8.2 Commission, Financing, and Interest Calculations

The Percentage Engine Behind Most Money Problems

Commission, interest, points, and loan-to-value problems are all variations of one relationship: part = rate x whole (often memorized as 'made x of'). Identify which two values you have and solve for the third. Convert every percentage to a decimal before multiplying (6% becomes 0.06), and keep dollars and rates separate from any time factor until the final step.

Commission Splits Step by Step

Total commission = sale price x commission rate. A $360,000 sale at a 6% rate produces 360,000 x 0.06 = $21,600. That total is then split, usually first between the listing and selling brokerages, and again between each brokerage and its agent.

If the $21,600 is divided 50/50 between two brokerages, each brokerage receives $10,800. If the selling agent keeps 60% of the brokerage's share, the agent earns 10,800 x 0.60 = $6,480, and the brokerage retains $4,320. Always track whose share each percentage applies to.

Working Backward From a Commission

If an agent's 3% share of the full commission equals $9,000, the full commission is 9,000 / 0.03 = $300,000... no. Read carefully: when the commission is known and you need the sale price, divide commission by the commission rate. A $19,500 commission at a 6.5% rate means sale price = 19,500 / 0.065 = $300,000. Dividing by the rate undoes the original multiplication.

Loan-to-Value and Down Payment

Loan-to-value ratio = loan amount / property value (lower of price or appraisal). A $285,000 loan on a $300,000 home is 285,000 / 300,000 = 0.95, a 95% LTV, leaving a 5% down payment of $15,000.

Lenders cap LTV by program. A common exam fact: conventional loans above 80% LTV typically require private mortgage insurance (PMI) until the borrower reaches 20% equity. When appraisal is below contract price, the lender uses the lower figure, so the buyer must cover the gap in cash.

Discount Points and Origination

One point equals 1% of the loan amount (not the sale price). Two discount points on a $250,000 loan cost 250,000 x 0.02 = $5,000. Points paid up front buy a lower interest rate; origination points are a lender fee. The exam tests the loan-amount base relentlessly, so never compute points from the purchase price when a separate loan figure is given.

Simple Interest and Monthly Payments

Most exam interest math uses simple interest: annual interest = principal x annual rate. A $200,000 loan at 7% accrues 200,000 x 0.07 = $14,000 per year, or 14,000 / 12 = $1,166.67 per month in interest.

For a fully amortizing loan, early payments are mostly interest; the principal portion of a payment = total payment minus that month's interest.

Quick reference for the percentage base in each problem type:

• Commission: percent of the sale price.
• Discount/origination points: percent of the loan amount.
• Interest: rate applied to the outstanding principal.
• LTV: loan amount over the lower of price or appraised value.
• Down payment: purchase price minus loan amount.

Worked Example: Annual Interest and Points

Simple interest = Principal x Rate x Time. A $250,000 loan at 6% annual interest accrues 250,000 x 0.06 = $15,000 per year, or $1,250 per month ($15,000 / 12). To find the first month's interest on an amortizing loan, use the monthly figure; the principal portion of the payment is whatever remains after subtracting interest. One point equals 1% of the loan amount. On that $250,000 loan, 2 discount points cost 250,000 x 0.02 = $5,000. Points are charged on the loan amount, never the sale price — a frequent trap when the question gives both numbers.

Worked Example: Down Payment and Seller Net

If a buyer finances 90% LTV on a $320,000 purchase, the loan is 320,000 x 0.90 = $288,000 and the down payment is 320,000 − 288,000 = $32,000. For a seller-net problem, remember the sale price must cover the net plus all selling costs, so you divide rather than subtract. A seller who must net $200,000 after paying a 6% commission needs a price of 200,000 / (1 − 0.06) = 200,000 / 0.94 = $212,766 (rounded). Subtracting 6% of $200,000 is the classic wrong answer; the commission is a percent of the unknown sale price, not of the net, so you must divide by (1 minus the rate).

Seller Net and Required Sale Price

A common multi-step problem asks what a property must sell for so the seller nets a target after paying commission. If the seller wants $200,000 net after a 6% commission, the sale price is not 200,000 x 1.06. The commission is a percent of the unknown sale price, so the net is 94% of the sale price.

Sale price = net / (1 - rate) = 200,000 / 0.94 = $212,766. Verify: commission = 212,766 x 0.06 = $12,766, and 212,766 - 12,766 = $200,000. The trap answer applies the rate to the net figure instead of dividing by (1 minus the rate).

Common Traps

Watch the base of every percentage: commission uses sale price, points and interest use the loan amount, and LTV uses the lower of price or appraisal. When solving backward for sale price or principal, divide by the rate. Confirm whether the question wants an annual or monthly figure before reporting the answer.

With multi-level commission splits, label each share before multiplying so a brokerage percentage is never applied to an agent's already-reduced amount. With seller-net problems, always divide by (1 - commission rate) rather than multiplying the net by the rate. These two patterns account for a large share of missed financing-math points.