8.2 Commission, Financing, and Interest Calculations

Commission, Financing, and Interest Calculations

This section covers the money math that brokers and lenders rely on daily, and it is the most heavily tested calculation category on the national exam. The unifying concept is the percentage relationship: Part = Total x Rate. Whether the question asks for a commission, a loan-to-value ratio, or annual interest, you are solving one version of that equation. Identify which of the three values is missing, then rearrange.

The percentage triangle (T-bar method)

Draw a T. Put the Part (the dollar amount) on top, and the Total and the Rate on the bottom. Cover the value you want:

• Cover Part: multiply Total x Rate
• Cover Total: divide Part / Rate
• Cover Rate: divide Part / Total

This single device solves commission, interest, profit-percent, and capitalization questions. Convert percentages to decimals first: 6 percent = 0.06, 5.5 percent = 0.055. A misplaced decimal is the most common scoring error on the exam.

Commission splits

Commission is computed on the sale price, then split. A 6 percent commission on a 350,000 dollar home = 350,000 x 0.06 = 21,000 dollars total.

Splits cascade. Suppose the listing and selling brokerages split 50/50, so each office gets 10,500 dollars. If the selling agent keeps 60 percent of their office's share, the agent earns 10,500 x 0.60 = 6,300 dollars. Read carefully: a split can be office-to-office, then office-to-agent. Solve the chain one multiplication at a time and never apply the agent split to the full commission.

Graduated commission and the order of operations

Some listings carry a graduated or tiered commission, such as 7 percent on the first 100,000 dollars and 5 percent on the balance. For a 250,000 dollar sale: tier one = 100,000 x 0.07 = 7,000; tier two = 150,000 x 0.05 = 7,500; total = 14,500 dollars. Do not apply a single blended rate to the whole price, because the tiers cover different dollar bands.

The order of operations matters in every split problem. First find the total commission from the sale price, then divide between offices, then divide the office share with the agent. Skipping a layer or applying a later split to an earlier figure produces a number that looks plausible but fails the answer key. Write each layer on its own line so you can see exactly which base you are multiplying.

Reverse commission and net-to-seller

A frequent trap asks for the sale price given the seller's net. If a seller must net 188,000 dollars after a 6 percent commission, the net represents 94 percent of the sale price. Sale price = 188,000 / 0.94 = 200,000 dollars. Verify: 200,000 x 0.06 = 12,000 commission; 200,000 - 12,000 = 188,000. The error candidates make is multiplying the net by 1.06; you must divide by (1 - rate).

Financing ratios and simple interest

Loan-to-value (LTV) = Loan / Value. A 240,000 dollar loan on a 300,000 dollar property is an 80 percent LTV. Lenders set maximum LTVs; multiply value by the max LTV to find the largest loan.

Simple annual interest = Principal x Rate. Annual interest on a 200,000 dollar loan at 5.5 percent = 200,000 x 0.055 = 11,000 dollars, or about 916.67 dollars per month. For partial periods, multiply by the fraction of a year (months / 12). Most exam interest questions are simple interest, not compound.

Points, profit, and percentage change

Discount points are a financing cost stated as a percent of the loan, where one point equals one percent of the loan amount. Two points on a 250,000 dollar loan = 250,000 x 0.02 = 5,000 dollars. Points apply to the loan, never the purchase price, which is a frequent exam trap.

Profit and loss use the same T-bar. If an owner bought for 180,000 dollars and sold for 207,000 dollars, the dollar profit is 27,000 and the percent profit = 27,000 / 180,000 = 15 percent. The denominator is always the original cost, the basis you started from, not the higher sale price. Reversing that ratio understates the gain and is the wrong answer the exam offers first. The same rule governs an appreciation or depreciation question: divide the change by the original value, then express it as a percent, and watch whether the prompt asks for the percent of change or the new total value, which is the original plus or minus that change.

Worked Example: Discount Points and Loan Origination

One point equals 1% of the loan amount, not the purchase price. Points include discount points (paid to buy down the rate) and origination fees.

Worked example: a buyer purchases a $320,000 home with a 20% down payment.

• Down payment = $320,000 × 0.20 = $64,000, so the loan = $320,000 − $64,000 = $256,000.
• The lender charges 2 discount points plus a 1% origination fee, totaling 3% of the loan.
• Point/fee cost = $256,000 × 0.03 = $7,680.

The single most common error is taking points against the sale price instead of the loan amount. Here, 3% of the $320,000 price would be $9,600, a $1,920 overstatement. Always identify the loan amount first, then apply points to it.

Worked Example: Seller Profit and Percentage Gain

Profit problems ask for either the dollar gain or the percent return, computed on the seller's original cost.

Worked example: an investor bought a property for $180,000, spent $20,000 on improvements, and sold it for $250,000, paying a 6% commission at sale.

• Total invested = $180,000 + $20,000 = $200,000.
• Commission paid = $250,000 × 0.06 = $15,000.
• Net sale proceeds = $250,000 − $15,000 = $235,000.
• Profit = $235,000 − $200,000 = $35,000.
• Percentage return = $35,000 ÷ $200,000 = 17.5%.

The trap is computing the percentage against the sale price rather than the original investment, or forgetting to deduct the commission. Percent gain is always profit divided by what the seller put in, not by what the buyer paid.