8.2 Commission, Financing, and Interest Calculations

Commission Math

Commission is the percentage-of-a-base skill the exam tests most. The base is almost always the sale price, and the percent must become a decimal: 6% = 0.06, 5.5% = 0.055.

Basic relationship:

Worked Split Example

A home sells for $385,000 at a 6% total commission. The listing and selling brokerages split it 50/50, and each brokerage pays its agent 60% of the brokerage share. What does the selling agent receive?

Step 1 — Total commission: $385,000 × 0.06 = $23,100. Step 2 — Selling brokerage share: $23,100 × 0.50 = $11,550. Step 3 — Agent share: $11,550 × 0.60 = $6,930.

The trap is collapsing the steps — multiplying $385,000 by a single blended percent. Always sequence: total, then split, then agent.

Loan-to-Value and Down Payment

Loan-to-value ratio (LTV) = loan amount ÷ the lower of price or appraised value. Lenders underwrite to the lower figure, so when an appraisal comes in below the contract price, use the appraised value.

Worked LTV Example

A buyer contracts at $300,000, but the appraisal is $290,000. The lender offers 80% LTV. How much must the buyer put down?

Step 1 — Use the lower figure: $290,000. Step 2 — Maximum loan: $290,000 × 0.80 = $232,000. Step 3 — Down payment: the buyer still owes the seller $300,000, so down = $300,000 − $232,000 = $68,000.

The planted error: computing 20% of $290,000 ($58,000) and forgetting the buyer must cover the $10,000 appraisal gap out of pocket. The loan shrinks to value; the price does not.

Simple Interest

Most license-exam interest questions use simple interest: Interest = Principal × Rate × Time. Time is in years; one month = 1/12 year.

Worked Interest Example

A $240,000 interest-only loan carries a 7.5% annual rate. What is the first month's interest?

Step 1 — Annual interest: $240,000 × 0.075 = $18,000. Step 2 — Monthly: $18,000 ÷ 12 = $1,500.

To find the rate when you know the payment, reverse it: $1,500 × 12 = $18,000 annual; $18,000 ÷ $240,000 = 0.075 = 7.5%.

Discount Points

One discount point = 1% of the loan amount, paid up front to lower the rate. The base is the loan, never the sale price.

A buyer borrows $250,000 and pays 2.5 points. Cost = $250,000 × 0.025 = $6,250. If the question gives a $300,000 price with that loan, using the price ($7,500) is the trap. Points follow the loan.

Seller's Net and Percentage-Profit Math

Two more commission-adjacent skills round out this section: solving for an unknown base and computing a seller's net.

Working backward from a net

When a question gives the dollars and the percent but hides the base (the sale price), divide rather than multiply. A seller wants to net $188,000 after paying a 6% commission and $2,000 in other closing costs. What sale price is required?

Step 1 - The seller keeps 100% - 6% = 94% of the price after commission. Step 2 - But $2,000 of fixed costs come out too, so: (Price x 0.94) - $2,000 = $188,000. Step 3 - Add the fixed cost back: Price x 0.94 = $190,000. Step 4 - Divide by the decimal: $190,000 / 0.94 = $202,128 (round to the listing increment).

The planted error is subtracting 6% of the desired net instead of dividing by 0.94. Commission is a percentage of the price, not of the net, so you must divide by (1 - rate). Multiplying $188,000 by 1.06 gives the wrong figure because it applies the rate to the smaller number.

Percentage of profit and loss

Profit and loss problems also pivot on identifying the base. Percent change = (new - old) / old. The base is always the original figure.

An investor buys a duplex for $320,000 and sells it for $384,000. What is the percentage gain?

Gain = ($384,000 - $320,000) / $320,000 = $64,000 / $320,000 = 0.20 = 20%.

Reverse it: a property sold for $270,000 at a 10% loss. What was the original cost? Here $270,000 represents 90% of the original (100% - 10%): $270,000 / 0.90 = $300,000. Dividing by 1.10 instead of 0.90 is the classic trap - a loss shrinks the base, so you divide by (1 - loss rate), exactly the mirror of the commission setup above. Master "divide by the decimal that remains" and the entire family of base-finding problems collapses into one move.

Amortization and the first payment split

Exam questions on monthly payments usually ask you to split the first payment into interest and principal. The interest portion always comes first: monthly interest = (current balance x annual rate) / 12, and whatever remains of the level payment reduces principal.

A fully amortizing loan of $300,000 at 6% has a level monthly payment of $1,799. Find the principal paid in month one.

Step 1 - Month-one interest: $300,000 x 0.06 = $18,000 annual; / 12 = $1,500. Step 2 - Principal portion: $1,799 - $1,500 = $299. Step 3 - New balance: $300,000 - $299 = $299,701, so month two's interest is computed on the slightly smaller balance.

Because the balance shrinks each month, the interest slice falls and the principal slice grows - the engine of amortization. The trap is reversing the split (assuming the payment is mostly principal early on); in fact early payments are overwhelmingly interest.