8.2 Commission, Financing, and Interest Calculations
Key Takeaways
- Commission equals sale price times commission rate; the broker splits it with cooperating brokers and agents.
- To find an unknown, use the T-method: Part = Total × Rate, Total = Part ÷ Rate, Rate = Part ÷ Total.
- Simple annual interest equals principal times rate; divide by 12 for one month's interest.
- Loan-to-value ratio equals loan amount divided by the lesser of price or appraised value.
- One discount point equals one percent of the loan amount and is paid to adjust the lender's yield.
Commission math
Commission is a percentage of the sale price: Commission = Sale Price × Rate. On a $350,000 sale at 6%, the total commission is $21,000.
That total is then split. If listing and selling brokers split 50/50, each brokerage gets $10,500. If the selling agent keeps 60% of the selling-side share, the agent earns 60% × $10,500 = $6,300, and the brokerage keeps $4,200.
The T-method for unknowns
Every percentage problem fits the triangle: Part = Total × Rate. Cover the unknown to solve.
| Unknown | Formula |
|---|---|
| Part (commission $) | Total × Rate |
| Total (sale price) | Part ÷ Rate |
| Rate (%) | Part ÷ Total |
If an agent earned $9,000 commission at a 3% rate, the sale price = $9,000 ÷ 0.03 = $300,000. Always convert the percent to a decimal (3% = 0.03) before dividing.
Splits, graduated commissions, and a multi-step worked example
Many items chain several percentages, so work left to right and label each result. A $480,000 sale at a 5% total rate yields $480,000 x 0.05 = $24,000. The listing and selling brokerages split 60/40 in favor of the listing side: listing brokerage $14,400, selling brokerage $9,600. The selling agent is on a 70% split with her brokerage, so she earns 0.70 x $9,600 = $6,720, and her brokerage keeps $2,880.
The discipline that prevents errors: identify whether each rate applies to the sale price, the total commission, or a prior split share. A favorite distractor applies the agent's split to the full $24,000 instead of the selling-side share — always carry the correct base from one step to the next.
Amortization, mortgage factors, and points vs. rate
Most loans are fully amortizing: each level payment covers the month's interest first, and the remainder reduces principal, so the interest portion shrinks while the principal portion grows over time. When a problem supplies a per-$1,000 factor (e.g., $6.32 to amortize $1,000 at a given rate/term), multiply by the number of thousands: a $250,000 loan x ($6.32 x 250) = $1,580/month.
Points buy down the rate: paying 2 discount points on a $300,000 loan costs 0.02 x $300,000 = $6,000 up front and typically lowers the rate by roughly a quarter to a half percent, raising the lender's yield. Exam items test whether you compute points on the loan amount (correct) rather than the sale price, and whether you keep monthly vs. annual interest straight when comparing the buy-down's payment savings.
Combining interest with a closing-day adjustment
A common hybrid item asks for the per-diem interest owed at closing. On a new $240,000 loan at 6%, annual interest = $240,000 x 0.06 = $14,400; daily interest using a 360-day banker's year = $14,400 ÷ 360 = $40/day. If the loan funds on the 21st of a 30-day month, the borrower prepays interest for the remaining 10 days at closing: 10 x $40 = $400.
The exam tests two traps here. First, prepaid (per-diem) interest is collected at closing for the days before the first scheduled payment, so it is a buyer debit. Second, candidates must choose the correct day-count — switch to a 365-day year and the daily figure becomes $14,400 ÷ 365 = $39.45, changing the answer. Read whether the problem specifies a 360- or 365-day basis before dividing.
Solving for sale price from a net or a known commission
Two reverse problems recur. First, given an agent's check and the splits, work backward to the sale price. If an agent nets $5,250 after a 70% personal split of the selling-side share, the selling-side share was $5,250 ÷ 0.70 = $7,500; if that side was half of a 6% total commission, the full commission was $15,000 and the sale price was $15,000 ÷ 0.06 = $250,000.
Second, the net-to-seller version: a seller wants $188,000 clear after a 6% commission and $0 other costs. Because the commission is taken from the unknown selling price, divide rather than add a flat percentage: price = $188,000 ÷ (1 − 0.06) = $188,000 ÷ 0.94 = $200,000. Verify: 6% of $200,000 = $12,000, and $200,000 − $12,000 = $188,000. The error item writers reward is multiplying $188,000 by 1.06, which overshoots the true price.
A broker received a $13,500 commission on a sale that closed at a 4.5% commission rate. What was the sale price?
Loan-to-value (LTV)
Lenders limit risk with the loan-to-value ratio: LTV = Loan Amount ÷ Value, where value is the lesser of sale price or appraised value. On an $250,000 purchase appraised at $240,000 with 80% LTV, the lender funds 80% × $240,000 = $192,000, not $200,000.
This is a classic trap: when appraisal comes in below price, the loan is based on the appraisal, and the buyer covers the gap in cash.
Discount points
A discount point equals 1% of the loan amount, paid up front to buy down the interest rate and raise the lender's yield. Two points on a $200,000 loan = 2% × $200,000 = $4,000.
Do not confuse points with the rate or with origination fees. Points are always calculated on the loan amount, never the sale price.
Simple interest
Mortgage exam problems use simple annual interest: Annual Interest = Principal × Rate. For monthly interest, divide by 12.
Example: a $180,000 loan at 6.5% annual interest. Annual interest = $180,000 × 0.065 = $11,700. One month = $11,700 ÷ 12 = $975. On an interest-only or first-payment problem, that monthly figure is the interest portion before any principal reduction.
Trap: a partial-month or prorated interest question may ask for a number of days — then use Annual ÷ 360 (banker's year) × days unless told otherwise.
A borrower takes a $150,000 loan at 7% annual simple interest. How much interest accrues in one month?