8.2 Commission, Financing, and Interest Calculations

Commission Calculations

Commission is almost always a percentage of the sales price, not the list price or loan amount.

Commission = Sales Price x Commission Rate

Basic Example

A home sells for $420,000 at a 6% commission rate. Total commission = 420,000 x 0.06 = $25,200.

Commission Splits

The total commission is first divided between the listing and selling (buyer's) sides, then each side splits between broker and agent. Splits always divide the dollar amount, never the percentage rate.

Split Example

The $25,200 commission splits 50/50 between sides, giving each side $12,600. If the listing agent is on a 60/40 split with the broker (agent keeps 60%), the agent earns 12,600 x 0.60 = $7,560 and the broker keeps $5,040.

Working Backward to the Rate or Price

If you know two of the three values, solve for the third:

• Rate = Commission / Sales Price
• Sales Price = Commission / Rate

A $30,000 commission on a $500,000 sale is a 30,000 / 500,000 = 6% rate.

Net to Seller Problems

A classic exam item asks for the sale price needed so the seller nets a target amount after commission. Do not subtract the commission percent from 100% incorrectly; instead divide the desired net by (100% minus the commission rate). If a seller must net $188,000 after a 6% commission, price = 188,000 / 0.94 = $200,000. Verify: 200,000 x 0.06 = $12,000 commission, leaving exactly $188,000.

Simple Interest

Most exam interest problems use simple interest:

Simple Interest = Principal x Rate x Time

Annual Example

A $250,000 loan at 7% for one year accrues 250,000 x 0.07 x 1 = $17,500 in annual interest.

Monthly Interest Portion

To find one month's interest on an amortized loan, divide annual interest by 12. On the loan above, 17,500 / 12 = $1,458.33 of the first month's payment is interest; the remainder reduces principal.

Discount Points

Discount points are prepaid interest paid at closing to buy down the note rate. One point equals 1% of the loan amount (not the sales price).

Points Cost = Loan Amount x Points (as a decimal)

Points Example

Three points on a $300,000 loan cost 300,000 x 0.03 = $9,000. A rough rule of thumb is that each point lowers the rate by about one-eighth to one-quarter percent, but the dollar cost is the testable figure.

Loan-to-Value Ratio

LTV = Loan Amount / Value (use the lower of sales price or appraised value)

A $360,000 loan on a $400,000 home is 360,000 / 400,000 = 90% LTV. Conventional loans above 80% LTV generally require private mortgage insurance (PMI) until the balance falls to roughly 78-80% of value.

Down Payment from LTV

LTV and down payment are mirror images. A 90% LTV loan means a 10% down payment; on a $400,000 home that is 400,000 x 0.10 = $40,000 down. When a problem gives the down payment, subtract it from price to find the loan amount before computing LTV.

APR vs. Note Rate

The note rate is the interest charged on the loan balance. The annual percentage rate (APR) adds points, origination fees, and certain other finance charges, then expresses the total cost as a yearly rate. APR is therefore always equal to or higher than the note rate, and it lets borrowers compare loans with different fee structures under the Truth in Lending Act.

Qualifying Ratios

Lenders test affordability with two debt ratios:

• Front-end (housing) ratio = monthly PITI / gross monthly income.
• Back-end (total debt) ratio = total monthly debt payments / gross monthly income.

Ratio Example

A borrower earns $8,000 per month. With a 28% front-end limit, the maximum housing payment is 8,000 x 0.28 = $2,240.

Financing Formula Sheet

Common Exam Traps

• Using sales price for points; points are a percent of the loan.
• Splitting the commission rate instead of the dollar commission.
• Forgetting to convert a percent to a decimal before multiplying.
• Assuming APR equals the note rate; APR includes finance charges.

Cash to Close and Principal, Interest, Taxes, Insurance

The cash to close is the total a buyer brings to settlement: the down payment plus closing costs, minus any earnest money already deposited and any seller credits. A buyer with a $40,000 down payment, $9,000 in closing costs, a $5,000 earnest money deposit, and a $2,000 seller credit needs 40,000 + 9,000 - 5,000 - 2,000 = $42,000 at the table.

PITI Components

A monthly mortgage payment on an escrowed loan bundles four parts, abbreviated PITI: Principal, Interest, Taxes, and Insurance. Only principal and interest repay the loan; taxes and insurance are held in escrow and paid by the servicer when due. If annual taxes are $4,800 and annual hazard insurance is $1,200, the escrow portion adds (4,800 + 1,200) / 12 = $500 per month on top of principal and interest.

Buydowns and Effective Rate

Because discount points are prepaid interest, paying points lowers the effective interest rate over the life of the loan but raises the cash needed at closing. Exam items frequently ask you to weigh the upfront point cost against monthly savings; the testable arithmetic is simply the point cost (loan amount times points as a decimal) and the resulting payment change.