Math Drills

Real Estate Math Drills

Formulas, worked examples and practice questions with hidden answers. Use a 360-day year for prorations. For timed practice, try the Math Test. To see setbacks and acreage, try the animated Visual Maths.

Sections

AreaCommissionsVATIncome & cap rateProrationsLTV & equityShow all answers

Section 1Area, Acreage & Price per Unit

Rectangle = Length × Width · Triangle = ½ × Base × Height
Acres = Sq ft ÷ 43,560 · Sq yards = Sq ft ÷ 9
Price per sq ft = Price ÷ Sq ft · Price per front foot = Price ÷ Frontage

Worked examples

1A — Area and acreage: lot 200 ft × 150 ft, price $390,000
  1. Area = 200 × 150 = 30,000 sq ft
  2. Acres = 30,000 ÷ 43,560 = 0.689 acres
  3. Per sq ft = $390,000 ÷ 30,000 = $13.00
  4. Sq yards = 30,000 ÷ 9 = 3,333.33 → per sq yd = $117.00
✓ 30,000 sq ft · 0.689 acres · $13.00/sq ft · $117.00/sq yd
1B — Building envelope: lot 100 ft wide × 120 ft deep; setbacks front 20, rear 15, sides 10 each
  1. Buildable depth = 120 − 20 − 15 = 85 ft
  2. Buildable width = 100 − 10 − 10 = 80 ft
  3. Envelope = 85 × 80 = 6,800 sq ft; with 3 storeys = 20,400 sq ft
✓ 6,800 sq ft footprint
1C — Beachfront: 75 ft of frontage sells for $2,250,000
  1. Price per front foot = $2,250,000 ÷ 75
✓ $30,000 per front foot

Practice — try it first, then check

1-A: A lot is 180 ft × 220 ft and sells for $475,200. Find the sq ft, acres, price per sq ft and price per sq yard.
Area = 39,600 sq ft · Acres = 39,600 ÷ 43,560 = 0.909 · $475,200 ÷ 39,600 = $12.00/sq ft · 39,600 ÷ 9 = 4,400 sq yd → $108.00/sq yd
1-B: A triangular lot has a base of 300 ft and a height of 200 ft. Area in sq ft and acres?
½ × 300 × 200 = 30,000 sq ft = 30,000 ÷ 43,560 = 0.689 acres
1-C: A lot is 80 ft wide × 100 ft deep. Setbacks: front 25, rear 20, sides 8 each. Building envelope?
Depth 100 − 25 − 20 = 55 · Width 80 − 8 − 8 = 64 · 55 × 64 = 3,520 sq ft
1-D: 50 ft of beach frontage sells for $1,750,000. Price per front foot?
$1,750,000 ÷ 50 = $35,000
1-E: A 150 ft × 160 ft lot sells for $540,000. Price per acre?
24,000 sq ft ÷ 43,560 = 0.55096 acres · $540,000 ÷ 0.55096 = $980,100 per acre (shortcut: $540,000 × 43,560 ÷ 24,000)

Section 2Commissions & Net to Gross

Commission = Price × Rate · Price = Commission ÷ Rate · Rate = Commission ÷ Price
Share = Total × broker split × salesperson split
Gross price = Net wanted ÷ (1 − total % the seller pays)

Worked examples

2A — $650,000 sale at 6%
  1. $650,000 × 0.06
✓ $39,000
2B — $22,500 commission at 6%: sale price?
  1. $22,500 ÷ 0.06
✓ $375,000
2C — $800,000, 6%, brokers split 50/50; listing agent gets 60% of listing side, buyer's agent 55% of selling side
  1. Total = $48,000 → $24,000 per side
  2. Listing agent = $24,000 × 0.60 = $14,400 (listing broker keeps $9,600)
  3. Buyer's agent = $24,000 × 0.55 = $13,200 (selling broker keeps $10,800)
✓ $14,400 / $9,600 / $13,200 / $10,800
2D — Seller wants to NET $550,000 after 6% commission
  1. Seller keeps 94% of the price
  2. $550,000 ÷ 0.94 = $585,106.38
✓ ≈ $585,106 — divide, never multiply by 1.06
2E — Bahamas: seller wants $900,000 net after 6% commission and their half of 10% VAT
  1. Seller pays 6% + 5% = 11% → keeps 89%
  2. $900,000 ÷ 0.89 = $1,011,235.96
  3. Check: commission $60,674 + half VAT $50,562 → net $900,000
✓ ≈ $1,011,236

Practice — try it first, then check

2-A: $425,000 at 6%. Commission?
$25,500
2-B: $18,000 commission at 5%. Sale price?
$18,000 ÷ 0.05 = $360,000
2-C: $1,200,000 at 6%, split 50/50. Listing agent gets 70% of the listing side; buyer's agent 60% of the selling side. Everyone's share?
Total $72,000 → $36,000 each side · Listing agent $25,200, listing broker $10,800 · Buyer's agent $21,600, selling broker $14,400
2-D: Seller wants to net $750,000 after a 6% commission. Minimum price?
$750,000 ÷ 0.94 = $797,872
2-E: Seller wants to net $500,000 after 6% commission and half of 10% VAT. Price?
6% + 5% = 11% · $500,000 ÷ 0.89 = $561,798
2-F: A vacant lot sells for $180,000 at the BREA minimum rate for undeveloped land. Commission?
Undeveloped land = 10% · $18,000

