8.2 Commission, Financing, and Interest Calculations

Commission, financing, and interest math

These items dominate the calculation portion because they mirror daily transaction work. Each is a percentage problem dressed in transaction vocabulary.

Commission and splits

Total commission equals the sale price times the commission rate. A $360,000 sale at a 6% commission generates $360,000 x 0.06 = $21,600. Splits then distribute that pool.

Suppose the listing and selling brokerages split the $21,600 evenly (50/50), so each brokerage receives $10,800. If the selling agent keeps 60% of her brokerage's share, she earns $10,800 x 0.60 = $6,480, and her broker keeps $4,320. Work splits in order: total first, brokerage share second, agent share last.

Net to seller

When a seller must net a specific amount after commission, do not subtract the commission from the desired net. Divide. If a seller needs $282,000 net and the commission is 6%, the seller keeps 94% of the price: Sale Price = $282,000 / 0.94 = $300,000. Check by computing 6% of $300,000 = $18,000, and $300,000 - $18,000 = $282,000.

Simple interest

Real estate loans are quoted with simple annual interest. Annual interest = Principal x Rate. A $200,000 loan at 5% costs $200,000 x 0.05 = $10,000 in interest for one year. For one month, divide by 12: $10,000 / 12 = $833.33. Monthly interest matters for proration and for the interest portion of an early payment.

Discount points

A point is 1% of the LOAN amount. The classic trap applies the percentage to the sale price instead. On a $240,000 loan, 2 points cost $240,000 x 0.02 = $4,800. If the buyer puts money down, points still attach to the loan, not the purchase price.

Distinguish discount points from an origination fee. Both are quoted in points and both compute against the loan amount, but a discount point buys down the interest rate while an origination fee pays the lender for processing. The arithmetic is identical; the exam usually only asks for the dollar amount, so apply the point percentage to the loan and report the figure.

Equity and the appreciation angle

Equity is value minus what is owed: Equity = Value - Loan Balance. A home worth $350,000 with a $210,000 remaining loan holds $140,000 in equity. Appreciation problems add a growth rate to the base value: a $300,000 home appreciating 4% in one year is worth $300,000 x 1.04 = $312,000. Over multiple simple-interest-style years the exam usually applies the rate to the original base each year unless it states compounding; read the wording before assuming compounding.

Loan-to-value (LTV)

LTV expresses the loan as a percentage of the property's value (the lesser of price or appraised value). LTV = Loan Amount / Value. A $270,000 loan on a $300,000 home is $270,000 / $300,000 = 0.90, or 90% LTV. The down payment is the remaining 10%, or $30,000.

Reverse the formula to find the loan: a 75% LTV on a $400,000 property means a loan of $400,000 x 0.75 = $300,000 and a $100,000 down payment. When price and appraisal differ, lenders base LTV on the LOWER figure, so a low appraisal shrinks the maximum loan.

Combining the pieces: a financing example

A buyer purchases a $320,000 home with an 80% LTV loan and pays 1.5 discount points.

1. Loan amount = $320,000 x 0.80 = $256,000.
2. Down payment = $320,000 x 0.20 = $64,000.
3. Discount points = $256,000 x 0.015 = $3,840 (points apply to the loan, not the price).
4. First month's interest at 5.5% = ($256,000 x 0.055) / 12 = $14,080 / 12 = $1,173.33.

Quick reference

• Total commission = Sale Price x Rate
• Net-to-seller price = Required Net / (1 - Commission Rate)
• Annual simple interest = Principal x Rate; monthly = annual / 12
• 1 point = 1% of loan amount
• LTV = Loan / Value; Down payment % = 1 - LTV

The recurring trap across all of these: applying a percentage to the wrong base. Commission applies to sale price, interest applies to outstanding principal, and points apply to the loan amount. Identify the base before you multiply.

More Worked Commission, Net, and Interest Problems

Because these items recur across the exam, drill several full variations end to end.

A Three-Way Net-to-Seller Problem

A California seller must net $564,000 after a 6% commission and $9,000 of closing costs. Do not subtract the commission from the net; solve for price. The seller keeps 94% of price minus fixed costs, so: Price x 0.94 = $564,000 + $9,000 = $573,000, giving Price = $573,000 / 0.94 = $609,574 (rounded). Check: 6% of $609,574 = $36,574; $609,574 - $36,574 - $9,000 = $564,000. The key move is adding the fixed costs into the numerator before dividing by (1 - rate).

A Per-Diem Interest Problem

Loan payoffs and closings prorate interest by the day. A $420,000 loan at 6.5% annual simple interest accrues $420,000 x 0.065 = $27,300/year. Per day (365-day basis) = $27,300 / 365 = $74.79. If the loan is paid off 12 days into the month, the interim interest = 12 x $74.79 = $897.53. Escrow shows this as a debit to the borrower being paid off.

A Points-and-LTV Combination

A buyer purchases a $550,000 home at 80% LTV and pays 2 discount points.

• Loan = $550,000 x 0.80 = $440,000.
• Down payment = $110,000.
• Points = $440,000 x 0.02 = $8,800 (on the loan, never the price).
• First-month interest at 6% = ($440,000 x 0.06) / 12 = $2,200.

Trap: When fixed closing costs accompany a net-to-seller problem, add them to the desired net before dividing by (1 - commission rate). Subtracting commission directly from the net, or forgetting the costs, produces the two most common wrong answers.