8.2 Commission, Financing, and Interest Calculations

Commission and financing problems test whether you can move between percentages and dollars cleanly. Almost every one reduces to the same core relationship.

The Percentage Triangle

Three quantities relate through one formula: a part equals the whole times the rate.

$\text{Part} = \text{Whole} \times \text{Rate}$

• To find the part (e.g., commission dollars): multiply whole by rate.
• To find the rate: divide part by whole.
• To find the whole (e.g., sale price): divide part by rate.

Convert every percent to a decimal before multiplying: 6 percent becomes 0.06, and a half-percent becomes 0.005.

Commission Calculations

$\text{Total Commission} = \text{Sale Price} \times \text{Commission Rate}$

A home sells for $385,000 at a 6 percent commission: 385,000 x 0.06 = $23,100 total.

Splitting the Commission

The total is usually divided between the listing and selling brokerages, then between each broker and agent.

• Listing side gets 50 percent: $23,100 x 0.50 = $11,550.
• That agent keeps a 70 percent split: $11,550 x 0.70 = $8,085 to the agent; $3,465 to the broker.

Read carefully whether a question asks for the brokerage's share or the agent's share after the internal split.

Net-to-Seller (The Classic Trap)

When a seller wants a specific amount after commission, you cannot simply add the commission rate to the net. The commission is a percentage of the sale price, not of the net. So the seller keeps (100% minus the commission rate) of the price.

$\text{Sale Price} = \frac{\text{Desired Net} + \text{Other Costs}}{1 - \text{Commission Rate}}$

Net Example

A seller wants to net $200,000 after paying a 6 percent commission (no other costs). Seller keeps 94 percent, so:

Sale Price = $200,000 / 0.94 = $212,766 (rounded). At that price, commission = $212,766 x 0.06 = $12,766, leaving exactly $200,000. Dividing by 0.94 is correct; multiplying $200,000 by 1.06 gives the wrong answer of $212,000.

Simple Interest

Most license-exam interest is simple interest, charged on principal only.

$\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}$

For a full year on a $250,000 loan at 7 percent: 250,000 x 0.07 = $17,500 annual interest. For one month, divide by 12: $17,500 / 12 = $1,458.33.

This monthly-interest step is essential for amortization questions, where each payment first covers the month's interest and the remainder reduces principal. On a fully amortizing loan, early payments are mostly interest; late payments are mostly principal.

Amortization Step Example

A $200,000 loan at 6 percent has a monthly payment of $1,199. First, find one month of interest: $200,000 x 0.06 / 12 = $1,000. The remaining $1,199 - $1,000 = $199 reduces principal, leaving a new balance of $199,801.

The next month's interest is computed on that slightly smaller balance, so the principal portion grows each month. Exam questions often ask only for the first month's interest and principal split, which you can solve with the simple-interest formula and one subtraction.

Loan-to-Value, Points, and Qualifying Ratios

Loan-to-value (LTV) measures loan risk:

$\text{LTV} = \frac{\text{Loan Amount}}{\text{Value or Price (lower of the two)}}$

A $360,000 loan on a $400,000 home is a 90 percent LTV. Above 80 percent on a conventional loan, lenders typically require private mortgage insurance (PMI). Note that LTV uses the lower of sale price or appraised value, so a low appraisal can shrink the maximum loan.

One discount point equals 1 percent of the loan amount, paid up front to lower the rate. On a $300,000 loan, 2 points = $300,000 x 0.02 = $6,000. Do not confuse points with the down payment: points are a financing fee on the loan, while the down payment is a percentage of the purchase price.

Qualifying-Ratio Example

A buyer earns $7,000 gross per month. Using a 28 percent front-end limit, the maximum housing payment is $7,000 x 0.28 = $1,960. Using a 36 percent back-end limit, total monthly debt cannot exceed $7,000 x 0.36 = $2,520, so up to $560 of other debt payments is allowed alongside the housing payment.

If the buyer already pays $700 in car and card debt, the back-end test caps the housing payment at $2,520 - $700 = $1,820, which is the binding limit. Always check both ratios and use the lower allowable housing payment.

Profit, Loss, and Appreciation

Percentage-change problems also appear in financing units.

$\text{Percent Change} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}}$

A home bought for $300,000 and sold for $345,000 gained $45,000, a 45,000 / 300,000 = 15 percent profit. Going forward, multiply by (1 + rate) to project appreciation: $345,000 x 1.10 = $379,500 after another 10 percent gain. The exam trap here is dividing by the new value instead of the original cost; percent change is always measured against the original figure.

Down Payment and Loan Amount

Many financing items hinge on splitting price into down payment and loan.

$\text{Loan Amount} = \text{Price} \times (1 - \text{Down Payment Rate})$

On a $360,000 home with 20 percent down, the down payment is $360,000 x 0.20 = $72,000 and the loan is $360,000 x 0.80 = $288,000. That 80 percent LTV avoids PMI on a conventional loan.

If the buyer puts only 10 percent down, the loan is $324,000 (a 90 percent LTV) and PMI applies. Read whether the percentage given is the down payment or the loan, then use the complementary share for the other figure.