8.2 Commission, Financing, and Interest Calculations

Commission, Financing, and Interest Calculations

This is the highest-yield math on the national exam because commission and interest problems appear almost every time. They all rest on the same percentage relationship: Part = Whole x Rate, often drawn as the T-bar (or "made-paid" triangle) with the Part on top and Whole x Rate on the bottom.

From that one relationship you can solve for any missing piece:

• Part = Whole x Rate
• Rate = Part / Whole
• Whole = Part / Rate

The whole skill is identifying which number is the Part, which is the Whole, and which is the Rate, then dividing or multiplying accordingly.

Commission Splits

Commission is usually a percentage of the SALE PRICE, not of the asking price. Total commission = Sale Price x Commission Rate. That total is then split, typically between listing and selling brokerages, and again between broker and agent.

Worked example: a home sells for $400,000 at a 6% total commission.

1. Total commission = 400,000 x 0.06 = $24,000
2. Listing/selling 50/50 split = $12,000 to each brokerage
3. Agent on a 60/40 split keeps 12,000 x 0.60 = $7,200

Trap: the exam often gives you the agent's split AND the brokerage split. Apply them in sequence; do not add the two percentages together.

Solving for Sale Price from Net

A seller wants to NET a specific amount after commission. Net is the WHOLE minus the commission, so the seller keeps (100% - rate) of the price.

Example: a seller must net $188,000 after a 6% commission, ignoring other costs.

• Seller keeps 100% - 6% = 94% of price
• Sale Price = 188,000 / 0.94 = $200,000
• Check: 200,000 x 0.06 = 12,000 commission; 200,000 - 12,000 = 188,000 net

The classic mistake is multiplying 188,000 x 1.06, which overstates the price. You must DIVIDE the net by the seller's retained percentage.

Simple Interest

Mortgage interest on the exam is simple interest: Interest = Principal x Rate x Time. Rate is annual; time is in years.

Example: a $250,000 loan at 5% annual interest. Annual interest = 250,000 x 0.05 = $12,500. One month of interest = 12,500 / 12 = $1,041.67.

On a fully amortizing loan, the first payment is mostly interest; subtract the monthly interest from the total payment to find the small principal portion.

Points, LTV, and Qualifying

A point equals 1% of the LOAN amount, not the sale price. On a $300,000 loan, 2 points = 300,000 x 0.02 = $6,000.

Loan-to-Value (LTV) = Loan / Value (or sale price, whichever is lower). A $270,000 loan on a $300,000 home is 270,000 / 300,000 = 90% LTV. To find the down payment, take 100% - LTV: here 10%, or $30,000.

Trap: points are charged on the loan amount; appraisal and value comparisons use the LOWER of price or appraised value, which can cut the maximum loan and force a larger down payment.

Low-Appraisal Down-Payment Trap

Lenders set the maximum loan against the lower of contract price or appraised value, so a low appraisal silently raises the buyer's cash. Suppose a buyer agrees to $300,000 with 80% financing, but the appraisal comes in at $285,000.

1. Max loan = 80% of the lower figure = 0.80 x $285,000 = $228,000
2. The buyer still owes the seller $300,000
3. Cash required = $300,000 - $228,000 = $72,000, versus the $60,000 the buyer planned (20% of $300,000)

The low appraisal added $12,000 to the cash needed even though the LTV percentage was unchanged. Recognize that the percentage applies to the appraisal, not the price, and the question becomes mechanical.

Amortization: Splitting a Payment Into Interest and Principal

A classic interest question gives the monthly payment and asks how much reduces principal in the first month. The interest portion is always computed on the current balance using simple interest for one month; whatever is left of the payment reduces principal.

Worked example: a $200,000 loan at 6% annual interest has a fixed monthly payment of $1,199.10.

1. Monthly interest = ($200,000 x 0.06) / 12 = $12,000 / 12 = $1,000.00
2. Principal reduction = $1,199.10 - $1,000.00 = $199.10
3. New balance = $200,000 - $199.10 = $199,800.90

The next month's interest is recalculated on the slightly lower balance, so the interest portion shrinks and the principal portion grows over time - the essence of amortization. The recurring trap multiplies the annual rate against the balance and forgets to divide by 12, overstating monthly interest twelvefold.

Discount Points and Yield

Discount points are prepaid interest a borrower pays to buy down the rate. A rough exam convention is that each point lowers the rate by about 1/8% (0.125%), though the tested skill is usually the dollar cost, not the rate change.

Worked example: a borrower takes a $240,000 loan and pays 1.5 discount points plus a 1-point origination fee.

1. Total points = 1.5 + 1.0 = 2.5 points
2. Cost = 2.5% x $240,000 = 0.025 x 240,000 = $6,000

Both origination and discount points are computed on the loan amount, never the purchase price. The distractor usually multiplies the points against the sale price, producing a slightly higher wrong answer.