8.2 Commission, Financing, and Interest Calculations

Commission Math

Commission uses the value circle: Commission = Sale Price x Rate. Reverse problems give the commission and ask for the price (divide) or the rate (divide).

Worked example

A house sells for $425,000 at a 6% total commission.

• Total commission = $425,000 x 0.06 = $25,500.

If the listing and selling brokerages split 50/50, each brokerage gets $12,750. If the selling agent keeps 60% of their brokerage's half, the agent earns $12,750 x 0.60 = $7,650. Read split order carefully: the brokerage split happens before the agent split.

Reverse commission trap

A seller wants to net $200,000 after paying a 5% commission. New agents wrongly compute $200,000 x 1.05. The seller's net is 95% of the price, so:

• Price = $200,000 / 0.95 = $210,526.32.

Check: $210,526.32 x 0.05 = $10,526.32 commission; $210,526.32 - $10,526.32 = $200,000. The base is the price (100%), and the net is the price minus the rate, so divide by (1 - rate).

Simple Interest

Mortgage and seller-financing problems use simple annual interest: I = P x R x T, where P is principal, R is the annual rate, and T is time in years.

Worked example

A $180,000 loan at 7% annual interest. Annual interest = $180,000 x 0.07 = $12,600. Monthly interest = $12,600 / 12 = $1,050.

For a partial period, set T as a fraction of a year. A $50,000 note at 8% held for 90 days: I = $50,000 x 0.08 x (90/360) = $1,000. Real estate math commonly uses a 360-day banker's year (12 months of 30 days) unless told otherwise.

Loan Ratios and Points

Worked example: LTV and points

A buyer purchases at $300,000 with an 80% LTV loan.

• Loan = $300,000 x 0.80 = $240,000.
• Down payment = $300,000 - $240,000 = $60,000.
• 2 discount points = $240,000 x 0.02 = $4,800.

If the appraisal comes in at $290,000, the lender uses the lower figure: loan = $290,000 x 0.80 = $232,000, and the buyer must cover the larger gap.

Choosing the right base

Nearly every commission and financing error traces back to using the wrong base in Total = Rate x Base. Commission's base is always the sale price. Interest's base is the outstanding principal. LTV's base is the lower of price or appraised value. Points are charged on the loan amount, never the purchase price. When a problem chains steps, isolate each formula, identify its base explicitly, and resist the urge to reuse a number just because it appeared earlier. A sale price of $360,000 is the commission base, but the $324,000 loan, not the price, is the base for computing points on that loan.

Qualifying ratios

Lenders qualify borrowers with two ratios. The front-end (housing) ratio = monthly housing payment (PITI) / gross monthly income. The back-end (total debt) ratio = (housing payment + other monthly debts) / gross monthly income.

A borrower earns $7,200 per month. At a 28% front-end limit, the maximum PITI = $7,200 x 0.28 = $2,016. At a 36% back-end limit, total allowable debt = $7,200 x 0.36 = $2,592, leaving $576 for car and credit-card payments after housing. If existing debts exceed that gap, the housing payment must shrink. The lower of the two resulting limits governs.

Amortization basics

An amortized loan payment covers interest first, then principal. Early in the loan most of the payment is interest. Using the first month from above ($1,050 interest on a $180,000 loan at 7%): if the total payment is $1,197.54, then principal reduction = $1,197.54 - $1,050 = $147.54, leaving a $179,852.46 balance. Next month's interest is computed on the smaller balance, so the principal portion grows each month. The exam rarely asks for a full schedule but often tests the first-month interest-versus-principal split.

Per-thousand payment factors

Some exams give an amortization factor stated per $1,000 of loan. Multiply the loan in thousands by the factor to get the principal-and-interest payment. A $200,000 loan with a factor of $6.65 per $1,000 at the given rate and term: 200 x $6.65 = $1,330 monthly P&I. Reverse it to find the loan a payment supports: a $1,500 budget at a $7.50 factor allows 1,500 / 7.50 = 200, or a $200,000 loan.

Putting commission and financing together

A combined problem: a home sells for $360,000 with a 90% LTV loan and a 6% commission split 50/50 between two brokerages. The loan = $360,000 x 0.90 = $324,000, so the down payment is $36,000. The total commission = $360,000 x 0.06 = $21,600, and each brokerage receives $10,800. If the listing agent retains 70% of their brokerage's share, that agent earns $10,800 x 0.70 = $7,560. Work each formula independently, label every dollar, and never blend the LTV base (price or appraised value) with the commission base (sale price).

Graduated commission schedules add one more layer. A broker who earns 7% on the first $200,000 and 5% on the balance of a $350,000 sale collects ($200,000 x 0.07) + ($150,000 x 0.05) = $14,000 + $7,500 = $21,500. Apply each tier to only the portion of value that falls inside it; multiplying the full price by a single blended rate is a classic trap answer.