Property Valuation and Appraisal Study Guide for the Real Estate License Exam

More About Real Estate Math

Problem Types

The real estate test will also ask you to solve different types of problems using basic mathematics. Problems types may include: percentages, commission calculations, interest, depreciation, profit and loss, and return on investment.

Percentage

A percentage is obtained by dividing one number by another. For example, an investor buys a property for $100,000 and sells it for $120,000, with a profit of $20,000. The profit percentage would be: $20,000 / $100,000 = 20%.

Commission

Commissions are usually expressed as a percentage, but they can also be a fixed fee. If a real estate agent is listing a $500,000 property for sale with a 6% commission, the dollar amount of the commission would be: $500,000 x .06 (which is 6%) = $30,000. However, as of the August 2024 update, commissions are now more transparent and negotiable. Buyers may now be responsible for paying their agent’s commission directly, rather than it being covered by the seller, depending on the agreement in place.

Interest

A simple way to think of interest is the profit that a lender makes on a loan. Let’s say a lender makes a 10 year loan for $100,000 with interest-only payments of $100 per month. The interest rate (or percentage) is calculated this way: ($100 per month x 120 months) / $100,000 = $12,000 / $100,000 = .12 or 12%.

Mortgage loans—Interest rates on mortgage loans use the interest that a Treasury Note is paying as a benchmark. Then, the mortgage interest rate is adjusted upward to compensate the lender for factors such as risk, profit, and to compete with the rates that other lenders are charging.

Loan discounts—Also known as discount points, loan discounts are fees a borrower pays directly to a lender to buy down or reduce the interest rate. One discount point equals 1% of the mortgage amount. For example, if a borrower has a $100,000 mortgage and pays 2 points, the borrower would pay: $100,000 x .02 = $2,000 in points.

Depreciation

Depreciation is a non-cash expense used to reduce the cash income of a property. Depreciation assumes that a property is only useful for a fixed period of time. For example, if a property has an annual net income of $12,000 and a depreciation expense of $1,000, the taxable net income would be: $12,000 – $1,000 = $11,000. While the investor has an actual cash profit of $12,000, she only pays tax on $11,000 due to the depreciation deduction.

Profit and Loss

Profit and loss is a financial statement that summarizes the gross revenues and expenses associated with an investment property. Also known as P&Ls, profit and loss statements are usually generated monthly and also generated at the end of the year to prepare annual tax returns.

Return on Investment

The return on investment is expressed as a percentage. It is used to measure the profitability of an investment. Also known as ROI, the formula is: (Investment Gain – Investment Cost) / Investment Cost = ROI. For example, if a homeowner sold a house for $150,000 that they originally paid $100,000 for their ROI would be: ($150,000 – $100,000 = $50,000) / $100,000 = 50%.

Proration

Proration means allocating or distributing between parties.

Use of Proration

Proration is used to make a pro-rata allocation between a buyer and a seller on the settlement statement when the property changes hands. Prorations do not have to occur, but they usually do. In real estate, the four things that can be prorated are: property taxes, interest on assumed loans, prepaids or later-paid rentals, and property insurance.

Property taxes—If a property changes hands before the property tax is due to be paid to the taxing authority, the seller would receive a credit for the taxes they paid in advance and the buyer would receive a debit.

Interest on assumed loans—Mortgage interest is paid in arrears. If a property changes hands on the last day of the month, the seller would receive a debit (or be charged for) interest that is due to the lender but not yet paid. The buyer would receive a credit if they are assuming the loan and making the next mortgage payment due.

Prepaid or later-paid rentals—Prepaids are items that have been paid for in advance. For example, let’s say a home with an HOA fee changes hands in the middle of the month and the seller has already paid the HOA dues of $50 for that month. The seller would receive a credit of $25 for the part of the dues they paid for a home they no longer own, and the buyer would receive a debit of $25.

Property insurance—Property insurance premiums are usually paid annually. A seller would receive a credit for the amount of insurance they paid for have not used, and the buyer would receive a debit for the portion of the property insurance premium that the seller paid for.

Proration Calculation

Specific terms and days are used in proration calculations. They include the closing day, the statutory year, the actual year, and rules regarding rounding amounts up or down.

Closing day—The closing day is the day when the property transfers from seller to buyer. The closing day also belongs to the buyer and affects how a proration is calculated. For example, if a property closes on the 15th of a month with 30 days, 14 days belong to the seller and 16 days belong to the buyer.

Statutory year—A statutory year—also known as a banker’s year—is made up of 12 months, each with 30 days, for a total of 360 days.

Actual year—The average or mean length of a year is 365.2422 days. In a non-leap year, there are 365 days, and in a leap year, there are 366 days.

Rounding—If a number ends in 5 or higher, it is generally rounded up, and if it ends in 4 or less, it is generally rounded down. For example, $75.99 would be rounded up to $76, while $75.45 would be rounded down to $75.

Closing Statements

A closing statement provides the details of a real estate transaction and is prepared by the real estate closing agent, usually an escrow officer or an attorney. As of the August 2024, NAR guidelines emphasize clarity in commission structures and payments, which must be accurately reflected in closing statements. The closing statement should also clearly indicate if the buyer is responsible for paying their agent’s commission directly, as this is a significant shift from previous practices.

Purpose

The purpose of a property closing statement is to show the financial details of a real estate transaction. The closing statement will include items such as purchase price, transaction-related fees, commissions, taxes and insurance paid, and any prorations.

Debits and Credits

A debit is when something is taken away, and a credit is when something is added to. For example, the money received for the sale of a home is a credit to the seller. The real estate sales commission paid is a debit to the seller. Prorations are also debited and credited.

For Buyer

A closing statement for the buyer is usually longer than a seller’s closing statement. A buyer closing statement includes items such as purchase price paid, mortgage and mortgage-related fees and financing fees, owner’s title insurance, and the buyer’s share of escrow fees and property taxes, plus any other prorated items.

For Seller

A closing statement for a seller includes the sales proceeds received, the mortgage balance paid off (if any), the real estate sales commission paid, and the seller’s share of escrow fees and any prorated items.

Real Estate Settlement Procedures Act

Also known as RESPA, the Real Estate Settlement Procedures Act was passed by Congress and became effective on June 20, 1975. The purpose of RESPA is to improve the disclosures of settlement costs provided to buyers and sellers, and to eliminate any abusive practices in real estate settlement.

Materials to Be Received

RESPA requires that lenders, mortgage brokers, and servicers of home loans provide borrowers with pertinent and timely disclosures of the source and true costs of the real estate settlement process throughout the transaction. Materials to be received include a Special Information Booklet, a GFE or good faith estimate, and a Mortgage Servicing Disclosure Statement.

Uniform Settlement Statement

Also known as a HUD-1, the uniform settlement statement is presented to the buyer at closing—or one day before—and discloses all closing costs so that the buyer understands the total costs of buying the property. The buyer also receives the booklet Settlement Costs and You, which gives a buyer a basic understanding of the mortgage process and fees and helps the buyer make an informed decision.

Reporting to the IRS

Sellers are required to report to the IRS the gross proceeds received from the sale of real estate. This is done as a result of the Tax Reform Act of 1986 and is meant to encourage taxpayer compliance and to assist the IRS in its audit and enforcement efforts. The IRS requires the settlement agent to deliver this information to the IRS using Form 1099S.