8.2 Commission, Financing, and Interest Calculations
Key Takeaways
- Part = Whole x Rate is the master percentage formula; convert percent to a decimal and divide to find the whole, multiply to find the part.
- Solve commission splits in layers from total to side to agent, and reverse by dividing when given the dollars and asked for the price.
- Simple annual interest = principal x rate; divide by 12 for monthly interest and subtract it from the payment to find principal reduction.
- Points and origination fees are 1% of the loan each and are charged on the loan amount, never the sale price.
- Loan-to-value uses the lower of sale price or appraised value, so a low appraisal increases the effective LTV.
The Master Formula: Made x Paid
Nearly every percentage problem on the exam fits one relationship, often drawn as a T or pie:
Part = Whole x Rate.
For commissions, the Whole is the sale price, the Rate is the commission percentage, and the Part is the commission dollars. Rearranged, Rate = Part / Whole and Whole = Part / Rate. Convert percentages to decimals before multiplying: 6% = 0.06. The number-one error is leaving the rate as a whole number, inflating the answer one hundredfold.
Commission Splits
Real transactions split commission several times: between the listing and selling brokerages, then between each brokerage and its agent. Solve in layers, top down.
Example: A home sells for $400,000 at a 6% total commission.
- Total commission: 400,000 x 0.06 = $24,000
- Split 50/50 between listing and selling sides: $12,000 each
- The selling agent keeps 70% of her side: 12,000 x 0.70 = $8,400
- Her broker keeps the remaining 30%: $3,600
Work one split at a time and label each dollar figure so you do not apply a percentage to the wrong base.
Solving Backward for Sale Price
The exam loves to give you the commission and ask for the price. If an agent earned $7,500 as 50% of a side that was 50% of a 6% total commission, reverse the layers:
- Agent's side total: 7,500 / 0.50 = $15,000
- Total commission (the side was 50%): 15,000 / 0.50 = $30,000
- Sale price: 30,000 / 0.06 = $500,000
When you are given a part and asked for the whole, you divide. Recognizing 'divide to go up, multiply to go down' the percentage ladder is the single most valuable commission skill.
A property sells for $250,000 with a 5% commission. The listing broker and selling broker split it equally, and the selling salesperson receives 60% of the selling broker's share. How much does the salesperson earn?
Simple Interest on Loans
Mortgage math on the exam almost always uses simple annual interest, not amortization tables. The formula is:
Annual Interest = Principal x Rate.
For a monthly figure, divide annual interest by 12. A $200,000 loan at 7.2% annual interest produces 200,000 x 0.072 = $14,400 per year, or $1,200 per month in interest. In an interest-only or first-payment scenario, that monthly interest is the entire interest portion of the payment. The principal balance only changes once a principal payment is applied.
First-Month Principal and Interest Split
Given a monthly payment, you can separate interest from principal for the first month.
Loan: $180,000 at 6% with a $1,150 monthly payment.
- Annual interest: 180,000 x 0.06 = $10,800
- Monthly interest: 10,800 / 12 = $900
- Principal reduction this month: 1,150 - 900 = $250
- New balance: 180,000 - 250 = $179,750
This confirms why early payments are mostly interest. Next month's interest is computed on $179,750, so it falls slightly while principal rises. The exam usually asks only for the first month, keeping the base simple.
If a question asks for the interest paid over a full year on a fixed-balance or interest-only loan, simply use the annual figure directly; do not multiply the monthly interest by twelve and then round, which can introduce a few dollars of error. On an amortizing loan the annual interest is slightly less than twelve monthly figures because the balance declines, but the exam rarely requires that level of detail.
Loan-to-Value, Points, and Qualifying Ratios
Three financing ratios show up repeatedly. Keep them straight with this table.
| Metric | Formula | Example |
|---|---|---|
| Loan-to-Value (LTV) | Loan / Value (lower of price or appraisal) | $160,000 / $200,000 = 80% |
| Discount/origination points | Each point = 1% of the loan amount | 2 points on $250,000 = $5,000 |
| Front-end (housing) ratio | Housing payment / gross monthly income | $1,400 / $5,000 = 28% |
LTV always uses the lesser of sale price or appraised value, so an appraisal below the price raises the effective LTV. Points are calculated on the loan, never the purchase price. These distinctions are favorite distractors.
A borrower obtains a $240,000 loan and pays 1.5 discount points plus a 1% origination fee. What is the total charged for points and origination?
Back-End Ratio and Qualifying
Lenders also test a back-end (total debt) ratio that adds recurring debts to the housing payment.
Back-end ratio = (Housing payment + other monthly debts) / gross monthly income.
A borrower with a $1,400 housing payment, $600 in car and card payments, and $6,000 gross monthly income has a back-end ratio of 2,000 / 6,000 = 33.3%. Conventional guidelines often cap the front-end near 28% and the back-end near 36%, though program limits vary. The exam may give a maximum ratio and a known income and ask for the largest payment that qualifies: multiply income by the ratio to find the ceiling.
Common Financing Pitfalls
First, never compute interest or points on the sale price when the question references the loan; they use the principal. Second, watch the time unit: a rate is annual, so divide by 12 for one month and by 360 for a daily banker's figure. Third, in LTV problems substitute the appraised value when it is lower than the contract price. Fourth, qualifying-ratio answers must use gross, pre-tax income, and remember that the front-end ratio counts only the housing payment while the back-end ratio adds all recurring debt. Labeling each base before you multiply prevents nearly all of these errors.