8.2 Commission, Financing, and Interest Calculations
Key Takeaways
- Commission = Sale Price × Rate; splits apply the percentage sequentially to the prior pool.
- Simple annual interest = Principal × Rate × Time; mortgage interest accrues on the declining balance.
- Each discount point equals 1% of the loan amount, paid up front to the lender.
- Loan-to-value ratio = Loan Amount / Value (or price, whichever is lower).
- Always identify the base: commission uses sale price, interest uses loan principal, LTV uses the lower of price or value.
Commission math
Commission is a percentage of the sale price:
Total Commission = Sale Price × Commission Rate
A $400,000 sale at a 6% rate produces $24,000. The challenge is splitting it. Commissions flow in layers: first between the listing and selling brokerages, then between each brokerage and its agent.
Example: $24,000 split 50/50 between listing and selling firms gives each firm $12,000. If the selling agent keeps 60% of the selling firm's share, the agent earns $12,000 × 0.60 = $7,200, and the firm keeps $4,800. Apply each split to the pool created by the previous split, never to the original total again.
The most common commission error is applying the agent's split percentage to the full commission rather than to the brokerage's share. A 60% agent on a $24,000 deal does not earn $14,400; the agent earns 60% of whatever reaches the brokerage after the co-op split. Read carefully whether a percentage refers to the whole commission, one brokerage's half, or the agent's slice of that half — exam writers deliberately blur this.
Working backward from commission
Exams often give the commission and ask for the sale price or rate. Rearrange the same formula:
- Sale Price = Commission / Rate
- Rate = Commission / Sale Price
If an agent earned $9,000 representing a 3% co-op share of a sale, and that $9,000 is the full commission at 3%, the sale price is $9,000 / 0.03 = $300,000. The key is matching the dollar figure to the rate that produced it — do not divide a partial split by the full rate.
A home sells for $350,000 with a 6% total commission. The listing and selling brokerages split it equally, and the selling agent receives 70% of the selling brokerage's share. How much does the selling agent earn?
Simple interest
Most exam interest questions use simple interest:
Interest = Principal × Rate × Time
A $200,000 loan at 5% annual interest accrues $200,000 × 0.05 = $10,000 in one year, or $833.33 per month ($10,000 / 12). For partial years, time is a fraction: a 90-day note is 90/360 = 0.25 year under the common 360-day banker's year, producing $200,000 × 0.05 × 0.25 = $2,500 of interest.
When a question gives a monthly interest dollar amount and asks for the rate or principal, rearrange the formula. If one month of interest is $1,000 on a loan at 6%, then annual interest is $12,000 and Principal = $12,000 / 0.06 = $200,000. Matching the time period of the interest figure to the rate is essential — a monthly amount must be annualized before dividing by an annual rate.
Mortgages are amortized, so interest accrues on the declining balance. The first month's interest on a $200,000 loan at 6% is $200,000 × 0.06 / 12 = $1,000. If the payment is $1,200, then $200 reduces principal and next month's interest is computed on $199,800.
Discount points and the loan-to-value ratio
A discount point is 1% of the loan amount, paid up front to buy down the interest rate:
Cost of Points = Loan Amount × (Points × 0.01)
On a $250,000 loan, 2 points cost $250,000 × 0.02 = $5,000. Points are based on the loan, never the sale price — a frequent trap when the down payment differs from the loan.
The loan-to-value (LTV) ratio measures lending risk:
LTV = Loan Amount / Value
Lenders use the lower of appraised value or sale price. A buyer borrowing $180,000 on a home that appraised at $200,000 but is priced at $210,000 has an LTV of $180,000 / $200,000 = 90%.
Down payment and qualifying ratios
Down payment is the price minus the loan, or the price times the down-payment percentage:
Down Payment = Sale Price × Down Payment %
A 20% down payment on a $300,000 home is $60,000, leaving an $240,000 loan and an 80% LTV. The two figures — down-payment percent and LTV — always sum to 100% when based on the same value.
Qualifying questions may give a monthly payment factor per $1,000 borrowed. Multiply the factor by the number of thousands financed: a $6.00 per $1,000 factor on a $240,000 loan yields 240 × $6.00 = $1,440 monthly principal and interest.
Front-end and back-end ratios round out qualifying math. The front-end (housing) ratio divides the proposed housing payment by gross monthly income; the back-end ratio adds all recurring debt. If a lender caps the housing ratio at 28% and a borrower earns $6,000 a month, the maximum housing payment is $6,000 × 0.28 = $1,680. Compare the calculated payment to that ceiling to decide whether the borrower qualifies.
A buyer obtains a $240,000 loan and pays 1.5 discount points at closing. How much do the points cost?
Worked Example: Simple Interest and Monthly Payments
Real estate math uses simple annual interest for most loan questions: Interest = Principal x Rate x Time.
A buyer carries a loan balance of $260,000 at 6.5% annual interest. The first month's interest is:
- Annual interest = $260,000 x 0.065 = $16,900.
- Monthly interest = $16,900 / 12 = $1,408.33.
If the fixed monthly payment is $1,650, then $1,408.33 goes to interest and $241.67 reduces principal in month one. Because the balance drops, next month's interest is slightly lower and a bit more goes to principal - the essence of amortization. The exam often asks for the first month's interest or the principal portion of an early payment; compute the monthly interest from the current balance, then subtract it from the payment to find the principal applied.