Real Estate Math — 10 Practice Questions With Step-by-Step Solutions

Fee simple (or fee simple absolute) is the highest and most complete form of real property ownership. The owner has the rights to possess, use, alter, transfer, and devise the property without an inherent time limit. Fee simple is what most residential homeowners hold. It is subject only to government powers (taxation, eminent domain, police power, escheat) and any private encumbrances (mortgages, easements, restrictive covenants). A life estate, by contrast, lasts only for the lifetime of a specified person and then passes to a remainderman. A leasehold is a tenant's interest, limited in duration. 'Fee simple defeasible' is a fee simple that can be lost if a specified condition occurs.

Joint tenancy with right of survivorship has a defining feature: when one joint tenant dies, their interest passes automatically and immediately to the surviving joint tenant(s) outside of probate. This 'right of survivorship' is the main reason couples and friends choose joint tenancy. The deceased's heirs receive nothing from the property, and a will cannot devise the joint tenancy interest because the interest is extinguished at death. Joint tenancy requires four unities: time, title, interest, and possession (acquired at the same time, in the same deed, equal shares, equal right to possess). Tenancy in common, by contrast, allows each owner to devise their share to heirs and does not include survivorship.

Eminent domain is the government's constitutional power to take private property for public use, with just compensation paid to the owner. It is one of the four government powers over private real estate (along with police power, taxation, and escheat). Common uses: highway construction, schools, public utilities, urban renewal. The process is called 'condemnation', and the property owner has the right to challenge the taking (whether it serves a true public purpose) and to challenge the valuation of just compensation. The Fifth Amendment to the US Constitution and parallel state constitutional provisions require just compensation; what 'just' means is often litigated. Adverse possession is a way private parties acquire ownership through long, open, hostile use, which is different from eminent domain.

Zoning laws are an exercise of police power — the government's authority to regulate private activity to protect public health, safety, morals, and general welfare. Zoning regulates the use of land (residential, commercial, industrial, agricultural), the density of development, the height and setback of buildings, and similar matters. Police power requires no compensation to property owners because it does not 'take' property — it regulates how property can be used, which is different from confiscation. However, regulations that go too far and effectively destroy the value of a property may constitute a 'regulatory taking' that does require compensation. The four government powers (PETE): Police power, Eminent domain, Taxation, Escheat.

Market value is determined by what willing, informed buyers and sellers would agree to in an arm's-length transaction. The main inputs are: (1) supply and demand in the local market, (2) comparable sales of similar properties (the 'sales comparison approach'), (3) the property's specific physical characteristics (size, condition, features, location), and (4) economic forces (interest rates, employment, demographic trends). The seller's asking price is just an offer; it has no inherent relationship to actual value. What the seller paid is sunk cost, irrelevant to today's value. A buyer's emotional attachment may make them pay more, but does not change market value generally. Appraisers use three approaches — sales comparison, cost, and income — depending on property type.

A mortgage and a deed of trust serve the same economic function — securing a loan with real property as collateral — but use different legal structures. A mortgage is a two-party agreement: the borrower (mortgagor) pledges the property to the lender (mortgagee) as security. If default occurs, the lender must go through judicial foreclosure (a court proceeding), which can take months to years. A deed of trust adds a third party, a trustee (often a title company), who holds title to the property as security on behalf of the lender (beneficiary). If the borrower (trustor) defaults, the trustee can conduct a non-judicial foreclosure outside court, typically a faster process. Which is used depends on state law: some states use mortgages, some use deeds of trust, and some allow both.

PITI stands for Principal, Interest, Taxes, and Insurance — the four standard components of a typical mortgage payment. Principal repays the loan balance; interest is the cost of borrowing; taxes are property taxes collected by the lender and held in escrow to pay the local government; insurance is homeowner's insurance (and sometimes private mortgage insurance, PMI, when the down payment was below 20%). Lenders use PITI as a stand-in for the borrower's total housing cost when calculating debt-to-income ratios for qualification. Some borrowers pay taxes and insurance themselves rather than escrowing through the lender; that arrangement is allowed when the down payment is large enough.

An agent owes fiduciary duties to their principal — the highest standard of care recognized in law. The mnemonic OLD-CAR captures the duties: Obedience to lawful instructions; Loyalty (acting in the principal's best interest, not the agent's); Disclosure (sharing all material facts known to the agent); Confidentiality (protecting the principal's private information); Accounting (handling money carefully); and Reasonable care (using skill and diligence). These duties apply whether the agent represents a buyer or a seller. They do not apply to the other party in the transaction — to whom the agent owes only honesty and disclosure of material defects. Dual agency (representing both sides) is allowed in some states with full informed consent of both parties, but compromises some of these duties.

'Puffing' is salesmanship — exaggeration or opinion that a reasonable person would not rely on as a statement of fact. Examples: 'This is the best house in the neighborhood', 'You'll love it here', 'This is a great investment'. Puffing is not actionable misrepresentation because no reasonable buyer would treat the statement as a guaranteed fact. Specific factual claims, however — 'The roof is two years old', 'The house has 2,400 square feet', 'There has never been a flood here' — are statements of fact that, if false and material to the buyer's decision, can constitute misrepresentation or fraud. The line between puffing and fraud is sometimes blurry; agents should stick to verifiable facts and clearly label opinions.

The federal Residential Lead-Based Paint Hazard Reduction Act of 1992 (Title X) requires that sellers and landlords of residential property built before 1978 disclose any known lead-based paint or lead hazards, provide a copy of the EPA pamphlet 'Protect Your Family from Lead in Your Home', and give buyers a 10-day opportunity to inspect for lead before becoming obligated under the contract. The pre-1978 date matters because lead-based paint was banned for residential use that year. The seller does not have to test for lead, only disclose what is known. Failure to comply can result in significant federal fines. The disclosure must be a separate document attached to the contract, signed by all parties.