8.2 Commission, Financing, and Interest Calculations

Commission Math

Commission is Sale Price x Commission Rate. The rate is always converted from a percent to a decimal (6% = 0.06).

A home sells for $385,000 at a 6% commission: 385,000 x 0.06 = $23,100 total commission.

Splits then divide that total. Suppose the listing and selling brokerages split 50/50, and each agent keeps 60% of their brokerage's share.

• Each brokerage: $23,100 x 0.50 = $11,550.
• Each agent: $11,550 x 0.60 = $6,930.

Work strictly in sequence: total, brokerage share, then agent share. Skipping a step or applying the agent split to the full commission is the most common error.

Working Backward From Commission

Some questions give the commission and ask for the sale price. Reverse the formula: Sale Price = Commission / Rate.

An agent earned $9,000, which was 3% of the sale price. Price = 9,000 / 0.03 = $300,000.

A "net to seller" problem is similar. A seller wants $200,000 net after a 5% commission. The price is not $200,000 x 1.05. Instead the seller keeps 95% of the price, so Price = 200,000 / 0.95 = $210,526.32. Dividing by (100% minus rate) is the correct move; multiplying by (100% plus rate) is the classic trap answer.

Loan-to-Value, Down Payment, and Points

Loan-to-value (LTV) = Loan Amount / (lesser of sale price or appraised value). A $320,000 home with an 80% LTV loan has a loan of 320,000 x 0.80 = $256,000 and a down payment of $64,000.

If the appraisal comes in low, the lender uses the lower figure. Price $320,000 but appraised $300,000 at 80% LTV: loan = 300,000 x 0.80 = $240,000, so the buyer must cover the larger gap.

Points are a percentage of the loan amount, one point = 1%. Three points on a $256,000 loan = 256,000 x 0.03 = $7,680. Points are computed on the loan, never the sale price.

Simple Interest

Mortgage interest on the exam is simple interest: Annual Interest = Principal x Rate. For monthly interest, divide by 12.

A $256,000 loan at 7% annual interest:

• Annual interest = 256,000 x 0.07 = $17,920.
• First month's interest = 17,920 / 12 = $1,493.33.

If a payment is given, remember it includes principal plus interest; subtract the interest portion to find principal reduction.

Profit, Loss, and the "Percentage-of-What" Trap

Percentage problems live or die on identifying the base — the number you take the percent of. Profit and loss are measured against what the seller originally paid, not the new sale price.

Profit example. An investor paid $180,000 and sold for $216,000.

• Profit = $216,000 − $180,000 = $36,000.
• Percent profit = $36,000 ÷ $180,000 = 20% (base is the cost, not the sale price).

Working backward from a percentage gain. A home sold for $253,000, which was a 15% profit over cost. Cost = $253,000 ÷ 1.15 = $220,000. Do not subtract 15% of $253,000 — that uses the wrong base and is the dominant wrong answer.

Mill Rates, Tax Math, and Amortization Factors

Property tax is often quoted in mills, where one mill = $1 per $1,000 of assessed value (0.001). Tax is computed on assessed value, which may be a percentage of market value.

Mill-rate example. A home has a market value of $250,000, an assessment ratio of 80%, and a tax rate of 25 mills.

• Assessed value = $250,000 × 0.80 = $200,000.
• Annual tax = $200,000 × 0.025 = $5,000.

Amortization factor. Monthly payment problems use a factor per $1,000 borrowed. If the factor for a 30-year, 6% loan is $6.00 per $1,000, the principal-and-interest payment on a $250,000 loan is (250,000 ÷ 1,000) × $6.00 = 250 × $6.00 = $1,500 per month. Multiply the per-thousand factor by the number of thousands borrowed.

Discount Points, Effective Yield, and Seller-Paid Costs

Discount points raise a lender's yield; the rough rule is that each point paid raises yield (or lowers the borrower's rate) by about 1/8% (0.125%), though the exam usually wants the dollar cost.

Points cost example. A buyer takes a $320,000 loan and pays 2.5 discount points.

• One point = $320,000 × 0.01 = $3,200.
• 2.5 points = 2.5 × $3,200 = $8,000 due at closing.

Seller-paid points example. If the seller agrees to pay 2 of those points to help the buyer, the seller is debited 2 × $3,200 = $6,400 at closing, reducing the seller's net proceeds. Points are always a percentage of the loan amount, never the sale price — if a problem supplies both figures, the sale price is the distractor. Confirm who pays the points, because that determines whose side of the settlement statement is charged.

Finally, watch the difference between a rate of commission and a flat fee: a flat fee is a fixed dollar amount regardless of sale price, so no percentage math applies. When a question mixes a flat referral fee with a percentage commission, compute each separately and add them.