8.2 Commission, Financing, and Interest Calculations
Key Takeaways
- Commission = Sale Price x Commission Rate; splits apply the rate sequentially to each tier.
- Loan-to-value (LTV) = Loan Amount / Value (or price); lenders use the lower of price or appraisal.
- Annual simple interest = Principal x Rate; divide by 12 for the monthly interest portion.
- Points cost 1% of the loan amount each; discount points buy down the interest rate.
- Profit/loss percentage is always based on the original cost (the 'made' or 'paid' figure).
Commission Math
Commission is the percentage problem you will see most. The base formula:
Commission = Sale Price x Commission Rate
A $325,000 sale at a 6% total commission generates $19,500. Splits then divide that pool. A common structure: 50/50 between listing and selling brokerages, then each agent keeps 60% of the brokerage's half.
- Total: $325,000 x 0.06 = $19,500
- Listing brokerage half: $19,500 x 0.50 = $9,750
- Listing agent (60% of half): $9,750 x 0.60 = $5,850
Trap: read the order of percentages carefully. "60% to the agent" applies to the brokerage's share, not the whole commission. Apply each rate to the correct base, working from the largest pool down.
Working Backward From Commission
The exam often gives the commission and asks for the sale price, or gives the seller's net and asks for the price needed. Rearrange the triangle:
Sale Price = Commission / Rate
If an agent earned $7,200 at a 3% selling-side rate, the sale price the agent's portion is based on is $7,200 / 0.03 = $240,000.
Net-to-seller problems are harder. A seller wants to net $200,000 after paying a 5% commission. You cannot multiply $200,000 by 1.05. Instead, the net is 95% of the price:
- Price = Net / (1 - Rate) = $200,000 / 0.95 = $210,526
Multiplying the desired net by the rate and adding it back is the classic wrong answer offered as a distractor.
Worked Points, Net-to-Seller, and Interest
Discount/origination points: one point = 1% of the loan amount. On a $240,000 loan, 2.5 points cost 240,000 × 0.025 = $6,000. Points are charged on the loan, never on the sale price — a planted trap when the question also gives the purchase price.
Net-to-seller (working backward): A seller wants to net $200,000 after a 6% commission and $3,000 in other closing costs. The price must cover net + costs and still leave 6% for commission: Price = (200,000 + 3,000) ÷ (1 − 0.06) = 203,000 ÷ 0.94 = $215,957 (round to the nearest dollar/contract increment). Never apply the 6% to the desired net directly — that understates the price.
Interest split at payoff: A $180,000 loan at 6.5% is paid off mid-month. Annual interest = 180,000 × 0.065 = $11,700; monthly = $975; daily (360-day) = $32.50. Fifteen days of interest = 15 × 32.50 = $487.50 owed at payoff in addition to principal. Real estate interest is paid in arrears, so the payment due covers the month just ended.
Worked Splits, Graduated Rates, and Annual Payment Reconstruction
Multi-tier split: A $385,000 sale carries a 6% total commission = $23,100. The listing and selling firms split 50/50, so each firm gets $11,550. The selling agent is on a 60% salesperson split with a $50 transaction fee: 11,550 × 0.60 = $6,930, minus $50 = $6,880 to the agent. Track the base at each step — the agent's split applies to the firm's share, not the whole commission.
Graduated commission: An agreement pays 7% on the first $100,000 and 4% on the balance of a $260,000 sale. First tier = 100,000 × 0.07 = $7,000; balance = 160,000 × 0.04 = $6,400; total = $13,400.
Rebuild a sale price from interest: A buyer's first monthly interest payment is $1,012.50 on a 30-year loan at 6.75%. Loan = (monthly interest × 12) ÷ rate = (1,012.50 × 12) ÷ 0.0675 = 12,150 ÷ 0.0675 = $180,000. If that loan is 90% LTV, price = 180,000 ÷ 0.90 = $200,000.
A seller wants to net $188,000 after paying a 6% brokerage commission and no other costs. What minimum sale price is required?
Loan-to-Value Ratio
Lenders limit risk with the loan-to-value (LTV) ratio:
LTV = Loan Amount / Value
When price and appraisal differ, the lender uses the lower of the two. A buyer offers $300,000 on a home that appraises at $290,000 and seeks an 80% loan.
- Loan = 80% x $290,000 = $232,000 (based on the lower appraised value)
- Down payment = $300,000 - $232,000 = $68,000
The buyer must cover the gap between the loan and the price in cash. Trap: candidates apply the LTV to the contract price when the appraisal is lower. The lender always uses the lesser figure, so the borrower's down payment grows when an appraisal comes in low.
Simple Interest and Points
Most loan-payment math on the exam uses simple annual interest on the principal:
Annual Interest = Principal x Rate
Divide by 12 for one month's interest. On a $180,000 loan at 6.5%: annual interest = $11,700, monthly interest = $975. In an amortized loan, the early payments are mostly interest; principal reduction grows over time.
Discount points lower the rate; each point costs 1% of the loan amount.
| Item | Calculation | Result |
|---|---|---|
| Loan | given | $180,000 |
| 2 discount points | $180,000 x 0.02 | $3,600 |
| 1 origination point | $180,000 x 0.01 | $1,800 |
Trap: points are a percentage of the loan amount, not the sale price. With a down payment, those figures differ.
Profit and Loss Percentage
Resale-profit questions confuse candidates because the base is the original cost, the amount paid or made (the building cost), never the new selling price.
Percentage = (Made or Lost) / Original Cost
An investor paid $250,000 and sold for $300,000.
- Profit = $300,000 - $250,000 = $50,000
- Percent = $50,000 / $250,000 = 20% profit
Working backward: a property sold for $276,000 at a 15% profit. The original cost is the base, so the sale equals 115% of cost: $276,000 / 1.15 = $240,000. Trap: dividing the sale price by 1.15 versus subtracting 15% of the sale price gives different (wrong) answers; the profit rate applies to cost.
An investor bought a property, later sold it for $322,000, and realized a 15% profit on the purchase price. What did the investor originally pay?