8.2 Commission, Financing, and Interest Calculations
Key Takeaways
- Commission equals sale price times commission rate; the parts must always reconcile to the whole.
- To find a sale price from a known net to seller, divide the net by (100% minus the commission rate).
- Annual simple interest equals principal times rate; divide by 12 for a monthly figure.
- Loan-to-value ratio equals loan amount divided by the lesser of price or appraised value.
- One discount point equals 1% of the loan amount and is paid up front to the lender.
The commission triangle
Commission is the cleanest example of the part = rate × whole relationship that underlies almost all real estate percentage math:
- Commission (part) = Sale price (whole) × Rate
- Sale price = Commission ÷ Rate
- Rate = Commission ÷ Sale price
A $360,000 home sells at a 6% total commission: 360,000 × 0.06 = $21,600. Always confirm the rate is in decimal form (6% = 0.06) before multiplying. To convert any percent to a decimal, move the decimal point two places left; to convert back, move it two places right.
Reading the question for the unknown
The same three facts — commission, rate, and price — generate three question types. Identify which one is missing:
| Given | Find | Operation |
|---|---|---|
| Price and rate | Commission | Multiply |
| Commission and rate | Price | Divide commission by rate |
| Commission and price | Rate | Divide commission by price |
If a broker earned $13,500 on a 4.5% listing: price = 13,500 ÷ 0.045 = $300,000. If the broker earned $13,500 on a $300,000 sale: rate = 13,500 ÷ 300,000 = 0.045 = 4.5%. Same numbers, different unknown.
Splitting the commission
Commissions split between brokerages, then between broker and salesperson. Work outward in layers.
$21,600 total, split 50/50 between listing and selling brokerages = $10,800 each. If the selling salesperson keeps 60% of their brokerage's share: $10,800 × 0.60 = $6,480 to the agent, $4,320 to that broker.
Trap: a question may give the agent's split first and ask for total sale price — reverse each layer with division, never re-multiply by the same rate.
Work backward layer by layer. If the agent received $6,480 on a 60% split, the brokerage's share was 6,480 ÷ 0.60 = $10,800. If that was half the total commission, the full commission was 10,800 ÷ 0.50 = $21,600. If 6% produced $21,600, the sale price was 21,600 ÷ 0.06 = $360,000. Each step is a division by the rate that created the prior layer.
Net-to-seller (working backward)
When a seller must net a target amount after commission, the net is the remaining percentage, not the price.
Seller wants $188,000 net after a 6% commission. The net represents 100% − 6% = 94% of the sale price. Sale price = 188,000 ÷ 0.94 = $200,000. Check: 200,000 × 0.06 = $12,000 commission; 200,000 − 12,000 = $188,000.
Trap: never multiply the net by 1.06 — that adds commission on top of the wrong base and overstates the price.
Simple interest
Mortgage and seller-financing questions use simple annual interest: Interest = Principal × Rate.
A $250,000 loan at 7% annual interest: 250,000 × 0.07 = $17,500 per year, or 17,500 ÷ 12 = $1,458.33 per month. For a partial period, multiply the annual interest by the fraction of the year (for example × 3/12 for one quarter). Watch whether the question asks for annual, monthly, or a single payment's interest portion.
Interest inside a mortgage payment
On an amortized loan, each payment splits into interest and principal. The interest portion is computed on the current balance for that month, so it shrinks over time while the principal portion grows.
First-month interest on a $200,000 loan at 6%: monthly rate = 0.06 ÷ 12 = 0.005, then 200,000 × 0.005 = $1,000. If the total payment is $1,199, principal repaid that month is 1,199 − 1,000 = $199, and the new balance is $199,801. Trap: always apply the monthly rate to the balance, not the annual rate.
Per-thousand payment factors
Many exams hand you a monthly payment factor expressed per $1,000 of loan. Multiply the factor by the number of thousands borrowed.
With a factor of $6.65 per $1,000 at a given rate and term, a $185,000 loan pays 185 × $6.65 = $1,230.25 per month (principal and interest). To isolate the first month's principal, subtract the first-month interest: if interest is $1,041, principal is 1,230.25 − 1,041 = $189.25. Trap: the factor already blends principal and interest — do not add interest on top of a factor-based payment.
Loan ratios and points
- Loan-to-value (LTV) = Loan ÷ (lesser of price or appraised value). A $240,000 loan on a $300,000 home = 0.80 = 80% LTV.
- Discount point = 1% of the loan amount, paid up front to buy down the rate. Two points on a $200,000 loan = 200,000 × 0.02 = $4,000.
- Origination fee is also a percentage of the loan, not the price.
| Item | Base | Example (loan $200,000) |
|---|---|---|
| 1 point | Loan amount | $2,000 |
| 2 points | Loan amount | $4,000 |
| 1.5% origination | Loan amount | $3,000 |
Trap: points and origination fees are figured on the loan amount, never on the purchase price.
LTV also drives mortgage insurance: conventional loans above 80% LTV generally require private mortgage insurance until the balance falls to 80% of original value. To find the loan from a required down payment, subtract: a 20% down payment on a $300,000 home is 300,000 × 0.20 = $60,000, leaving a $240,000 loan and an 80% LTV. Confirm whether a question gives you the down-payment percent or the loan percent — they are complements that sum to 100%.
A seller wants to net $235,000 after paying a 6% brokerage commission and no other costs. What minimum sale price is required?
A borrower takes a $180,000 loan and pays 2 discount points plus a 1% origination fee. What is the total of these charges?