8.2 Commission, Financing, and Interest Calculations
Key Takeaways
- Commission equals sale price times commission rate; split it by the agreed brokerage and agent percentages.
- Loan-to-value ratio (LTV) is loan amount divided by the lesser of price or appraised value.
- One discount point equals 1% of the loan amount, not 1% of the sale price.
- Simple annual interest equals principal times rate; divide by 12 for one month's interest.
- PITI combines principal, interest, taxes, and insurance into the monthly housing payment.
The Percentage Backbone
Nearly every financing problem is a variation of the T-bar: Part = Whole x Rate. Cover the unknown to solve for it.
- Part (commission, interest, down payment) = Whole x Rate
- Whole (sale price, loan, value) = Part / Rate
- Rate = Part / Whole
The judgment skill the exam tests is identifying which dollar figure is the whole. Commission uses sale price; points use loan amount; LTV uses the lesser of price or appraised value.
Commission Calculations
Commission is the brokerage fee for a transaction, almost always a percentage of the sale price.
Total commission = Sale price x Commission rate
A $420,000 sale at 6% generates $25,200 total. That figure is then split. A common chain: listing and selling brokerages split 50/50, then each agent keeps 70% of the brokerage half.
| Step | Calculation | Result |
|---|---|---|
| Total | $420,000 x 6% | $25,200 |
| Selling side | $25,200 x 50% | $12,600 |
| Selling agent | $12,600 x 70% | $8,820 |
A home sells for $315,000 at a 7% total commission. The listing and selling brokerages split it equally, and the listing agent earns 60% of the listing brokerage's share. How much does the listing agent receive?
Loan-to-Value Ratio
Loan-to-value (LTV) measures the loan against property worth and drives down-payment and mortgage-insurance rules.
LTV = Loan amount / Lower of (sale price or appraised value)
Lenders use the lesser of price and appraisal to protect against overpaying. If a buyer pays $300,000 but the appraisal comes in at $290,000, an 80% LTV loan is based on $290,000, yielding a $232,000 loan and forcing a larger cash down payment. The down payment is simply price minus loan, plus any appraisal gap the buyer must cover.
Discount Points and Origination Fees
A discount point is a prepaid interest charge that buys down the interest rate. The critical rule:
One point = 1% of the LOAN amount
Points are never a percentage of the sale price. On a $250,000 loan, 2 points cost $250,000 x 2% = $5,000. An origination fee is calculated the same way against the loan. A frequent trap multiplies points by the purchase price; always confirm the base is the loan.
Simple Interest
Residential mortgages accrue interest on the outstanding balance, but the exam tests simple annual interest:
Annual interest = Principal x Annual rate
Divide by 12 for one month's interest. A $200,000 loan at 6% accrues $12,000 per year, or $1,000 per month. In an amortized loan, each early payment is mostly interest; the principal portion grows over time. To find a single month's interest, always apply the rate to the current balance, not the original loan.
The PITI Payment
PITI stands for principal, interest, taxes, and insurance and represents the total monthly housing obligation lenders use for qualifying.
| Component | Source |
|---|---|
| Principal | Reduces loan balance |
| Interest | Rate x current balance / 12 |
| Taxes | Annual property tax / 12 |
| Insurance | Annual hazard premium / 12 |
Lenders compare PITI to income through qualifying ratios. The exam may ask you to add monthly taxes and insurance to a given principal-and-interest figure to reach the full PITI, so read whether a question wants P&I only or full PITI.
Commission Split Walkthrough and Net Listings
Commission questions chain several multiplications. Solve left to right and label each step.
Scenario. A $480,000 home sells at a 6% total commission. The listing and selling firms split 50/50. The selling agent keeps 65% of the selling firm's half. How much does the selling agent earn?
- Total commission = $480,000 x 6% = $28,800.
- Selling firm's half = $28,800 x 50% = $14,400.
- Selling agent's share = $14,400 x 65% = $9,360.
Trap: the question asks for the agent, not the firm. Stopping at step 2 ($14,400) is the most common wrong answer baited in the options.
Net listing reminder. In a net listing the broker keeps everything above a price the seller names. Wisconsin licensees are prohibited from obtaining or negotiating net listings under REEB 24.10 because they invite a conflict of interest, so a math question that hands you a "net listing" may be testing legality, not arithmetic.
Points, Interest, and Reverse Percentage Problems
Three calculations round out the financing math:
| Calculation | Formula | Example |
|---|---|---|
| Discount points cost | Loan x (points x 1%) | $250,000 x 2% = $5,000 |
| One month's interest | (Balance x annual rate) / 12 | ($180,000 x 6%) / 12 = $900 |
| Effective yield from points | Roughly +1/8% rate per point | 2 points ≈ +1/4% yield |
Worked interest split. On a $200,000 loan at 6%, the first payment's interest is ($200,000 x 0.06) / 12 = $1,000. If the total P&I payment is $1,199, then $199 reduces principal in month one. Next month interest is computed on $199,801 — slightly less — so the principal portion grows each month. This is the heart of amortization, and the exam loves to ask for the principal portion of the first payment.
Reverse percentage (most-missed). "A buyer paid $315,000, which was 90% of list price. What was the list price?" Divide, do not multiply: $315,000 / 0.90 = $350,000. The percentage given is the part; the unknown list is the whole. Multiplying $315,000 x 0.90 (the trap) gives $283,500, a baited wrong answer. Whenever a value already reflects a percentage, recover the original by dividing by that percentage.