8.2 Commission, Financing, and Interest Calculations

Commission math

Commission is the heart of brokerage pay. Always start from the sale price, not the list price, unless the question says otherwise.

• Total commission = sale price x commission rate
• Each party's share = total commission x that party's split percentage

Worked example: split commission

A home sells for $320,000 at a 6% commission. The listing and selling brokerages split the total 50/50, and the listing agent keeps 60% of the listing brokerage's half.

• Total commission = 320,000 x 0.06 = $19,200
• Listing brokerage half = 19,200 x 0.50 = $9,600
• Listing agent share = 9,600 x 0.60 = $5,760

Trap: Apply percentages in sequence. Multiplying 19,200 by 60% directly skips the brokerage split and overstates the agent's pay.

A second common framing gives the agent's check and the split and asks for the sale price. Reverse each step: divide the agent's pay by the agent's split to get the brokerage half, double it for the total commission, then divide by the commission rate to recover the price. Working backward through the same chain in reverse order is the reliable method.

Solving backward for sale price

If you know the commission dollars and the rate, divide to recover the price.

Worked example

A broker earned $13,500 on a 4.5% commission. Sale price = 13,500 / 0.045 = $300,000.

The same logic recovers net-to-seller problems: if a seller must net $188,000 after a 6% commission, the price is 188,000 / (1 - 0.06) = 188,000 / 0.94 = $200,000. Note you divide by (1 - rate), not subtract 6% of $188,000 - that is the most common error on seller-net calculations.

Simple interest

Most exam loan questions use simple annual interest:

• Annual interest = principal x rate x time (years)
• Monthly interest = annual interest / 12

Worked example

A $240,000 interest-only loan at 5.5% annual interest:

• Annual = 240,000 x 0.055 = $13,200
• Monthly = 13,200 / 12 = $1,100

Units matter: rate is per year, so if a question gives a 60-day or 90-day note, multiply annual interest by the fraction of a year (60/360 or 90/360 on a banker's year). A $50,000 note at 6% for 90 days earns 50,000 x 0.06 x (90/360) = $750.

Many loan questions ask only for the first month's interest, then the principal balance. On a fully amortizing loan, the first payment is mostly interest; subtract the interest portion from the total payment to find how much principal was retired that month. If a $1,200 payment includes $1,100 interest, only $100 reduced the balance, leaving $239,900 owed.

Loan-to-value and down payment

LTV = loan amount / value, using the lower of price or appraised value. The down payment is value minus loan.

Worked example

A buyer purchases at $350,000 with 80% LTV.

• Loan = 350,000 x 0.80 = $280,000
• Down payment = 350,000 - 280,000 = $70,000

Trap: When appraisal is below price, the lender uses the lower figure. If the appraisal came in at $340,000, an 80% loan is 340,000 x 0.80 = $272,000, and the buyer covers the gap.

Discount points

Each point = 1% of the loan amount, paid up front to buy down the rate (raise the lender's yield).

Worked example

On a $280,000 loan, the lender charges 2 discount points.

• 280,000 x 0.02 = $5,600

Points are figured on the loan, not the sale price - using price overstates the cost.

One point raises the lender's yield by roughly 1/8% (0.125%) as a rule of thumb the exam may test, though the dollar cost is always exactly 1% of the loan per point. Do not confuse discount points with the loan origination fee, which is also quoted in points but compensates the lender for processing rather than buying down the rate.

Qualifying ratios

Lenders cap how much income can go to housing and to total debt. Two ratios appear on the exam:

Worked example

A buyer earns $7,000 gross per month. Using a 28% front-end ratio:

• Max housing payment = 7,000 x 0.28 = $1,960

With $400 in other monthly debt and a 36% back-end cap:

• Max total debt = 7,000 x 0.36 = $2,520
• Max housing = 2,520 - 400 = $2,120

The binding (lower) limit is the front-end $1,960, so that governs.

Trap: Income figures must be monthly. If income is stated annually, divide by 12 first.

When both ratios are given, compute each and let the lower maximum payment control - the borrower must satisfy both limits at once. Remember PITI stands for principal, interest, taxes, and insurance; if the question adds HOA dues or mortgage insurance to housing cost, include them in the front-end test as well.

Worked Example: Net-to-Seller After Commission

A frequent exam item asks for the sale price needed to net a target after commission. The seller wants $188,000 net after a 6% commission and $2,000 in other closing costs.

• The seller keeps (100% - 6%) = 94% of the price, then pays $2,000.
• Required price x 0.94 - $2,000 = $188,000.
• Required price x 0.94 = $190,000.
• Required price = $190,000 / 0.94 = $202,127 (rounded).

The classic error is to add 6% to the desired net; commission is a percentage of the sale price, so you must divide by (1 - rate), not multiply.

Worked Example: Interest Allocation in an Early Payment

On an amortizing loan, early payments are mostly interest. A $240,000 loan at 5% annual interest has a first month's interest of:

• Annual interest = $240,000 x 0.05 = $12,000.
• Monthly interest = $12,000 / 12 = $1,000.

If the monthly principal-and-interest payment is $1,288, then $1,000 goes to interest and only $288 reduces principal in month one. Next month, interest is computed on the slightly lower balance ($239,712), so a bit more goes to principal — the essence of amortization. The exam tests this to confirm you know interest is charged on the outstanding balance, not the original amount.