Connecticut Real Estate Exam Math: Practice Problems With Solutions

Math questions appear on both the national and state sections of the Connecticut PSI exam. They cover a predictable set of formulas — and once you know them, they become reliable points. Here are the key formulas and worked examples you need.

Commission Calculations

Formula: Commission = Sale Price × Commission Rate

Example: A home sells for $480,000. The total commission is 5%. The listing broker and buyer's broker split it 50/50. The listing salesperson gets 60% of the listing broker's share. How much does the listing salesperson earn?

Total commission: $480,000 × 0.05 = $24,000
Listing broker's share: $24,000 × 0.50 = $12,000
Salesperson's share: $12,000 × 0.60 = $7,200

Loan-to-Value Ratio

Formula: LTV = Loan Amount ÷ Property Value

Example: A buyer purchases a home for $350,000 and puts 15% down. What is the LTV?

Down payment: $350,000 × 0.15 = $52,500
Loan amount: $350,000 − $52,500 = $297,500
LTV: $297,500 ÷ $350,000 = 85%

Proration (Day-Count Method)

Connecticut uses a 365-day year (actual days) for prorations unless stated otherwise.

Example: A seller has prepaid annual property taxes of $5,840. Closing is on September 15. How much does the seller get credited for prepaid taxes?

Days remaining after closing: Sept 16 through Dec 31 = 107 days
Daily tax rate: $5,840 ÷ 365 = $16.00/day
Seller credit: $16.00 × 107 = $1,712

Capitalization Rate

Formula: Cap Rate = NOI ÷ Value (or Value = NOI ÷ Cap Rate)

Example: An apartment building has a potential gross income of $120,000, vacancy loss of 8%, and operating expenses of $40,000. The cap rate is 7%. What is the estimated value?

Effective Gross Income: $120,000 × (1 − 0.08) = $110,400
NOI: $110,400 − $40,000 = $70,400
Value: $70,400 ÷ 0.07 = $1,005,714

Square Footage / Area

Formula: Area = Length × Width (for rectangles)

Example: A rectangular lot is 150 feet wide and 210 feet deep. How many square feet is it?

- 150 × 210 = 31,500 sq ft

Bonus: How many acres? 31,500 ÷ 43,560 = 0.72 acres

Percentage Problems (Price Appreciation)

Example: A home was purchased for $300,000 and sold for $345,000. What was the percentage gain?

Gain: $345,000 − $300,000 = $45,000
Percentage: $45,000 ÷ $300,000 = 15%

Points

Formula: 1 point = 1% of the loan amount

Example: A buyer borrows $280,000 and pays 2 discount points. How much does the buyer pay for points?

- $280,000 × 0.02 = $5,600

Study Strategy for Math

Memorize the core formulas (commission, LTV, cap rate, proration, area)
Practice 10–15 math problems per study session
Write out each step — don't try to do it in your head
On exam day, write the formulas on your scratch paper at the start

For more Connecticut practice problems, visit [CARealestate.com/states/connecticut](https://carealestate.com/states/connecticut).