Formulas and reference sheets

1 acre = 43,560 square feet.

1 mile = 5,280 feet.

1 square mile = 640 acres.

1 standard section = 1 square mile.

1 standard township = 36 sections.

1 square yard = 9 square feet.

1 cubic yard = 27 cubic feet.

1 foot = 12 inches.

These are unit conversions or standard survey assumptions, not a guarantee that every actual surveyed section contains exactly 640 acres. S01 S08

Rectangle area = length × width.

Triangle area = base × perpendicular height ÷ 2.

Trapezoid area = (parallel side 1 + parallel side 2) ÷ 2 × perpendicular height.

Volume = length × width × depth, with matching units.

Acres = square feet ÷ 43,560.

Price per square foot = price ÷ square feet.

Price per front foot = price ÷ frontage feet.

Part = whole × decimal rate.

Whole = part ÷ decimal rate.

Rate = part ÷ whole.

Percentage change = (new amount − original amount) ÷ original amount × 100.

Compensation = agreed base × negotiated rate.

Agent compensation = applicable brokerage compensation × agent's agreed share, after any other specified allocations.

Required sale price = (desired seller net + payoff + fixed seller costs) ÷ (1 − total price-based cost rate), when the problem's costs fit that structure.

Loan-to-value ratio = loan ÷ lender's applicable property-value base.

Down payment toward price = price − acquisition loan proceeds.

Points cost = loan × points percentage.

Simple interest = principal × annual rate × fraction of year.

Monthly interest = beginning balance × annual rate ÷ 12, under the stated monthly convention.

Principal reduction = principal-and-interest payment − interest component.

New balance = prior balance − principal reduction.

Housing ratio = qualifying housing expense ÷ qualifying gross income.

Total-debt ratio = qualifying total debt expense ÷ qualifying gross income.

PITI = principal, interest, taxes, and insurance; association dues and other obligations may also matter to underwriting.

Proration = amount for entire period × allocated portion of period.

Buyer cash due = buyer debits − loan proceeds − deposits already held − other applicable buyer credits.

Seller proceeds = seller credits − payoffs − seller costs − other applicable seller debits.

Unpaid seller-period expense later paid by buyer: seller debit, buyer credit.

Assignable buyer-period expense already paid by seller: buyer debit, seller credit.

Buyer-period rent already collected by seller: seller debit, buyer credit.

Always determine the billing period, paid status, closing-day owner, and day-count convention before using these relationships.

Effective gross income = potential gross income − vacancy and collection loss + applicable other income.

NOI = effective gross income − operating expenses, using the stated convention.

Value = NOI ÷ capitalization rate.

Capitalization rate = NOI ÷ value.

NOI = value × capitalization rate.

Gross multiplier = sale price ÷ gross income for the chosen period.

Value by multiplier = matching-period gross income × multiplier.

Cost indication = land value + current improvement cost − accrued depreciation.

Simplified age-life depreciation = improvement cost × effective age ÷ total economic life.

Before-tax cash flow = NOI − debt service − other specified cash deductions.

Cash-on-cash return = annual before-tax cash flow ÷ cash invested.

Debt-service coverage ratio = NOI ÷ annual debt service.

Natural percentage-rent breakpoint = base rent ÷ percentage rate, when the lease uses that structure.

Months of supply = relevant active inventory ÷ average relevant monthly sales.

Pre-1978: the construction-age starting point for most federal lead disclosure coverage. Ten days: ordinary buyer lead inspection opportunity, subject to permitted waiver or written change. Three years: required retention period for covered disclosure records. S22

Three business days: general LE delivery deadline after a covered application; also the CD receipt waiting period, but with a different business-day definition. Seven business days: general LE waiting period before consummation. These are not interchangeable clocks. S26 S28 S55

Three business days: ordinary TILA rescission period for qualifying transactions after the latest required triggering event; not a general right to cancel every purchase loan. S31

80% and 78%: key original-value thresholds in covered conventional PMI cancellation and termination rules, with conditions; not universal FHA insurance rules. S33

Forty-five and 180 days: key deferred 1031 exchange periods, with the replacement-property deadline also limited by the applicable tax-return due date, including extensions. S44

$250,000 and $500,000: potential qualifying principal-residence gain exclusions, not automatic exclusions of sale price or cash proceeds. S42

27.5 and 39 years: common general-system building depreciation periods for residential rental and nonresidential real property, with methods, conventions, and exceptions. S45 S56

One year and two years: general federal FHA administrative-complaint and private-action periods respectively, subject to applicable statutory calculation and procedural rules. S61 S62

Ordinary broker education: 168 hours; the six subject allocations appear in Chapter 22. Independent and employing-broker qualifications are separate. CO03 CO33

Ordinary continuing education: 24 hours in the usual three-year cycle, including three different four-hour Annual Commission Update courses and 12 elective hours. Verify special initial, inactive, reactivation, and portability treatment. CO05 CO02

Broker trust deposits: distinguish the three-business-day ordinary funds rule from the five-business-day property-management rule, using the applicable receipt/mutual-execution trigger. These are not the tenant security-deposit refund periods. CO06

Trust reconciliation and records: monthly three-way reconciliation; four-year brokerage records under the governing record-retention rule. Keep any other legally required longer records. CO06 CO07

Residential security-deposit refund: ordinarily 30 days after termination or surrender and acceptance, whichever occurs last, unless the lease permits a longer period not exceeding 60 days. Apply the current statute’s conditions and exceptions. CO14

Colorado nonresident withholding: lesser of 0.02 × sales price or seller net proceeds, when the statute applies and no exemption is established. CO17

Colorado documentary fee: $0.01 per $100 or major fraction of covered consideration exceeding $500. Check the applicable fractional calculation; do not substitute a universal ceiling function. CO18

Hypothetical property tax: taxable assessed value × mill levy ÷ 1,000. A supplied assessment percentage is an exercise assumption, not a permanent statement of Colorado assessment law.

Buyer cash to close: buyer debits − buyer credits. Seller proceeds: seller credits − seller debits. Apply the actual settlement entries; earnest money already deposited is not counted as a second payment.

Three separate foreclosure clocks: ordinary cure notice at least 15 calendar days before sale and cure payment by noon the day before sale; qualifying equity-purchase cancellation until midnight of the third business day after signing or noon the day before sale, whichever comes first; qualifying junior-lienor redemption is a separate process. Consult Chapter 29 for conditions. CO21 CO32 CO31

Do not memorize a contract deadline that the parties must fill in. Identify the completed date, clock time, extension selection, delivery requirement, and consequence. CO11