Section 3Bahamas VAT on a Sale

Find the bracket from the value → that rate applies to the WHOLE value
Gross sale: buyer and seller each pay half · Non-Bahamian buyer or company: 10%

Worked examples

3A — Bahamian buyer, $450,000 home (not a first home)
  1. $450,000 falls in the $300,001–$500,000 bracket → 6%
  2. VAT = $450,000 × 6% = $27,000
  3. Split: buyer $13,500, seller $13,500
✓ $27,000 total · $13,500 each
3B — Non-Bahamian buyer, $450,000 condo
  1. Flat 10% → $45,000
  2. Split: $22,500 each
✓ $45,000 total · $22,500 each

Practice — try it first, then check

3-A: A Bahamian buys a $250,000 lot. Total VAT and the seller's share?
$100,001–$300,000 → 4% · $10,000 total · seller pays $5,000
3-B: A company buys a $780,000 building. Total VAT?
Transfer to a company = 10% · $78,000
3-C: A Bahamian buys a $1,200,000 home. Total VAT?
Over $1M → 10% · $120,000

Section 4Income Approach & Cap Rate

Potential gross − Vacancy = EGI · EGI − Operating expenses = NOI
Value = NOI ÷ Cap rate · Cap rate = NOI ÷ Value · NOI = Value × Cap rate
Cash-on-cash = (NOI − annual debt service) ÷ cash invested

Worked examples

4A — 10 units at $1,800/month, 8% vacancy, $72,000 expenses, 9.5% cap rate
  1. PGI = 10 × $1,800 × 12 = $216,000
  2. Vacancy = $17,280 → EGI = $198,720
  3. NOI = $198,720 − $72,000 = $126,720
  4. Value = $126,720 ÷ 0.095 = $1,333,895
✓ ≈ $1,333,895
4B — Value $2,500,000, NOI $200,000: cap rate?
  1. $200,000 ÷ $2,500,000
✓ 8%

Practice — try it first, then check

4-A: 6 units at $2,200/month, 5% vacancy, $48,000 expenses, 9.5% cap. Value?
PGI $158,400 · EGI $150,480 · NOI $102,480 · ÷ 0.095 = $1,078,737
4-B: NOI $180,000, value $1,800,000. Cap rate?
10%
4-C: Bought for $950,000 at a 7% cap rate. NOI?
$950,000 × 0.07 = $66,500
4-D: 8 units at $1,500/month, 10% vacancy, $40,000 expenses, 9% cap. Value?
PGI $144,000 · EGI $129,600 · NOI $89,600 · ÷ 0.09 = $995,556
4-E: $700,000 purchase, $210,000 down, $490,000 interest-only at 6%, NOI $54,600. Cash-on-cash?
Interest $29,400 · cash flow $25,200 · ÷ $210,000 = 12%

Section 5Prorations (360-day year)

Daily rate = Annual amount ÷ 360 · Every month = 30 days
Arrears (unpaid): debit seller, credit buyer for the seller's days
Prepaid by seller: credit seller, debit buyer for the buyer's days

Worked examples

5A — $7,200 tax unpaid (arrears); closing 15 September
  1. Daily = $20.00
  2. Seller's days: 8 months × 30 + 15 = 255
  3. $20 × 255 = $5,100
✓ Debit seller / credit buyer $5,100
5B — Seller prepaid $3,600 annual fee; closing 30 April
  1. Daily = $10.00
  2. Buyer's days: May–Dec = 8 × 30 = 240
  3. $10 × 240 = $2,400
✓ Credit seller / debit buyer $2,400

Practice — try it first, then check

5-A: $9,000 annual tax unpaid; closing 20 July. Seller owes?
$25/day × (6 × 30 + 20 = 200) = $5,000
5-B: Seller prepaid $2,400 insurance; closing 15 March. Buyer owes?
Buyer's days: 15 (rest of March) + 9 × 30 = 285 · $2,400 ÷ 360 × 285 = $1,900
5-C: $300 monthly fee paid for October; closing 10 October. Buyer owes?
$10/day × 20 days = $200

Section 6LTV, Down Payment & Equity

Loan = Value × LTV (use the LOWER of price or appraisal)
Down payment = Price − Loan · Equity = Value − Amount owed

Worked examples

6A — $480,000 home, 80% LTV
  1. Loan = $384,000
  2. Down payment = $96,000 (20%)
✓ $384,000 loan · $96,000 down
6B — Worth $560,000, owes $340,000
  1. Equity = $220,000
  2. Equity % = 39.3%
✓ $220,000 equity

Practice — try it first, then check

6-A: 75% LTV on a $650,000 home. Loan and down payment?
Loan $487,500 · down $162,500
6-B: Owes $310,000 on a home worth $430,000. Equity and LTV?
Equity $120,000 · LTV = 310 ÷ 430 = 72.1%
6-C: Lender allows 80% LTV. Appraisal $380,000, price $395,000. Maximum loan?
Use the lower ($380,000) × 0.80 = $304,000
6-D: 2 points on a $250,000 loan?
2% × $250,000 = $5,000