8.2 Commission, Financing, and Interest Calculations

Commission math

Total commission = sale price x commission rate. A home sells for $350,000 at a 6% commission: 350,000 x 0.06 = $21,000 total commission.

Splits then divide that pool. If the listing and selling brokerages split 50/50, each office receives $10,500. If an agent keeps 70% of the office's share, that agent earns 10,500 x 0.70 = $7,350.

Working backward from commission

If you know the commission and rate but need the price, divide: a $15,000 commission at a 5% rate implies a price of 15,000 / 0.05 = $300,000. The percentage base is always the sale price, not the commission.

Graduated and tiered commissions appear in listing-agreement questions. A schedule might pay 7% on the first $100,000 and 5% on the amount above $100,000. On a $250,000 sale: 100,000 x 0.07 = $7,000, plus 150,000 x 0.05 = $7,500, for $14,500 total. Compute each tier on its own band and add; never apply one rate to the whole price.

Net listings ask the reverse question: the seller wants a guaranteed net, and the broker adds expenses and desired commission on top. If a seller must net $190,000 and closing costs are $10,000 with a 5% commission, solve price as (190,000 + 10,000) / (1 - 0.05) = 200,000 / 0.95 = $210,526. Dividing by 0.95 (not multiplying by 1.05) is the step candidates miss.

Interest calculations

Real estate exams use simple interest: Interest = Principal x Rate x Time.

A $200,000 loan at 6% annual interest costs 200,000 x 0.06 = $12,000 per year, or $1,000 per month in interest.

Interest on the remaining balance

Mortgage interest each period is charged on the current outstanding balance, not the original loan. After a payment reduces principal, the next month's interest is smaller.

Example: a $180,000 loan at 5% has a first-month interest charge of 180,000 x 0.05 / 12 = $750. If the monthly payment is $966, then $966 - $750 = $216 goes to principal, leaving a balance of $179,784. Month two's interest is calculated on $179,784, slightly less than $750.

Loan-to-value and down payment

LTV = loan amount / value, where value is the lower of appraised value or sale price. Lenders cap LTV; the rest is the down payment.

A home priced at $250,000 with an 80% LTV loan: loan = 250,000 x 0.80 = $200,000. The down payment is 250,000 - 200,000 = $50,000 (the remaining 20%).

When appraisal and price differ, use the lower figure. If the appraisal is $240,000 but the price is $250,000, an 80% loan is based on $240,000 = $192,000, and the buyer must cover the extra gap in cash. Here the buyer pays the $50,000 down plus the $10,000 appraisal shortfall, a $60,000 total cash outlay.

Working LTV backward is also tested. If a borrower can produce a $45,000 loan and wants 90% financing, the maximum price is 45,000 / 0.90 = $50,000. And to find the down-payment percentage, subtract LTV from 100%: a 90% loan means a 10% down payment.

Discount points

One discount point = 1% of the loan amount, paid up front to buy down the interest rate and increase the lender's yield. Points are calculated on the loan, not the sale price.

Three points on a $200,000 loan cost 200,000 x 0.03 = $6,000. The trap is multiplying points by the purchase price or property value instead of the loan amount.

A related distinction: an origination fee is also quoted in points but pays for processing the loan, while discount points specifically buy down the rate. Both are calculated on the loan balance, so the dollar math is identical even though the purpose differs.

Qualifying ratios

Lenders test affordability with two ratios that the national exam loves. The front-end (housing) ratio divides monthly PITI (principal, interest, taxes, insurance) by gross monthly income. The back-end (total debt) ratio divides PITI plus all recurring debts by gross monthly income.

Example: a borrower earns $6,000 per month, with proposed PITI of $1,560 and car and card payments of $540.

• Front-end ratio: 1,560 / 6,000 = 26%.
• Back-end ratio: (1,560 + 540) / 6,000 = 35%.

If the lender's limits are 28% and 36%, this borrower qualifies on both. To find the maximum payment instead, multiply income by the ratio: 6,000 x 0.28 = $1,680 maximum housing payment.

When both ratios apply, the borrower must satisfy the lower of the two ceilings. Using the same $6,000 income, the back-end limit allows total debt of 6,000 x 0.36 = $2,160. If existing debts are $540, the maximum PITI under the back-end test is 2,160 - 540 = $1,620, which is tighter than the $1,680 front-end allowance. The qualifying payment is therefore $1,620, the smaller figure. Always compute both and use the more restrictive result.

The percentage-base rule

Every financing percentage attaches to a specific base. Commissions attach to sale price; points and interest attach to the loan; LTV attaches to the lower of price or value; qualifying ratios attach to gross income.

Name the base first, multiply second. Choosing the wrong base, not the arithmetic, is what sinks most financing questions.