Commission & Net Proceeds
~11 min read · Split commissions through brokers and agents and back into list price from seller net.
Commission problems are percentage chains: price × rate, split through brokers and agents — and the reverse gear, solving list price from a seller's required net. Master the chain and the T-bar, and this category becomes guaranteed points.
The forward chain
Total commission = sale price × commission rate. Co-brokerage splits divide it between listing and selling sides per the offer of compensation; each agent's share then follows their split with their own broker. Chain them: price × rate × side-split × agent-split. The generic tool is the T-bar: Part = Whole × Rate; Rate = Part ÷ Whole; Whole = Part ÷ Rate.
- Total = price × rate; then side split; then agent split
- Part / (Whole × Rate) — cover the unknown
- Read WHOSE share the question wants
The reverse gear: net-to-seller
'The seller must NET $X after a Y% commission' — the trap is adding Y% to the net. Correct: the net is what remains after commission, so list price = net ÷ (1 − rate) (plus any flat costs added to the net first). Netting $300,000 at 6%: 300,000 ÷ 0.94 = $319,148.94 — NOT 300,000 × 1.06 = $318,000. The divide-by-the-complement move also solves 'price after X% appreciation/depreciation' backwards.
- Net ÷ (1 − rate) = required price
- Never multiply the net by (1 + rate)
- Add fixed costs (payoff, closing costs) to the net before dividing
Related percentage problems
Profit/loss: percent = (gain or loss) ÷ COST (original investment) — not ÷ selling price. Appreciation chains multiply (three years at 5% = ×1.05³, not +15%). Rate extraction: commission dollars ÷ sale price. Every problem is the same T-bar with different costumes.
Worked example
A house sells at $480,000 with a 5.5% commission, split 50/50 between listing and selling brokerages; the selling agent keeps 70% of her side. Separately, the same seller had said 'I must walk away with $450,000 after paying off my $190,000 loan and the 5.5% commission — what must it sell for?' Compute the agent's check and the required price.
Forward: total = 480,000 × 0.055 = $26,400. Selling side = 26,400 × 0.50 = $13,200. Agent = 13,200 × 0.70 = $9,240. Reverse: the seller needs net-of-everything $450,000 PLUS the $190,000 payoff = $640,000 remaining after commission. Price = 640,000 ÷ (1 − 0.055) = 640,000 ÷ 0.945 = $677,248.68 — round per the answer choices. Check: 677,248.68 × 5.5% = 37,248.68 commission; 677,248.68 − 37,248.68 − 190,000 = 450,000 ✓. The two disciplines: chain the splits in order, and divide by the complement — never multiply the net upward.
Common exam pitfalls
Grossing up a required net by (1 + rate).
Commission applies to the PRICE, not the net — divide the net (plus fixed costs) by (1 − rate).
Paying the agent from the total instead of her side.
Split to the brokerage side first, then apply the agent's split.
Computing profit percent on the sale price.
Profit and loss percentages divide by the ORIGINAL COST.
Chain forward through the splits; divide backward by the complement.
Recap
- Total commission = price × rate; then side and agent splits in order
- T-bar: Part = Whole × Rate, rearranged for any unknown
- Net-to-seller: (net + fixed costs) ÷ (1 − rate)
- Profit % = gain ÷ original cost
- Appreciation compounds multiplicatively
- Verify by recomputing forward
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