8.2 Commission, Financing, and Interest Calculations

Commission, Financing, and Interest Calculations

These problems drive the largest share of exam math because every transaction involves a commission and most involve a loan. Read carefully for which number is the base: commissions are a percentage of sale price, while interest is a percentage of the loan balance.

Commission and splits

Commission = sale price x commission rate. Splits are applied afterward, in sequence: first between the brokerages, then between each brokerage and its agent.

Worked example

A home sells for $400,000 at a 6% total commission, split 50/50 between listing and selling brokerages. The listing agent keeps 60% of the listing brokerage's share.

1. Total commission = $400,000 x 0.06 = $24,000.
2. Listing brokerage share = $24,000 x 0.50 = $12,000.
3. Listing agent share = $12,000 x 0.60 = $7,200.

Trap: Apply splits step by step. Do not multiply all the percentages together unless the question asks only for the final agent dollar amount.

Net-to-seller (the most-missed problem)

When a seller wants to net a specific amount after paying a commission, you cannot simply add the commission rate to the net. The commission is charged on the sale price, which is the unknown.

Formula: Sale Price = Net + Costs / (100% - Commission Rate)

Worked example

A seller wants to net $188,000 after a 6% commission (no other costs).

Sale Price = $188,000 / (1.00 - 0.06) = $188,000 / 0.94 = $200,000.

Check: $200,000 x 6% = $12,000 commission; $200,000 - $12,000 = $188,000. Correct.

Trap: Adding 6% to $188,000 gives $199,280 - which is wrong, because the commission would then be 6% of the larger figure. Always divide by (1 minus the rate).

Loan-to-value and down payment

LTV = loan amount / value, where value is the lower of appraised value or sale price.

• A buyer purchases at $300,000; the appraisal comes in at $290,000. The lender bases an 80% LTV loan on $290,000 -> loan = $232,000.
• The buyer must cover the $10,000 gap plus the normal down payment.

Down payment = price - loan amount.

Simple interest

Mortgage interest on the exam is computed as simple annual interest: Interest = Principal x Rate x Time.

Worked example

A $240,000 loan at 5% interest. First month's interest = ($240,000 x 0.05) / 12 = $12,000 / 12 = $1,000. If the total monthly payment of principal and interest is $1,288, then $1,288 - $1,000 = $288 reduces principal in month one.

Discount points and origination fees

A point equals 1% of the loan amount (not the sale price). Points are prepaid interest that buy down the rate or increase the lender's yield.

• Loan = $250,000; 2 discount points = $250,000 x 0.02 = $5,000.
• A 1% origination fee on the same loan = another $2,500.

Trap: Calculate points on the loan amount, never the purchase price. The rule of thumb that each point changes yield by roughly 1/8% is conceptual, not a precise calculation.

Graduated splits and the percentage-of-a-percentage trap

Many brokerages pay graduated splits — the agent's share rises after they hit a production threshold. Apply each rate to the correct base in sequence.

Worked example: tiered split

An agent closes a $500,000 sale at a 5% total commission. Their brokerage takes the full commission, then pays the agent 70% of it but charges a flat $300 transaction fee.

1. Total commission = $500,000 x 0.05 = $25,000.
2. Agent's pre-fee share = $25,000 x 0.70 = $17,500.
3. Net to agent = $17,500 - $300 = $17,200.

Reverse-engineering the commission rate and price

The exam often gives two of the three commission variables and asks for the third. Rearrange Commission = Price x Rate.

• Find the rate: An agent earned $13,500 on a $225,000 sale. Rate = $13,500 / $225,000 = 0.06 = 6%.
• Find the price: A 5% commission produced $19,000. Price = $19,000 / 0.05 = $380,000.

Per-payment interest and the amortization split

Because each mortgage payment is mostly interest early on, the exam tests the split for a single month. Compute the interest on the current balance, then subtract it from the total payment to find principal applied.

Worked example

A $300,000 loan at 6% has a fixed monthly payment of $1,799. First month's interest = ($300,000 x 0.06) / 12 = $18,000 / 12 = $1,500. Principal applied = $1,799 - $1,500 = $299. New balance = $300,000 - $299 = $299,701, and next month's interest is computed on that slightly smaller balance.

Trap: Never apply the annual rate to a monthly base. Divide the annual rate by 12 (or multiply principal x rate then divide by 12). Using the full annual rate on one month overstates interest twelvefold.

Discount points and an LTV down-payment drill

Points and loan-to-value calculations round out financing math. One discount point = 1% of the loan amount (not the purchase price), paid at closing to buy down the rate. On a $260,000 loan, 1.5 points cost 0.015 x $260,000 = $3,900.

Loan-to-value uses the lesser of price or appraised value as the base. A buyer agrees to pay $320,000, but the appraisal returns $310,000. For an 80% LTV loan the lender lends 0.80 x $310,000 = $248,000, so the buyer's cash is $320,000 - $248,000 = $72,000 — $8,000 more than if the appraisal had matched the price.

Trap: Always compute points on the loan, and always base LTV on the lower of sale price or appraised value — using the contract price after a low appraisal overstates the loan a lender will actually fund.