8.2 Commission, Financing, and Interest Calculations
Key Takeaways
- Every financial item reduces to Part = Rate x Whole; identify the part, rate, and whole, then rearrange to solve for the unknown.
- Commission flows from sale price down through brokerage splits to the agent's share; reverse the chain to back out the sale price from an agent's check.
- Loan-to-value uses the lesser of sale price or appraised value, so a low appraisal forces a larger down payment.
- One discount point equals 1% of the loan amount, not the sale price, so find the loan first when given a purchase price.
- The exam uses simple interest, I = PRT; match the time unit to the rate (an annual rate needs time in years).
Percentage problems run the brokerage
Commission, interest, loan-to-value, and points are all percentage problems built on a single relationship: Part = Rate x Whole. Rearranged, Whole = Part / Rate and Rate = Part / Whole. If you can identify which value is the part, which is the rate, and which is the whole, you can solve nearly every financial item on the exam. Convert percentages to decimals first (divide by 100) to avoid the most common arithmetic slip.
Commission basics
Commission is the part, the sale price is the whole, and the commission rate is the rate. The flow then splits the commission between brokerages and agents.
- Total commission = Sale Price x Commission Rate.
- Listing/selling split divides the total between the two brokerages.
- Agent share applies the agent's split to the brokerage's portion.
Example: a home sells for $450,000 at a 6% total commission. Total = 450,000 x 0.06 = $27,000. If the listing and selling sides split 50/50, each brokerage receives $13,500.
Carrying a commission split all the way down
Continuing the example, suppose the selling agent works on a 60/40 split favoring the agent. The selling brokerage's $13,500 is divided: agent gets 13,500 x 0.60 = $8,100, and the brokerage keeps $5,400.
The exam often gives only the agent's final check and asks you to back out the sale price. Work backward through each split: divide the check by the agent split, then by the brokerage split, then by the commission rate. Reversing the chain is the skill being tested.
Loan-to-value ratio (LTV)
LTV expresses the loan as a percentage of value, where value is the lesser of sale price or appraised value.
- LTV = Loan Amount / Property Value.
- Loan Amount = Value x LTV.
- Down payment = Value - Loan Amount.
Example: a buyer purchases a $300,000 home with 20% down. The loan is 300,000 x 0.80 = $240,000, an 80% LTV, and the down payment is $60,000. When sale price and appraised value differ, lenders use the lower figure, so a low appraisal forces a larger down payment.
Discount points and origination fees
One point equals 1% of the loan amount, not the sale price. This distinction is a frequent trap.
- Cost of points = Loan Amount x (Number of Points / 100).
Example: paying 2 points on a $240,000 loan costs 240,000 x 0.02 = $4,800. Discount points buy down the interest rate; origination fees pay the lender for processing. Both are calculated against the loan, so if a question gives the purchase price, find the loan first.
Simple interest, the exam's interest model
The exam uses simple interest, not compound interest. The formula is Interest = Principal x Rate x Time, abbreviated I = PRT.
- Annual interest = Loan Balance x Annual Rate.
- Monthly interest = Annual interest / 12.
Example: a $200,000 loan at 7% annual interest accrues 200,000 x 0.07 = $14,000 per year, or 14,000 / 12 = $1,166.67 in the first month. On an amortized loan, the first payment is mostly interest; principal grows over time, but the exam usually only asks for the first month's interest portion.
Solving for the missing variable
I = PRT can solve for any one unknown when the other three are given:
| Unknown | Rearranged formula |
|---|---|
| Interest | I = P x R x T |
| Principal | P = I / (R x T) |
| Rate | R = I / (P x T) |
| Time | T = I / (P x R) |
If a borrower paid $9,000 interest on a $150,000 loan over one year, the rate is 9,000 / (150,000 x 1) = 0.06 = 6%. Match the time unit to the rate: an annual rate needs time in years.
Worked Example: Commission and Simple Interest
Commission is a percentage of sale price: commission = sale price x rate. Worked example: a home sells for $720,000 at a 5% total commission, so the total fee is $720,000 x 0.05 = $36,000. If the listing and selling brokerages split 50/50, each office receives $18,000; if the agent's split with the broker is 60/40 in the agent's favor, that agent earns $18,000 x 0.60 = $10,800.
Work commission backward to find price: if a seller wants to net $475,000 after a 5% commission and $5,000 in closing costs, then sale price x (1 - 0.05) = $475,000 + $5,000, so price = $480,000 / 0.95 = $505,263. Simple interest = principal x rate x time. Annual interest on a $300,000 loan at 6.5% is $300,000 x 0.065 = $19,500, or $1,625 per month; this monthly interest figure is the basis for separating interest from principal on an amortized payment.
A house sells for $380,000 with a 6% total commission split evenly between two brokerages. The selling agent is on a 70/30 split favoring the agent. How much does the selling agent earn?
A borrower pays 3 discount points on a $260,000 loan. What is the total cost of the points?
keyTakeaways
- Every financial item is Part = Rate x Whole; identify part, rate, and whole, then rearrange.
- Commission flows from sale price down through brokerage splits to the agent's share; reverse the chain to find sale price.
- LTV uses the lesser of sale price or appraised value; a low appraisal raises the down payment.
- One discount point equals 1% of the loan amount, not the sale price.
- The exam uses simple interest, I = PRT; match the time unit to the rate.
Summary
Commission, financing, and interest questions are percentage problems in disguise. Convert percentages to decimals, anchor on Part = Rate x Whole, and you can solve commission splits, LTV, points, and simple interest with one mental model. The traps are calculating points on the wrong base, forgetting that lenders use the lower of price or appraisal, and mixing time units in I = PRT. Working examples backward is the highest-yield practice for this section.