Reference / Real estate math
Real estate math
Formulas, units, and worked examples for exam problems.
| Concept | Formula | Example |
|---|---|---|
| Commission | Price × negotiated rate | $600,000 × 0.025 = $15,000. A 2.5% rate is illustrative, not a standard fee. |
| Loan-to-value ratio | Loan ÷ property value × 100 | $360,000 ÷ $450,000 = 80%. Use the value basis specified in the question. |
| Simple interest | Principal × annual rate × time in years | $10,000 × 0.06 × (3 ÷ 12) = $150. |
| Discount points | Loan amount × points ÷ 100 | Two points on a $300,000 loan = $6,000. |
| Capitalization | Value = annual NOI ÷ cap rate | $48,000 ÷ 0.06 = $800,000. Do not divide by 6. |
| Net operating income | Effective gross income − operating expenses | $90,000 − $30,000 = $60,000. Debt service is not an operating expense. |
| Gross rent multiplier | Price ÷ gross rent for the specified period | $480,000 ÷ $4,000 monthly rent = 120 monthly GRM. Keep periods consistent. |
| Cash-on-cash return | Annual before-tax cash flow ÷ cash invested | $12,000 ÷ $150,000 = 8%. Cash flow here is after debt service. |
| Proration | Periodic charge ÷ days in period × allocated days | $3,600 annual expense ÷ 360 × 45 = $450, only when a 360-day convention is specified. |
| Area | Length × width | A rectangular 100 ft × 150 ft parcel has 15,000 square feet. |
| Acreage | Square feet ÷ 43,560 | 87,120 square feet = 2 acres. |
| Net proceeds | Sale price − seller costs − liens paid off | $700,000 − $35,000 − $400,000 = $265,000 before any other specified adjustments. |
Amortizing loan payment
Monthly principal and interest$2,398.20
Illustrative fixed-rate loan with monthly payments. Excludes taxes, insurance, fees, and mortgage insurance.
Set up the problem before calculating
- Identify what is being asked: a dollar amount, a rate, an area, or a time period.
- Convert percentages to decimals and match the time units. A monthly rent multiplier cannot be applied to annual rent without conversion.
- Use the question's stated convention for proration days and rounding. Do not assume every transaction uses a 360-day year.
- Check the scale of the answer. A 1% point is one-hundredth of the loan amount, not one-hundredth of the property price.
Value and financing are different calculations
A property's investment NOI is calculated before the owner's debt service. Changing the owner's loan does not, by itself, change that property's NOI. Cash flow after debt service and cash-on-cash return do depend on financing.
Property-tax appraisal can use a tax-loaded capitalization convention. Do not combine an income figure that already deducts property tax with a capitalization rate that also loads the same tax. The income analysis chapter explains the distinction.