What is the property's value?

  1. $92,000 ÷ 0.08 = $1,150,000
  2. Answer: $1,150,000
Capitalization rate — Cap rate = NOI ÷ Value × 100

Example. An investor buys a building for $1,150,000 that generates $57,500 of annual net operating income. What is the capitalization rate?

  1. $57,500 ÷ $1,150,000 = 0.05
  2. 0.05 × 100 = 5%
  3. Answer: 5%
Net operating income — NOI = Potential gross income − Vacancy − Operating expenses

Example. An apartment building has 21 units renting for $1,500 per month each. Vacancy and collection losses are 5% of potential gross income, and annual operating expenses are $143,000. What is the net operating income?

  1. Potential gross income: 21 × $1,500 × 12 = $378,000
  2. Effective gross income: $378,000 × 0.95 = $359,100
  3. $359,100 − $143,000 = $216,100
  4. Answer: $216,100
Value from gross rent multiplier — Value = Monthly gross rent × GRM

Example. Comparable rental homes sell for about 123 times their monthly gross rent. A similar home rents for $1,300 per month. What is its estimated value using the gross rent multiplier?

  1. $1,300 × 123 = $159,900
  2. Answer: $159,900
Gross rent multiplier — GRM = Sale price ÷ Monthly gross rent

Example. A rental home sold for $297,000 and rents for $2,200 per month. What is the gross rent multiplier?

  1. $297,000 ÷ $2,200 = 135
  2. Answer: 135
Percentage appreciation — Percent change = (New − Old) ÷ Old × 100

Example. A home was purchased for $310,000 and is now worth $325,500. What is the percentage increase in value?

  1. $325,500 − $310,000 = $15,500
  2. $15,500 ÷ $310,000 × 100 = 5%
  3. Answer: 5%
New price after a reduction — New price = Old price × (1 − Reduction %)

Example. A home listed at $600,000 is reduced in price by 10%. What is the new list price?

  1. $600,000 × 0.9 = $540,000
  2. Answer: $540,000
Investor profit after commission — Profit = Sale price − Commission − Purchase price − Repairs

Example. An investor buys a house for $300,000, spends $20,000 on repairs, and sells it for $370,000 paying a 5% commission. What is the investor's profit?

  1. Commission: $370,000 × 0.05 = $18,500
  2. $370,000 − $18,500 − $300,000 − $20,000 = $31,500
  3. Answer: $31,500
Straight-line depreciation — Annual depreciation = Cost ÷ Useful life

Example. A building has a depreciable cost of $187,500 and a useful life of 25 years. Using straight-line depreciation, what is the annual depreciation?

  1. $187,500 ÷ 25 = $7,500
  2. Answer: $7,500
Owner equity — Equity = Market value − All liens

Example. A home is worth $420,000. The owner has a first mortgage of $115,000 and a home-equity loan of $25,000. What is the owner's equity?

  1. $420,000 − $115,000 − $25,000 = $280,000
  2. Answer: $280,000

Appraisal & Value

Cost approach: building cost — Cost = (Living area × rate) + (Garage area × rate)

Example. A builder estimates 2,500 sq ft of living area at $125 per sq ft and a 500 sq ft garage at $65 per sq ft. What is the total replacement cost of the building?

  1. 2,500 × $125 = $312,500
  2. 500 × $65 = $32,500
  3. $312,500 + $32,500 = $345,000
  4. Answer: $345,000
Price per square foot — Price per sq ft = Price ÷ Square feet

Example. A 2,800 sq ft home sold for $714,000. What was the price per square foot?

  1. $714,000 ÷ 2,800 = $255
  2. Answer: $255
Estimate value from a comparable — Value = (Comp price ÷ Comp sq ft) × Subject sq ft

Example. A comparable 1,600 sq ft home sold for $256,000. Using price per square foot, what is the estimated value of a similar 1,700 sq ft subject home?

  1. $256,000 ÷ 1,600 = $160 per sq ft
  2. $160 × 1,700 = $272,000
  3. Answer: $272,000
Adjusting a comparable — Adjust the COMPARABLE: subtract what it has that the subject lacks; add what the subject has that it lacks

Example. A comparable sold for $305,000. It has a garage worth $14,000 that the subject lacks, and the subject has a pool worth $22,000 that the comparable lacks. What is the comparable's adjusted price?

