Percentages: commissions, interest, appreciation and depreciation, and points

Start with the base

Percent means per hundred. Convert a percent to a decimal by dividing by 100. Then use part = base × decimal rate, rate = part ÷ base, or base = part ÷ decimal rate. Convert a decimal rate back to percent by multiplying by 100.

Commissions and splits

For a $400,000 sale with an agreed 5% commission: 5 ÷ 100 = 0.05; $400,000 × 0.05 = $20,000. If a brokerage receives 50%, its share is $20,000 × 0.50 = $10,000. A salesperson receiving 60% of that share earns $10,000 × 0.60 = $6,000. Apply each split to the correct share. Commission rates and splits are negotiated; these examples are not required rates.

Interest

Simple interest = principal × annual decimal rate × years. With unchanged principal of $120,000 at 6% for three months: 6 ÷ 100 = 0.06; 3 ÷ 12 = 0.25 year; $120,000 × 0.06 = $7,200 annual interest; $7,200 × 0.25 = $1,800. This is interest, not the full payment on an amortizing loan.

Appreciation and depreciation

A $200,000 property appreciating 10% gains $200,000 × 0.10 = $20,000; its new value is $200,000 + $20,000 = $220,000. A subsequent 10% decline loses $220,000 × 0.10 = $22,000; the resulting value is $220,000 − $22,000 = $198,000. Equal opposite percentages do not cancel when their bases differ. Repeated annual changes apply to each year's starting value. To recover an original value, divide the final value by the applicable growth or decline factor.

Points and rate distinctions

One point equals 1% of the loan amount. Two points on a $300,000 loan: 2 ÷ 100 = 0.02; $300,000 × 0.02 = $6,000. Use the loan, not the sale price. Discount points are upfront interest charges, not a guaranteed percentage point reduction in the interest rate.

The contract interest rate differs from the annual percentage rate, which reflects borrowing costs under federal disclosure rules. Federal Truth in Lending law applies in New York: 15 U.S.C. § 1638(a)(4) requires disclosure of the finance charge expressed as an annual percentage rate for covered transactions. Use the contract interest rate for a simple interest calculation.