8.2 Commission, Financing, and Interest Calculations

Commission, financing, and interest

This cluster is the heaviest scored math on the national exam because it touches every transaction. The unifying skill is the percentage equation: Part = Whole × Rate. Commission, interest, and points are all percentages of some base — the trick is identifying the correct base. Convert every percent to a decimal before multiplying: 6% becomes 0.06, and 0.5% becomes 0.005.

Commission basics

Commission is almost always a percentage of the sale price, not the list price or the loan. A home sells for $425,000 at a 6% total commission: 425,000 × 0.06 = $25,500.

Work backward when the problem gives commission and rate but not price. If a broker earned $18,000 at a 5% rate, the sale price is $18,000 ÷ 0.05 = $360,000. Dividing by the decimal rate reverses the multiplication.

Watch for seller-net back-solve problems where the seller wants a specific amount after a stated percentage commission; that math alone is not a net listing. If a seller must net $200,000 and the commission is 5%, the seller keeps 95% of the price, so price = 200,000 ÷ 0.95 ≈ $210,526. The base is the full price, not the net, so you divide by (1 − rate). Dividing the net by 0.05 or multiplying the net by 1.05 are both planted wrong moves.

Commission splits

Splits are sequential. First find total commission dollars, then divide between listing and selling brokerages, then between brokerage and agent.

The error to avoid is applying the agent's 60% to the full $24,000 instead of to the side's $12,000. Always carry the correct base down each step.

Loan-to-value ratio

Loan-to-value (LTV) measures the loan against the property's value: LTV = Loan amount ÷ (lesser of sale price or appraised value). Lenders use the lower figure to protect themselves.

A buyer purchases at $300,000, but the appraisal comes in at $290,000. With a $232,000 loan, LTV = 232,000 ÷ 290,000 = 0.80, or 80%. Using the $300,000 price instead would understate LTV and is the planted wrong answer. When appraisal is below price, the buyer must cover the gap in cash or renegotiate.

To find a down payment from LTV: an 80% LTV on a $250,000 value means a $200,000 loan, so the down payment is $250,000 − $200,000 = $50,000, which is 20% down.

Simple interest

Most exam interest is simple interest: Interest = Principal × Rate × Time, with time in years. A $180,000 loan at 6.5% annual interest accrues 180,000 × 0.065 = $11,700 in one year.

For the interest portion of a single monthly payment, take one month of annual interest: $11,700 ÷ 12 = $975. On a fixed loan the first payment is mostly interest; principal grows over time as the balance shrinks (amortization). The exam usually asks only for the first month's interest, which uses the full starting balance.

A two-month variation tests the same idea. After the first payment reduces principal by, say, $200, the new balance is $179,800, and the second month's interest is 179,800 × 0.065 ÷ 12 ≈ $973.92 — slightly less than the first month's $975. The exam point is that interest each month is computed on the remaining balance, which is why early payments are interest-heavy and later payments are principal-heavy.

Discount points

A discount point is a prepaid finance charge equal to 1% of the loan amount, paid at closing to lower the interest rate. Points are calculated on the loan, never on the purchase price — this is the most tested distinction.

On a $240,000 loan, 2.5 points cost 240,000 × 0.025 = $6,000. If the same buyer paid $260,000 for the home, using the price would wrongly produce 260,000 × 0.025 = $6,500, which is the trap answer. Read carefully for "loan" versus "price."

A rough rule of thumb sometimes appears: each discount point paid typically lowers the rate by about one-eighth of a percent (0.125%), though the exact tradeoff is set by the lender. The exam rarely needs the rate reduction itself, but it may ask which costs more — paying points up front or accepting a higher rate — so know that points are an up-front cost to buy down a long-term rate.

Qualifying with payment math

Exam financing problems sometimes combine interest and points. Suppose a buyer takes a $200,000 loan at 7% with 3 discount points.

• First-year interest: 200,000 × 0.07 = $14,000
• First month's interest portion: 14,000 ÷ 12 ≈ $1,166.67
• Cost of points at closing: 200,000 × 0.03 = $6,000

Each figure rests on the loan amount as its base. List the base first, choose the decimal rate, then multiply. A clean habit — base, rate, multiply — prevents the percentage-base errors that cause most missed financing questions.

Another financing ratio worth memorizing is the down payment as a percentage of price. A $60,000 down payment on a $300,000 home is 60,000 ÷ 300,000 = 0.20, or 20% down, which leaves an 80% LTV loan. Down-payment percent and LTV always sum to 100% when the price equals the appraised value, so a 25% down payment implies a 75% LTV loan.

Profit and loss percentage

Profit problems use the same equation with cost as the base. A seller bought for $250,000 and sells for $300,000: profit = $50,000, and percent profit = 50,000 ÷ 250,000 = 0.20, or 20%. The base is the original cost, not the sale price; dividing by $300,000 gives a wrong 16.7%.

Reverse profit problems give the selling price and the percent gain and ask for the original cost. If a home sold for $345,000 at a 15% profit, the seller received 115% of cost, so cost = 345,000 ÷ 1.15 = $300,000. The same logic handles a loss: a 10% loss means the sale equals 90% of cost, so divide the sale price by 0.90. The trap is multiplying the sale price by 0.85 or 0.90 instead of dividing.