  1. $305,000 − $14,000 (garage) = $291,000
  2. $291,000 + $22,000 (pool) = $313,000
  3. Answer: $313,000
Cost approach value — Value = Replacement cost − Depreciation + Land value

Example. The replacement cost new of a building is $420,000. Accrued depreciation is 10% of that cost, and the land is valued at $95,000. What is the property value under the cost approach?

  1. Depreciation: $420,000 × 0.1 = $42,000
  2. $420,000 − $42,000 + $95,000 = $473,000
  3. Answer: $473,000

Property Taxes

Property tax with a mill rate — Assessed value = Market value × Ratio; Tax = Assessed ÷ 1,000 × Mills

Example. A home has a market value of $200,000. The county assesses property at 40% of market value and the tax rate is 21 mills. What are the annual property taxes? (1 mill = $1 per $1,000 of assessed value)

  1. Assessed value: $200,000 × 0.4 = $80,000
  2. $80,000 ÷ 1,000 × 21 = $1,680
  3. Answer: $1,680
Tax rate per $100 — Tax = Assessed value ÷ 100 × Rate

Example. A property is assessed at $215,000. The tax rate is $2.40 per $100 of assessed value. What is the annual tax bill?

  1. $215,000 ÷ 100 = 2150
  2. 2150 × 2.4 = $5,160
  3. Answer: $5,160
Transfer tax — Tax = Price ÷ 500 × Rate per $500

Example. A state charges a deed transfer tax of $0.50 for each $500 (or fraction) of the sale price. The home sells for $600,000 (an exact multiple of $500). What is the transfer tax?

  1. $600,000 ÷ 500 = 1200
  2. 1200 × $0.50 = $600
  3. Answer: $600

Prorations

Proration of unpaid property taxes — Seller's share = Annual tax ÷ 360 × Days owned (Jan 1 through the day before closing)

Example. Annual property taxes of $1,800 for the calendar year are unpaid at closing on October 16. Use a 360-day year with 30-day months; the buyer owns the day of closing. How much is the seller charged for taxes?

  1. Days: 9 full months × 30 + 15 days = 285
  2. Daily tax: $1,800 ÷ 360 = $5
  3. $5 × 285 = $1,425
  4. Answer: $1,425
Proration of prepaid rent — Buyer credit = Monthly rent ÷ 30 × Days the buyer owns

Example. A landlord collected $2,100 rent on the 1st of a 30-day month. The property closes on the 22th and the buyer owns the day of closing. How much is the buyer credited for the rent?

  1. Buyer owns days 22 through 30 = 9 days
  2. $2,100 ÷ 30 = $70 per day
  3. $70 × 9 = $630
  4. Answer: $630
Proration of assumed-loan interest — Seller interest = Balance × Rate ÷ 360 × Days (1st through day before closing)

Example. A buyer assumes the seller's $288,000 mortgage at 5% interest. Interest is paid in arrears on the 1st for the previous month. Closing is on the 19th and the buyer owns the day of closing. Using a 360-day year, how much interest is charged to the seller?

  1. Daily interest: $288,000 × 0.05 ÷ 360 = $40
  2. Days: 18
  3. $40 × 18 = $720
  4. Answer: $720
Proration of prepaid insurance — Reimbursement = Annual premium ÷ 12 × Unused months

Example. The seller paid a $960 annual homeowner's insurance premium in advance. At closing, 4 full months of the policy have been used and the buyer will take over the policy. How much does the buyer reimburse the seller?

  1. Unused months: 12 − 4 = 8
  2. $960 ÷ 12 = $80
  3. $80 × 8 = $640
  4. Answer: $640

Closing & Leases

Cash needed at closing — Cash to close = Price − Loan + Buyer closing costs − Earnest money

Example. A buyer purchases a home for $420,000 with a 90% loan. Closing costs paid by the buyer are $7,000, and the buyer already deposited $4,000 in earnest money. How much more cash must the buyer bring to closing?

  1. Loan: $378,000
  2. $420,000 − $378,000 + $7,000 − $4,000 = $45,000
  3. Answer: $45,000
Percentage lease — Annual rent = Base rent × 12 + % × (Sales − Breakpoint)

Example. A retail lease requires base rent of $3,000 per month plus 6% of annual gross sales above $350,000. Tenant sales for the year were $500,000. What is the total rent for the year?

  1. Base rent: $3,000 × 12 = $36,000
  2. Overage: $500,000 − $350,000 = $150,000; × 0.06 = $9,000
  3. $36,000 + $9,000 = $45,000
  4. Answer: $45,000