6.2 Real Estate Math and Calculations

Commission and Percentages

The core formula is commission = sale price × rate, and any split is applied afterward. Use the T-method: cover the unknown, the other two terms show whether to multiply or divide.

Worked example: A home sells for $400,000 at a 6% total commission. Total = 400,000 × 0.06 = $24,000. If the listing and selling brokerages split 50/50, each brokerage gets $12,000. If a salesperson keeps 60% of her brokerage's $12,000, she earns 12,000 × 0.60 = $7,200.

To find a missing piece, divide. If commission was $21,000 at a 6% rate, price = 21,000 / 0.06 = $350,000.

Area and Acreage

Memorize these land conversions:

Worked example: A lot is 150 ft × 290.4 ft. Area = 150 × 290.4 = 43,560 sq ft = 1 acre exactly. A parcel is half of a quarter-section: a section is 640 acres, a quarter-section is 160 acres, and half of that is 80 acres.

To convert square feet to acres, divide by 43,560. A 2-acre commercial pad equals 2 × 43,560 = 87,120 square feet. To price land per acre: a 5-acre tract listed at $475,000 is 475,000 / 5 = $95,000 per acre. Front-foot problems multiply the lot frontage by a per-front-foot rate: 80 front feet at $1,200 per front foot = $96,000.

Loan-to-Value, Points, and Profit

Loan-to-value (LTV) = loan ÷ value (the lower of price or appraisal). A buyer borrows $240,000 on a home appraised at $300,000: LTV = 240,000 / 300,000 = 80%. To find a loan from LTV: an 80% LTV on a $300,000 value gives a 0.80 × 300,000 = $240,000 loan.

Discount points are prepaid interest. One point = 1% of the LOAN amount (not the price). On a $240,000 loan, 2 points cost 240,000 × 0.02 = $4,800. A common trap is multiplying by the sale price; always use the loan.

Profit / appreciation uses made ÷ paid. A property bought for $200,000 and sold for $250,000 earned 50,000 / 200,000 = 25% profit. Reverse it: if a $250,000 sale represents a 25% gain, original cost = 250,000 / 1.25 = $200,000. For straight-line appreciation over years, divide total appreciation by the original value, then by the number of years. If a $180,000 home appreciates to $216,000 over 4 years, total gain = $36,000, which is 36,000 / 180,000 = 20% over 4 years, or 5% per year.

Net-to-seller problems reverse a commission: a seller who must net $188,000 after a 6% commission needs a price of 188,000 / (1 − 0.06) = 188,000 / 0.94 = $200,000. A common trap is taking 6% of the desired net instead of dividing by 0.94, which understates the price.

Investment Math: Cap Rate and GRM

Capitalization rate values income property: Value = Net Operating Income ÷ Cap Rate. NOI is gross income minus operating expenses, excluding mortgage payments (debt service).

Worked example: A building produces $60,000 NOI and the market cap rate is 8%. Value = 60,000 / 0.08 = $750,000. Rearranged: a $750,000 property earning $60,000 NOI has a cap rate of 60,000 / 750,000 = 8%.

Gross Rent Multiplier (GRM) = price ÷ gross annual (or monthly) rent. A home priced at $300,000 renting for $2,500/month has a monthly GRM of 300,000 / 2,500 = 120. Using annual rent of $30,000, GRM = 300,000 / 30,000 = 10. GRM uses gross rent and ignores expenses, which is why it is a quick screen rather than a true value like cap rate.

Florida Doc Stamps and Property Tax

Documentary stamp tax on the deed is $0.70 per $100 (or fraction) of the sale price in every Florida county except Miami-Dade ($0.60, plus surtax on non-single-family). Round the price up to the next $100 first.

On the note/mortgage: doc stamps are $0.35 per $100 of the loan, and a nonrecurring intangible tax of $0.002 (2 mills) per dollar of the loan applies (no rounding on intangible).

Worked example (deed): A $325,000 sale → 325,000 / 100 = 3,250 increments × $0.70 = $2,275.00.

Property tax in mills: one mill = $0.001 = $1 per $1,000 of assessed value. A home assessed at $200,000 taxed at 20 mills owes 200,000 × 0.020 = $4,000.

Florida property-tax problems often apply the homestead exemption first: up to $50,000 off assessed value for a primary residence (the first $25,000 applies to all taxing authorities; the second $25,000 applies to value above $50,000 and not to school taxes). A $200,000 homesteaded home taxed at a simplified 20 mills on a $150,000 taxable value owes 150,000 × 0.020 = $3,000. Always subtract exemptions to reach taxable value before multiplying by the millage rate.

Putting Doc Stamps Together

A single financed purchase often combines all three Florida taxes. Worked example: a $300,000 non-Miami-Dade sale with a $240,000 loan:

• Deed doc stamps: 300,000 / 100 = 3,000 × $0.70 = $2,100.00
• Note doc stamps: 240,000 / 100 = 2,400 × $0.35 = $840.00
• Intangible tax: 240,000 × 0.002 = $480.00

Total Florida transfer/loan taxes = $3,420.00. Remember the deed tax is on the full price, while the note tax and intangible tax are on the loan amount only; mixing those bases is the single most common doc-stamp error on the exam.