8.2 Commission, Financing, and Interest Calculations
Key Takeaways
- Total commission = Sale Price x Rate; then multiply down each split (broker, then agent) rather than across.
- LTV = Loan / Value; down payment = Price x (1 - LTV); lenders use the lower of price or appraisal.
- Simple interest = Principal x Rate x Time; divide annual interest by 12 for one month.
- In an amortized payment, principal = payment minus the period's interest on the current balance.
- One discount point = 1% of the loan amount, never of the purchase price.
Commission Math
Commission is a percentage of the sale price, then split among brokers and agents. The chain of calculations is always: total commission, then broker-to-broker split, then broker-to-agent split. Convert percentages to decimals (6% = 0.06) before multiplying.
Total commission = Sale Price x Commission Rate. If two brokerages split 50/50 and your broker then pays you 60%, you multiply down the chain, never across percentages added together.
Worked Commission Example
A property sells for $425,000 at a 6% total commission. The listing and selling brokerages split it equally, and the selling broker pays the salesperson 70%.
- Total commission: $425,000 x 0.06 = $25,500
- Selling brokerage share: $25,500 x 0.50 = $12,750
- Salesperson's check: $12,750 x 0.70 = $8,925
Reverse problems are just as common: if an agent earned $8,925 on these same splits, divide back up the chain. $8,925 / 0.70 = $12,750 (brokerage share); $12,750 / 0.50 = $25,500 (total commission); $25,500 / 0.06 = $425,000 (sale price). The rule to internalize is that you multiply going down from sale price to your check, and divide going up when working backward from your check to the sale price. Never add the split percentages together, because a 50% then 70% chain yields 35% of the total, not 120%.
Loan-to-Value and Down Payment
Lenders express risk as loan-to-value ratio (LTV): Loan Amount / Value (or price, whichever is lower). The down payment is the complement.
| Item | Formula |
|---|---|
| Loan amount | Price x LTV |
| Down payment | Price x (1 - LTV) |
| LTV | Loan / Price |
Example: an 80% LTV loan on a $360,000 home means a $288,000 loan (360,000 x 0.80) and a $72,000 down payment (360,000 x 0.20).
When the appraisal comes in below the contract price, the lender uses the lower figure as the value base, a frequently tested wrinkle. In that case the buyer must cover the gap in cash on top of the normal down payment, because the loan is capped at the LTV times the lower appraised value, not the higher contract price. For instance, if that $360,000 home appraises at only $340,000, an 80% loan funds just $272,000, and the buyer now needs $88,000 down to close at the $360,000 contract price.
Interest Calculations
Most license-exam interest problems use simple annual interest on the outstanding balance:
Interest = Principal x Rate x Time
Rate is annual unless told otherwise, and time is in years. For a single month, divide the annual interest by 12. The starting principal for any payment is the loan balance at the beginning of that period.
Example: a $200,000 loan at 6.5% interest. Annual interest = 200,000 x 0.065 = $13,000. One month of interest = 13,000 / 12 = $1,083.33.
Amortization and Principal Reduction
In an amortized loan, the first payment is mostly interest. To find the principal portion of a payment:
- Compute one month of interest on the current balance.
- Subtract that interest from the total monthly payment.
- The remainder reduces principal; the new balance is the old balance minus that principal portion.
Example: $200,000 balance, 6% rate, payment of $1,199.10. Month-one interest = (200,000 x 0.06) / 12 = $1,000. Principal applied = $1,199.10 - $1,000 = $199.10. New balance = $199,800.90. Because the balance barely moved, month two's interest is nearly identical, which is why early payments build little equity. The reverse is true near the end of the term, when most of each payment retires principal. License exams typically test only the first month or two, so you rarely need a full amortization schedule, only the single-period subtraction shown here.
Discount Points and Buydowns
One discount point equals 1% of the loan amount (not the sale price), paid up front to lower the rate. Compute points on the loan figure.
Example: a $288,000 loan with 2 discount points costs 288,000 x 0.02 = $5,760 in points. The frequent trap is charging points against the $360,000 purchase price; points always apply to the loan.
Qualifying Ratios and PITI
Lenders test affordability with two ratios. The front-end (housing) ratio divides monthly PITI (Principal, Interest, Taxes, Insurance) by gross monthly income; a common ceiling is 28%. The back-end (total debt) ratio divides PITI plus all other recurring debt by gross monthly income, often capped near 36%.
Example: a buyer earns $7,500 gross per month. The maximum PITI under a 28% front-end ratio is $7,500 x 0.28 = $2,100. If the buyer also has $400 in car and card payments, the back-end test allows $7,500 x 0.36 = $2,700 total, leaving $2,300 for PITI, so the front-end ceiling of $2,100 governs. Always convert annual income to monthly first, and use the lower of the two resulting PITI limits. Including only principal and interest while ignoring taxes and insurance is a frequent error that overstates affordability.
A house sells for $480,000 at a 5% total commission. The listing brokerage keeps 55% of the total and the selling brokerage gets the rest. How much does the selling brokerage receive?
A borrower has a $150,000 loan balance at 7% annual interest with a monthly payment of $997.95. How much of the first payment goes to principal?
Trap Checklist
Convert every percentage to a decimal first; multiply down a commission chain rather than adding splits; apply LTV and the down payment to the lower of price or appraised value; remember discount points are a percent of the loan, not the price; and always compute interest on the current outstanding balance, not the original loan.