8.2 Commission, Financing, and Interest Calculations
Key Takeaways
- Total commission equals sale price times commission rate; brokerage splits and agent splits are applied in sequence, never to the full price twice.
- Simple annual interest equals principal times rate times time; one month of interest is the annual figure divided by 12.
- Loan-to-value ratio equals loan amount divided by value (or price, whichever is lower); points equal one percent of the loan amount each.
- Always identify whether a rate applies to sale price, to loan amount, or to a commission subtotal before multiplying.
Commission math
Commission is the agent's paycheck and the exam's favorite topic. The base formula is Commission = Sale Price × Commission Rate. A $350,000 home sold at a 6% commission generates $350,000 × 0.06 = $21,000 in total commission.
The complication is the split. That $21,000 is usually divided first between the listing brokerage and the cooperating (selling) brokerage, and then each brokerage splits with its own agent. Work the splits in sequence — never multiply the full price by two different percentages and add them as if both came off the top.
A worked commission split
A home sells for $400,000 at a 6% total commission, split 50/50 between the listing and selling brokerages. The listing salesperson keeps 60% of the listing brokerage's share.
| Step | Calculation | Result |
|---|---|---|
| Total commission | $400,000 × 0.06 | $24,000 |
| Listing brokerage share | $24,000 × 0.50 | $12,000 |
| Listing salesperson share | $12,000 × 0.60 | $7,200 |
The salesperson earns $7,200. The trap answer of $14,400 comes from taking 60% of the whole $24,000 — ignoring the brokerage split. Apply each percentage only to the subtotal directly above it.
Graduated Splits, Seller-Net Pricing, and First-Payment Interest
Real exam commission items often chain a co-brokerage split with an agent split and a desk fee, so work strictly top-down.
Worked full-chain commission
A property sells for $525,000 at 5% total commission, split 60% to the listing brokerage / 40% to the selling brokerage. The listing agent is on a 70/30 split with the brokerage and pays a flat $300 transaction fee.
- Total commission = $525,000 x 0.05 = $26,250.
- Listing brokerage share = $26,250 x 0.60 = $15,750.
- Listing agent gross = $15,750 x 0.70 = $11,025.
- Agent net after the desk fee = $11,025 - $300 = $10,725.
Each percentage applies only to the subtotal directly above it; never multiply the full price by two percentages at once.
Net-to-seller pricing
A seller must net $235,000 after a 6% commission and $4,000 in closing costs. First add the fixed cost into the net the price must cover, then divide by (1 - rate):
Price = ($235,000 + $4,000) / (1 - 0.06) = $239,000 / 0.94 = $254,255 (round up to list at $254,300).
Verify: 6% of $254,255 is $15,255; $254,255 - $15,255 - $4,000 = $235,000.
First-payment interest split
On a fully amortized loan the first payment's interest equals one month of simple interest on the full balance. A $240,000 loan at 6%: annual interest $14,400; first month = $14,400 / 12 = $1,200. If the monthly payment is $1,438.92, then $1,200 is interest and $238.92 reduces principal. The next month's interest is computed on the slightly smaller balance, which is why early payments are interest-heavy and late payments are principal-heavy.
A property sells for $250,000 at a 7% commission. The listing and selling sides split it 50/50. If the selling salesperson receives 70% of the selling side's share, how much does that salesperson earn?
Net listings and finding the price
Sometimes the commission is known and the price is the unknown. If a seller wants $188,000 net after a 6% commission, you cannot simply add 6% to $188,000 — the commission is a percentage of the selling price, not the net. The seller keeps 100% − 6% = 94% of the price, so price = $188,000 / 0.94 = $200,000. Verify: 6% of $200,000 is $12,000, leaving exactly $188,000.
This "net deal" structure is the most-missed commission problem because the percentage applies to the larger unknown number, not to the figure given. Divide the net by (1 − rate) to recover the price.
Simple interest
Mortgage problems on the exam use simple annual interest: Interest = Principal × Rate × Time, written I = P × R × T. For a full year, time equals 1. For one month, divide the annual interest by 12.
A $200,000 loan at 6% annual interest accrues $200,000 × 0.06 = $12,000 per year, or $12,000 / 12 = $1,000 in the first month. On an amortized loan the first payment's interest portion equals that monthly figure; the rest of the payment reduces principal. Knowing the monthly interest lets you separate the interest and principal halves of any payment.
Solving for the missing variable
The interest formula rearranges the same way the value triangle did:
- Principal = Interest ÷ (Rate × Time)
- Rate = Interest ÷ (Principal × Time)
- Time = Interest ÷ (Principal × Rate)
If a borrower paid $9,600 in interest in one year on a loan at 8%, the principal was $9,600 / 0.08 = $120,000. If a $150,000 loan generated $10,500 of annual interest, the rate was $10,500 / $150,000 = 0.07 = 7%. Identify which variable is missing, then isolate it before plugging in numbers.
Points and loan-to-value
Lenders charge discount points to adjust yield; one point equals 1% of the loan amount (not the sale price). On a $180,000 loan, 2 points cost $180,000 × 0.02 = $3,600. The classic error multiplies points against the purchase price instead of the loan.
The loan-to-value (LTV) ratio equals loan amount divided by the lesser of price or appraised value. A buyer pays $250,000 for a home appraised at $240,000 and borrows $200,000. Lenders use the lower $240,000, so LTV = $200,000 / $240,000 = 83.3%. The down payment is the price minus the loan: $250,000 − $200,000 = $50,000.
Qualifying a buyer with ratios
Exams test the two debt ratios lenders use. The front-end (housing) ratio is monthly housing cost divided by gross monthly income; the back-end (total debt) ratio adds all recurring debts. A buyer earning $6,000 per month with a lender front-end limit of 28% can spend up to $6,000 × 0.28 = $1,680 on housing.
If the same buyer carries $400 in other monthly debt and the back-end cap is 36%, total debt cannot exceed $6,000 × 0.36 = $2,160; subtracting the $400 leaves $1,760 for housing. The lender uses the lower of the two limits, so this buyer qualifies for $1,680. Always compute both and take the smaller figure.
A buyer obtains a $160,000 loan and pays 3 discount points at closing. How much do the points cost?