8.2 Commission, Financing, and Interest Calculations
Key Takeaways
- Commission = sale price x commission rate; always convert the percentage to a decimal first.
- Splits cascade: broker share is taken from the total, then the agent share is taken from the broker's portion.
- Simple annual interest = principal x rate x time; monthly interest divides the annual rate by 12.
- Loan-to-value (LTV) equals loan amount divided by the lesser of price or appraised value.
- One discount point equals 1% of the loan amount, not 1% of the purchase price.
Commission Math
Commission is the simplest percentage problem: Commission = Sale Price x Rate. Convert the rate to a decimal first (6% = 0.06).
Example: A home sells for $325,000 at a 6% commission. Total commission = 325,000 x 0.06 = $19,500.
To find the sale price when you know the commission and rate, divide: Sale Price = Commission / Rate. A $21,000 commission at 5% means 21,000 / 0.05 = $420,000.
Splitting the Commission
Splits cascade in steps. First the total commission is divided between the listing and selling brokerages, then each brokerage splits with its agent.
| Step | Calculation | Result |
|---|---|---|
| Total commission | $300,000 x 6% | $18,000 |
| Listing brokerage (50%) | $18,000 x 0.50 | $9,000 |
| Listing agent (60% of broker share) | $9,000 x 0.60 | $5,400 |
The trap is applying the agent's 60% to the full $18,000. The agent split is taken only from that brokerage's portion, here $9,000.
Reverse commission and seller-net problems
The exam often runs commission math backwards — solving for price or rate.
Solve for price: An agent earns $15,300 at a 4.5% rate. Price = Commission / Rate = 15,300 / 0.045 = $340,000.
Seller-net problem (the classic trap): A seller wants to net $200,000 after a 6% commission (ignore other costs). You cannot add 6% to $200,000. The net is 94% of the price, so Price = 200,000 / 0.94 = $212,766 (rounded). Commission = $212,766 x 0.06 = $12,766; price minus commission = $200,000. Adding 6% of $200,000 gives only $212,000, which under-nets the seller.
Worked interest and balance problems
Interest for part of a month: A $240,000 loan at 6% accrues 240,000 x 0.06 = $14,400/year, or $1,200/month, or $40/day (30-day month). Fifteen days of interest = 15 x $40 = $600.
Principal reduction: On a $180,000 balance at 6%, monthly interest = $900. A $1,250 payment applies $900 to interest and $350 to principal, leaving $179,650. Because next month's interest is figured on the lower balance, early payments are mostly interest — the core of amortization.
Points and LTV recap with a twist
| Concept | Formula | Example |
|---|---|---|
| Commission | Price x Rate | $340,000 x 4.5% = $15,300 |
| Seller net | Price = Net / (1 − Rate) | $200,000 / 0.94 = $212,766 |
| Discount points | Loan x Point% | $250,000 x 2% = $5,000 |
| Max loan (LTV) | Lesser of price/value x LTV | $290,000 x 80% = $232,000 |
Points trap: A buyer with a $260,000 loan pays 1.5 points plus a 1% origination fee. Points = 260,000 x 0.015 = $3,900; origination = 260,000 x 0.01 = $2,600; total = $6,500 — both figured on the loan, never the purchase price.
Annual-percentage and per-diem interest recap
Two more lender-math patterns appear regularly. Per-diem (daily) interest at closing: lenders collect prepaid interest from the closing date to the end of that month using a 365-day year unless told otherwise. A $300,000 loan at 5% accrues 300,000 x 0.05 = $15,000/year; daily = 15,000 / 365 = $41.10. Closing on the 21st of a 31-day month leaves 10 days of prepaid interest = 10 x $41.10 = $411.00.
Effective cost of points: Paying 2 points on a $250,000 loan costs 250,000 x 0.02 = $5,000 up front to lower the rate. If the lower rate saves $60/month, the break-even is 5,000 / 60 = about 83 months — useful when a question asks whether buying down the rate is worthwhile for a buyer who plans to sell in five years (60 months), in which case paying the points loses money.
A property sells for $450,000 with a total commission of 6%. The listing and selling brokerages split it equally. The selling agent receives 70% of her brokerage's share. How much does the selling agent earn?
Simple Interest
Mortgage exam problems use simple interest: Interest = Principal x Rate x Time. The rate is annual, so for one month divide the annual interest by 12.
Example: A $200,000 loan at 5% annual interest. Annual interest = 200,000 x 0.05 = $10,000. One month of interest = 10,000 / 12 = $833.33. This monthly interest figure is what appears in the first payment of an amortized loan.
Principal and Interest in a Payment
In an amortizing loan, each payment covers that month's interest first; the remainder reduces principal.
Example: $180,000 balance at 6%. Monthly interest = (180,000 x 0.06) / 12 = $900. If the payment is $1,200, then $1,200 - $900 = $300 goes to principal, leaving a balance of $179,700. Next month's interest is computed on the new, slightly lower balance, which is why early payments are mostly interest.
Loan-to-Value Ratio
LTV = Loan Amount / Value, where value is the lesser of sale price or appraised value. Lenders cap LTV to limit risk.
Example: A buyer purchases at $300,000 but the appraisal comes in at $290,000. With an 80% LTV cap, the maximum loan = 290,000 x 0.80 = $232,000, not $240,000. The trap is using the higher purchase price. The buyer must cover the gap with extra down payment.
Discount Points
One point = 1% of the loan amount, paid up front to buy down the rate. Points are calculated on the loan, never on the purchase price.
Example: A $250,000 loan with 2 discount points = 250,000 x 0.02 = $5,000. If the buyer also pays a 1% origination fee, that is another $2,500. A frequent error is applying points to a $312,500 purchase price instead of the $250,000 loan, overstating the cost.
A borrower takes a $240,000 loan and pays 1.5 discount points plus a 1% origination fee. What is the total of points and origination fee?