8.2 Commission, Financing, and Interest Calculations

Commission math

Commission is the most common money calculation on the exam. The first step never changes: 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. The mistakes start with the splits.

Splitting commission

Splits are percentages of the total commission, not of the sale price. Suppose the $21,000 is divided 50/50 between the listing brokerage and the selling brokerage, and each brokerage gives its agent 60%.

• Each brokerage receives: 21,000 x 0.50 = $10,500
• The listing agent receives: 10,500 x 0.60 = $6,300
• The listing brokerage keeps: 10,500 x 0.40 = $4,200

The trap is applying the 60% agent split to the full $21,000 instead of to the brokerage's $10,500 share.

Working backward from a net

When a seller wants a specific net amount, divide, do not multiply. If a seller must net $188,000 after a 6% commission (and no other costs), the sale price is net / (1 - rate): 188,000 / 0.94 = $200,000. Multiplying $188,000 by 1.06 gives the wrong answer ($199,280) because the commission is charged on the higher sale price.

Loan-to-value and down payment

Loan-to-value (LTV) ratio = loan amount / value, where lenders use the lesser of the appraised value and the sale price. This protects the lender from overpayment.

A buyer agrees to pay $300,000, but the appraisal comes in at $290,000. With a required 80% LTV, the lender lends 80% of the lower figure: 290,000 x 0.80 = $232,000. The buyer must cover the rest: 300,000 - 232,000 = $68,000 down (the $10,000 appraisal gap plus the standard 20%).

Computing the down payment

If value and price match at $250,000 and LTV is 90%, the loan is 250,000 x 0.90 = $225,000 and the down payment is 250,000 x 0.10 = $25,000. The down-payment percentage is simply (1 - LTV).

Interest and discount points

Simple interest

Annual interest = principal x rate. Monthly interest = annual interest / 12. On a $200,000 loan at 6%: annual interest = 200,000 x 0.06 = $12,000; one month's interest = 12,000 / 12 = $1,000.

This monthly figure also drives interim or prepaid interest at closing. For a partial month of 10 days using a 30-day month: $1,000 x (10/30) = $333.33.

Discount points

One discount point = 1% of the loan amount, paid to buy down the rate. Points are charged on the loan, never on the purchase price.

The most-tested trap: charging points against the sale price instead of the loan amount. If the price is $250,000 but the loan is $200,000, two points cost $4,000, not $5,000.

Points-to-yield and the lender's return

Lenders charge discount points to raise the loan's effective yield. A useful rule of thumb the exam may invoke: each discount point paid increases the lender's yield by roughly 1/8% (0.125%). So a borrower paying 3 points to buy down a rate raises the lender's yield about 3 x 0.125% = 0.375%, which is why the up-front charge can lower the borrower's note rate by a comparable amount over the life of the loan.

Origination fees vs. discount points

Both are quoted as a percentage of the loan amount, but they serve different purposes. An origination fee compensates the lender for processing the loan; discount points prepay interest to lower the rate. On a $240,000 loan, a 1% origination fee is 240,000 x 0.01 = $2,400, and 2 discount points are 240,000 x 0.02 = $4,800, for $7,200 in combined up-front charges. Both are computed on the loan, never the price.

Working backward from a payment to a loan amount

Some problems give the monthly interest-only figure and ask for the principal. Reverse the simple-interest formula: principal = (annual interest) / rate, where annual interest = monthly interest x 12.

Worked example: A borrower's first month of interest on an interest-only note is $1,200 at a 7.2% annual rate.

• Annualize: $1,200 x 12 = $14,400.
• Principal = $14,400 / 0.072 = $200,000.

Tax and assessment quick math

Property tax often appears via a millage rate, where one mill = $1 per $1,000 of assessed value (0.001). A home assessed at $180,000 in a district with a 22-mill rate owes 180,000 x 0.022 = $3,960 in annual tax. If an assessment ratio applies — say market value $200,000 assessed at 90% — first compute the assessed value (200,000 x 0.90 = $180,000), then apply the millage. Mixing market value and assessed value is the classic error here.

Qualifying ratios

Lenders test affordability with two ratios. The housing (front-end) ratio = monthly housing payment (PITI) / gross monthly income. The total debt (back-end) ratio = (PITI + other monthly debts) / gross monthly income.

A borrower earns $6,000 per month with a proposed PITI of $1,620 and $300 in other debt:

• Front-end: 1,620 / 6,000 = 27%
• Back-end: (1,620 + 300) / 6,000 = 1,920 / 6,000 = 32%

If the program caps the ratios at 28% and 36%, this borrower qualifies on both. The trap is using net income instead of gross, or forgetting to add the other debts to the back-end ratio.

Equity

Equity = current market value - loans against the property. A home worth $400,000 with a $250,000 mortgage balance has 400,000 - 250,000 = $150,000 in equity. As value rises or the balance amortizes, equity grows.

Amortization and the first payment

In an amortizing loan, each payment covers interest first, then the remainder reduces principal. Compute one month's interest from the current balance, then subtract it from the payment to find principal reduction.

On a $200,000 loan at 6% with a $1,199 monthly payment:

1. First-month interest: 200,000 x 0.06 / 12 = $1,000
2. Principal paid: 1,199 - 1,000 = $199
3. New balance: 200,000 - 199 = $199,801

Because the balance barely drops at first, early payments are almost all interest. The second month's interest is computed on $199,801, so the interest portion shrinks slightly and the principal portion grows each month.

The key exam idea: interest is always charged on the remaining balance, not the original loan. A question that asks for the second month's interest expects you to use the reduced balance, not the starting figure.