8.2 Commission, Financing, and Interest Calculations
Key Takeaways
- Commission equals sale price times rate; the broker's split, then the agent's split, are taken sequentially from that total.
- To find sale price from a net-to-seller amount, divide the net by (100% minus the commission rate), never multiply.
- Simple annual interest equals principal times rate times time; one month of interest is the annual figure divided by 12.
- Loan-to-value ratio equals loan amount divided by value (or price, whichever is lower); points equal a percentage of the loan amount.
- Discount points and the LTV ratio both reference the loan balance, not the purchase price.
Commission
Commission is a percentage of the sale price: Commission = Sale Price x Rate. On a $375,000 sale at 6%, the total commission is $375,000 x 0.06 = $22,500.
Splits
Commission flows in steps. Suppose two brokerages split the $22,500 equally; each brokerage receives $11,250. If the listing salesperson has a 60/40 split with her broker (60% to agent), she earns $11,250 x 0.60 = $6,750. Work the splits in sequence, never as one combined percentage, and read carefully whether a percentage is of the whole commission or of one side. A 60/40 split of one $11,250 side is not the same as a 60/40 split of the full $22,500, and the wrong reading is always among the answer choices.
Graduated splits add a layer: an agent might keep 50% up to a threshold and 70% above it. Compute each tier separately and add. Read whether a 'split' favors the agent or the broker, since the larger number is not always the agent's.
| Step | Calculation | Result |
|---|---|---|
| Total commission | $375,000 x 6% | $22,500 |
| Listing brokerage share | $22,500 x 50% | $11,250 |
| Listing agent share | $11,250 x 60% | $6,750 |
Net to Seller (the reversal)
The hardest commission item asks: if a seller must net a specific amount after a percentage commission, what sale price is required? The price is the base (100%); the commission is a slice of it. So the net is (100% - rate) of the price.
Sale Price = Net Required / (1 - Commission Rate)
A seller wants to net $235,000 after a 6% commission (ignore other costs). Price = $235,000 / 0.94 = $250,000. Verify: $250,000 x 6% = $15,000 commission; $250,000 - $15,000 = $235,000. The trap is multiplying $235,000 by 1.06, which overstates the price because the commission is figured on the larger sale price, not the smaller net.
Worked: down payment, loan amount, and points together
A buyer purchases at $340,000 with a 90% LTV loan and pays 2 discount points.
- Loan = $340,000 x 0.90 = $306,000.
- Down payment = $340,000 - $306,000 = $34,000 (the mirror of 10%).
- Points = 0.02 x $306,000 = $6,120 — points are figured on the loan, never the price. Using $340,000 ($6,800) is the planted error.
Mortgage insurance threshold and the per-diem interest at closing
When LTV exceeds 80% on a conventional loan, lenders require private mortgage insurance (PMI) until the borrower reaches roughly 20% equity; the 90% LTV above would carry PMI. At closing, lenders collect prepaid (per-diem) interest from the closing date to month-end. On the $306,000 loan at 6%, annual interest is $306,000 x 0.06 = $18,360; daily (360-day basis) = $18,360 / 360 = $51.00. A closing on the 21st of a 30-day month collects 10 days x $51.00 = $510 of prepaid interest.
Trap reminder: a discount point = 1% of the loan amount and buys down the rate; do not confuse it with a percentage of the sale price or with the down payment.
A seller wants to net $188,000 after paying a 6% commission. What sale price is required (ignore other closing costs)?
Loan-to-Value and Points
Loan-to-Value (LTV) = Loan Amount / Lesser of Price or Appraised Value. On a $300,000 purchase appraised at $300,000 with a $240,000 loan, LTV = $240,000 / $300,000 = 80%. Lenders quote LTV to set down payment and mortgage-insurance requirements.
Discount points are prepaid interest that buy down the rate; one point = 1% of the loan amount (not the price). Three points on a $240,000 loan cost 0.03 x $240,000 = $7,200. The recurring trap is computing points on the $300,000 purchase price instead of the $240,000 loan, which inflates the cost.
A related calculation is the down payment: it is the price minus the loan, not a figure derived from the loan alone. On the $300,000 purchase with a $240,000 loan, the down payment is $60,000, or 20% of price, which is the mirror of the 80% LTV. Exam items often give the down-payment percentage and ask for the loan amount; the loan is (100% - down %) of price.
Simple Interest
Mortgage and exam interest problems use simple interest = Principal x Rate x Time (I = P x R x T), with time in years.
Annual interest on a $200,000 loan at 7% is $200,000 x 0.07 = $14,000. One month's interest is $14,000 / 12 = $1,166.67. This monthly figure matters for proration and for the first mortgage payment, where most of the payment is interest.
- To find the rate, divide annual interest by principal: $14,000 / $200,000 = 7%.
- To find the principal, divide annual interest by rate: $14,000 / 0.07 = $200,000.
- For partial years, multiply by the fraction: 90 days is 90/360 = 0.25 of a year on the 360-day banker's calendar the exam typically uses.
Always confirm whether the question wants annual, monthly, or per-diem interest before answering.
A fully amortizing payment differs from interest-only because each payment also repays principal, so the balance, and therefore next month's interest, shrinks over time. The exam rarely asks you to build a full amortization schedule, but it does test the concept: in the early years a large share of each payment is interest, and only late in the term does principal dominate.
To find the interest portion of a single payment, apply the monthly rate to the current outstanding balance, then subtract that interest from the payment to get the principal portion. If a $200,000 balance at 6% (0.5% monthly) has a $1,199 payment, the first month's interest is $1,000 and only $199 reduces principal.
A borrower takes a $180,000 interest-only loan at 6.5% annual interest. What is the monthly interest payment?