8.2 Commission, Financing, and Interest Calculations
Key Takeaways
- Commission = sale price x rate; then apply broker/agent splits in sequence to find each party's share.
- One discount point = 1% of the loan amount, paid upfront as prepaid interest to lower the rate.
- Loan-to-value (LTV) = loan amount / property value; LTV above 80% typically triggers PMI on conventional loans.
- Simple interest = principal x rate x time; isolate the unknown by dividing the interest by the other two factors.
- APR includes the note rate plus fees and points, so APR is always equal to or higher than the stated interest rate.
Commission and financing problems are pure percentage arithmetic, but they are framed as multi-step word problems. The key skill is sequencing: find the total dollar amount first, then apply each split or fee in order. Convert every percentage to a decimal before multiplying.
Commission Calculations
Commission is a percentage of the sale price.
Commission = Sale Price x Commission Rate.
Example: A home sells for $425,000 at a 6% commission. Total commission = 425,000 x 0.06 = $25,500. This is the gross commission the listing brokerage receives before any split with the cooperating brokerage or the agents.
Multi-Level Split Example
Total commission is $25,500. The listing and selling brokerages split it 50/50, so each side receives $12,750. The listing agent has a 70/30 split with the broker.
- Listing agent: 12,750 x 0.70 = $8,925
- Listing broker: 12,750 x 0.30 = $3,825
Work the splits one layer at a time. The exam often asks only for the agent's final take-home, which requires all the prior steps.
A property sells for $300,000 with a 5 percent commission split 60/40 between the broker and the agent (agent receives 40 percent). How much does the agent earn?
Discount Points and Origination Fees
A discount point equals 1% of the loan amount and is prepaid interest that buys down the interest rate. An origination fee is also commonly quoted as a percentage of the loan (often 1%) but compensates the lender for processing.
Points Cost = Loan Amount x Points (as a decimal).
Example: 2 points on a $250,000 loan = 250,000 x 0.02 = $5,000. Note that points apply to the loan amount, not the purchase price.
Loan-to-Value (LTV) and PMI
LTV = Loan Amount / Property Value.
Example: A buyer borrows $228,000 on a $285,000 home. LTV = 228,000 / 285,000 = 80%.
| LTV | Typical consequence |
|---|---|
| 80% or below | No PMI required on conventional loans |
| Above 80% | PMI generally required until equity reaches 20% |
| 95%-97% | High-LTV programs; higher rate and insurance cost |
Trap: down payment percentage and LTV are complements. A 10% down payment means a 90% LTV, which usually triggers PMI.
Simple Interest
Most exam interest problems use simple interest.
Interest = Principal x Rate x Time.
Example: A $180,000 loan at 7% for one year. Interest = 180,000 x 0.07 x 1 = $12,600.
To find an annual rate from a monthly payment, isolate the variable. If a $200,000 loan generates $1,000 of interest in one month, the annual interest is 1,000 x 12 = $12,000, so the rate = 12,000 / 200,000 = 6%.
A borrower pays $750 in interest for one month on a $150,000 interest-only loan. What is the annual interest rate?
APR vs. Note Rate
The note rate (interest rate) is the cost of borrowing on the loan balance alone. The APR (annual percentage rate) folds in the note rate plus finance charges such as points, origination fees, and mortgage insurance. Because APR adds costs, it is always equal to or higher than the note rate. APR is required by the Truth in Lending Act so borrowers can compare loans with different fee structures on one number.
Common Financing Traps
- Points and origination fees apply to the loan amount, not the sale price.
- A prepayment penalty charges for early payoff; a balloon loan has one large final payment.
- LTV uses the lesser of sale price or appraised value as the denominator in practice; on most exam problems they are equal.
- Amortized loans front-load interest, so early payments are mostly interest and late payments are mostly principal.
Seller's Net and Interest Worked Examples
Seller's net (solving for sale price): A seller wants to net $200,000 after a 5% commission and $4,000 in closing costs. The price must cover the net plus costs as 95% of the price. Price = ($200,000 + $4,000) / (1 - 0.05) = $204,000 / 0.95 = $214,737 (rounded).
Simple interest: Interest = Principal x Rate x Time. On a $250,000 loan at 6% for one year, interest = $250,000 x 0.06 = $15,000 per year, or $1,250 per month.
Discount points: Each point is 1% of the loan amount. On a $300,000 loan, 2 points = $300,000 x 0.02 = $6,000, paid at closing to lower the rate.
Exam trap: Points are a percentage of the loan, not the sale price; commission is a percentage of the sale price. Read which base the question uses.
Splits, Amortization Factors, and Per-Diem Interest
Three-way split: A $360,000 sale pays a 6% total commission = $21,600. The listing and selling brokerages split it 50/50 ($10,800 each). The listing agent on a 70/30 split with her broker earns $10,800 x 0.70 = $7,560.
Per-diem interest: On a $200,000 loan at 5.4%, annual interest is $200,000 x 0.054 = $10,800; daily interest (365-day) is $10,800 / 365 = about $29.59/day, used for prepaid interest at closing.
Exam trap: Commission flows brokerage-to-brokerage first, then brokerage-to-agent, never directly to the agent from the client.
Solving for Rate and Base
Many items hide the unknown. To find a commission rate, divide the commission by the sale price: a $15,000 commission on a $300,000 sale is $15,000 / $300,000 = 5%. To find the sale price from a known commission and rate, divide the commission by the rate: a $12,000 commission at 4% means $12,000 / 0.04 = $300,000. The same percentage triangle (Part = Total x Rate) solves interest, points, and LTV problems, so identify which two values the question gives and solve for the third.
Exam trap: Decide whether the question gives you the part, the rate, or the whole before plugging numbers in; misreading the base is the most common math error.