8.2 Commission, Financing, and Interest Calculations

The master percentage formula

Nearly every financial calculation on the exam is a variation of one relationship:

Part = Whole x Rate

Rearrange it to solve for whatever is missing: Rate = Part / Whole, and Whole = Part / Rate. Some study programs draw this as the "T" or pie with the part on top and the whole and rate on the bottom. Whatever memory device you use, always convert the percentage to a decimal first by moving the decimal point two places left: 6% becomes 0.06, 5.5% becomes 0.055, and 0.5% (a half point) becomes 0.005. Forgetting to convert is the most common arithmetic error candidates make.

Commission math and multi-step splits

Commission = sale price x commission rate. A $325,000 home at a 6% total commission generates $325,000 x 0.06 = $19,500.

Splits are sequential, so resolve the brokerage-level split before the agent-level split. If the listing and selling brokerages split that $19,500 equally, each brokerage receives $9,750. If the selling agent then keeps 60% of the selling brokerage's share, the agent earns $9,750 x 0.60 = $5,850, and the brokerage keeps $3,900.

Reverse problems give you the commission and ask for the sale price. If an agent's 3% share equals $7,500, the sale price is $7,500 / 0.03 = $250,000. Always identify which base the rate is applied to before dividing.

Simple interest, annual and monthly

Real estate loans on the exam use simple interest: Interest = Principal x Rate x Time.

For one year, a $200,000 loan at 7% costs $200,000 x 0.07 = $14,000 in annual interest. Divide by 12 for a monthly figure: $14,000 / 12 = $1,166.67 per month.

Many questions hide interest inside a payment. If a borrower's monthly payment on a $180,000 balance at 6% is $1,200, the interest portion is $180,000 x 0.06 / 12 = $900, so the principal reduction is $1,200 - $900 = $300. The next month's interest is computed on the new, slightly lower balance, which is why early payments are mostly interest. Match the period: an annual rate must be divided by 12 before applying it to a monthly payment.

Loan-to-value, down payment, and points

LTV = loan amount / value (or price, whichever is lower). A $240,000 loan on a $300,000 home is $240,000 / $300,000 = 80% LTV, which also means a 20% down payment of $60,000.

Work it backward too: a 90% LTV loan on a $250,000 purchase is $250,000 x 0.90 = $225,000, leaving a $25,000 down payment.

A discount point equals 1% of the loan amount. Two points on a $225,000 loan cost $225,000 x 0.02 = $4,500. The classic trap applies points to the sale price instead of the loan; always use the loan amount as the base.

A combined commission-and-net example

Seller-net problems combine percentage and subtraction. Example: A seller wants to net $200,000 after paying a 6% commission and $4,000 in other closing costs. What must the sale price be?

The seller keeps 94% of the price (100% minus the 6% commission), and that 94% must cover both the $200,000 net and the $4,000 costs:

• Required from price = $200,000 + $4,000 = $204,000
• Price = $204,000 / 0.94 = $217,021 (rounded)

Note that you divide by 0.94, not by 1.06; the commission is taken out of the price, so the seller keeps the complement of the rate. Decimal conversion, choosing the correct base, and respecting the step order will carry you through the commission and financing questions in this section.

Choosing the correct base

The most frequent error in financial math is applying a rate to the wrong number. Train yourself to ask, before multiplying or dividing, what the rate is a percentage of.

A commission rate is a percentage of the sale price, so multiply by the price, never the loan or the seller's equity. A discount point is a percentage of the loan amount, not the sale price, so a loan of $225,000 with two points costs $4,500 even if the home sold for more. Simple interest is a percentage of the outstanding principal, which is why interest shrinks as the balance is paid down. Loan-to-value divides the loan by the lesser of price or appraised value, so a low appraisal can raise the effective LTV and trigger a larger down payment.

Write the base next to the rate before you compute. A note that says "3% commission to the selling agent" should be read as 3% of the sale price; a note that says "two points" should be read as 2% of the loan. Pinning down the base first eliminates the trap answers the exam plants for students who multiply by whatever number appears first.

Matching annual and monthly periods

Interest problems punish students who mix annual and monthly figures. An interest rate quoted as an annual percentage must be divided by 12 before you apply it to a single monthly payment, and a monthly interest figure must be multiplied by 12 to compare it to an annual cost.

Example: A $150,000 loan carries a 6% annual rate. Annual interest is $150,000 x 0.06 = $9,000, and the first month's interest is $9,000 / 12 = $750. If the monthly payment is $1,000, the principal reduction in that first month is $1,000 - $750 = $250, and next month's interest is computed on the slightly smaller balance of $149,750.

This is why early payments are mostly interest and late payments are mostly principal, the pattern called amortization. When a question gives an annual rate but asks about one month, divide by 12 first; when it gives a monthly cost but asks for the yearly total, multiply by 12. Keeping the period consistent, converting percentages to decimals, and choosing the right base together resolve the commission, interest, and loan questions on this section.