8.2 Commission, Financing, and Interest Calculations
Key Takeaways
- Commission equals sale price times commission rate; split it by the co-broke and house percentages in order.
- Simple interest = Principal x Rate x Time; most license-exam loan questions use simple annual interest.
- Loan-to-value (LTV) ratio = loan amount divided by the lesser of price or appraised value.
- Discount points cost 1% of the loan amount each and are paid to adjust the lender's yield.
- Always identify the base (what 100% refers to) before applying any percentage.
The master percentage equation
Nearly every money problem reduces to Part = Base x Rate. Rearranged:
- Part = Base x Rate
- Base = Part / Rate
- Rate = Part / Base
The single biggest error is choosing the wrong base. Commission's base is the sale price. A salesperson's split base is the brokerage's share, not the full commission. Loan interest's base is the outstanding principal. Identify the base, then decide whether you multiply or divide.
Commission basics
Total commission = Sale Price x Commission Rate.
Example: A home sells for $340,000 at a 6% commission. Total commission = $340,000 x 0.06 = $20,400.
Commission rates are negotiable and not set by law; the exam tests the arithmetic, not a fixed rate. When a problem gives a flat dollar fee plus a percentage of any amount over a threshold, compute each piece separately and add. For example, a $2,000 flat fee plus 4% of price above $200,000 on a $260,000 sale equals $2,000 + (0.04 x $60,000) = $4,400.
Splitting the commission
Splits apply in sequence. Suppose the $20,400 is divided 50/50 between the listing and selling brokerages, and the selling salesperson keeps 60% of their brokerage's share.
| Step | Calculation | Result |
|---|---|---|
| Selling brokerage share | $20,400 x 50% | $10,200 |
| Salesperson share | $10,200 x 60% | $6,120 |
| Brokerage retains | $10,200 x 40% | $4,080 |
Trap: the 60% applies to the brokerage's $10,200, not to the full $20,400. Reading the base wrong here produces the most common distractor.
Working backward to price
If a salesperson earned $6,120 under the same split, you reverse each step: $6,120 / 0.60 = $10,200 brokerage share; $10,200 / 0.50 = $20,400 total; $20,400 / 0.06 = $340,000 sale price.
A property sells for $250,000 with a 7% total commission. The listing and selling sides split 50/50, and the listing salesperson receives 70% of the listing side. What does the listing salesperson earn?
Simple interest
License exams use simple interest: Interest = Principal x Rate x Time. Time is in years (6 months = 0.5).
Example: A $200,000 loan at 5.5% annual interest. Annual interest = $200,000 x 0.055 = $11,000. Monthly interest = $11,000 / 12 = $916.67.
On an amortized loan the first payment is mostly interest. If the monthly payment is $1,135.58, then the principal applied in month one = $1,135.58 - $916.67 = $218.91, and next month's interest is computed on the slightly reduced balance.
Loan-to-value (LTV)
LTV = Loan Amount / Value, where value is the lesser of sale price or appraised value.
Example: Price $300,000, appraisal $290,000, buyer wants 80% LTV. The lender uses $290,000. Max loan = $290,000 x 0.80 = $232,000, so the buyer must add cash to cover the $10,000 appraisal gap plus the normal down payment.
Down payment is the mirror of LTV: an 80% LTV loan means a 20% down payment. On a $300,000 price with an 80% loan against price, the buyer puts down $60,000. Watch whether the question bases LTV on price or on the lower appraised value, because the two can differ and the lender always uses the lower figure.
Discount points, origination, and PMI
One discount point = 1% of the loan amount, paid up front to buy down the lender's yield (roughly 1/8% rate reduction per point, but the exam usually just tests the cost). An origination fee is also quoted in points but compensates the lender for processing rather than reducing the rate.
Example: 2 discount points plus a 1% origination fee on a $232,000 loan = $232,000 x 0.03 = $6,960 in up-front charges.
Private mortgage insurance (PMI) is generally required when LTV exceeds 80% and is quoted as an annual percentage of the loan. A $232,000 loan with 0.5% annual PMI costs $1,160 per year, or about $96.67 per month, added to PITI.
Qualifying ratios
Qualifying ratios screen the borrower:
- Front-end (housing) ratio = monthly housing (PITI) / gross monthly income.
- Back-end (total debt) ratio = (PITI + other debt) / gross monthly income.
Example: Gross monthly income $6,000, max front-end ratio 28%. Maximum PITI = $6,000 x 0.28 = $1,680. If total debt allowed is 36%, max total debt payment = $6,000 x 0.36 = $2,160, leaving $480 for car and card payments.
PITI stands for Principal, Interest, Taxes, and Insurance. The exam expects you to know that the housing ratio uses PITI, not just principal and interest, and that gross (pre-tax) income is always the base, never take-home pay.
Splitting a Commission Through the Chain
Commission flows from seller to listing broker, then is split with the cooperating broker and finally with the salespeople.
Worked example: A home sells for $400,000 at a 6% total commission = $24,000. The listing and selling sides split 50/50, so each side receives $12,000. If the selling salesperson keeps 60% of their side's share, the salesperson earns 0.60 × $12,000 = $7,200, and that brokerage keeps $4,800.
Always identify (1) the total commission, (2) the broker-to-broker split, then (3) the broker-to-salesperson split, in that order — working out of sequence is the usual error.
Interest, Points, and the T-Bar Method
Simple interest = Principal × Rate × Time. For a partial year, multiply by the fraction of the year.
Worked example (interest): A $250,000 loan at 6% annual interest accrues 250,000 × 0.06 = $15,000 per year, or $1,250 per month. For 73 days, use 73/360 (banker's year): 15,000 × 73/360 = $3,041.67.
Discount points each equal 1% of the loan amount and are paid to lower the rate. On a $250,000 loan, 2 points = 0.02 × 250,000 = $5,000. Use the T-bar (Total = Part ÷ Rate; Part = Total × Rate) to solve any "made/paid/rate" question by covering the unknown.
A property sells for $325,000 with a 7% commission. The listing and selling brokerages split it 50/50, and the listing salesperson receives 70% of the listing side. How much does the listing salesperson earn?
A borrower has gross monthly income of $7,200 and the lender allows a 28% front-end (housing) ratio. What is the maximum monthly PITI payment the borrower qualifies for?