Pennsylvania Real Estate Exam Math Practice Problems

How Much Math Is on the Pennsylvania Exam?

Math questions account for roughly 10–15% of the 110-question Pennsylvania salesperson exam. That is approximately 11–17 questions. Passing requires 83 correct answers, so strong math performance meaningfully improves your margin.

The Pennsylvania exam includes both standard national math (commission splits, prorations, loan calculations) and Pennsylvania-specific math (transfer tax calculations). Master both.

Core Formulas

Memorize these before exam day:

Commission: Commission = Sale Price x Commission Rate

Transfer Tax (PA): Tax = Sale Price x 0.02 (split: Buyer's share = Sale Price x 0.01; Seller's share = Sale Price x 0.01 if split 50/50)

Loan-to-Value: LTV = Loan Amount / Property Value

Debt-to-Income: DTI = Monthly Debt Payments / Gross Monthly Income

Proration Daily Rate: Daily Rate = Annual Amount / 365

Capitalization Rate: Cap Rate = NOI / Property Value

Net Operating Income: NOI = Gross Income - Operating Expenses

Practice Problem 1 — Pennsylvania Transfer Tax

A home in Philadelphia sells for $320,000. The purchase agreement allocates transfer tax as is customary in Pennsylvania. How much does the buyer pay in transfer tax?

Step 1: Total transfer tax = 320,000 x 0.02 = 6,400

Step 2: Buyer's share (50%) = 6,400 / 2 = 3,200

Answer: Buyer pays $3,200

Note: The seller also pays $3,200. Always check the agreement — the 50/50 split is customary but not legally required.

Practice Problem 2 — Commission Calculation

A property sells for $455,000 with a 6% commission split equally between listing and buyer's broker. The listing agent receives 55% of the listing broker's share. How much does the listing agent earn?

Step 1: Total commission = 455,000 x 0.06 = 27,300

Step 2: Listing broker's share = 27,300 / 2 = 13,650

Step 3: Listing agent's share = 13,650 x 0.55 = 7,507.50

Answer: $7,507.50

Practice Problem 3 — Proration (Seller-Paid Tax)

A seller has paid annual property taxes of $5,840 for the full year. Closing is on April 1. How much tax credit does the buyer receive? (Using 365-day year; seller paid through December 31.)

Step 1: Daily tax rate = 5,840 / 365 = 16.00 per day

Step 2: Days remaining April 1 to December 31 = 275 days

Step 3: Buyer's credit (seller's prepaid tax covering buyer's period) = 16.00 x 275 = 4,400

Answer: Buyer receives a $4,400 credit

Practice Problem 4 — Loan Qualification

A buyer earns $6,500 per month gross income. The lender uses a 28% front-end ratio and a 36% back-end ratio. Monthly non-housing debts are $600. What is the maximum monthly mortgage payment?

Step 1: Front-end maximum = 6,500 x 0.28 = 1,820

Step 2: Back-end maximum total debt = 6,500 x 0.36 = 2,340

Step 3: Back-end maximum mortgage = 2,340 - 600 = 1,740

Step 4: Take the lower of the two = $1,740

Answer: Maximum monthly mortgage payment = $1,740

Practice Problem 5 — Capitalization Rate

An office building sells for $1,250,000. Annual gross rents are $140,000. Annual operating expenses are $48,000. What is the cap rate?

Step 1: NOI = 140,000 - 48,000 = 92,000

Step 2: Cap Rate = 92,000 / 1,250,000 = 0.0736 = 7.36%

Answer: 7.36%

Pennsylvania Transfer Tax: Key Details

Total rate: 2% (1% state + 1% local)
Typical allocation: 50/50 buyer/seller
Based on the greater of: sale price or assessed value (for certain properties)
Paid at closing through the settlement statement
Exam questions may test: total tax, buyer's share, seller's share, or allocation if the split is stated differently in the agreement

Exam Day Math Tips

Use the on-screen calculator PSI provides — do not try to do multi-step problems in your head
Write intermediate steps on your scratch paper
For proration: always confirm whether the daily rate should be based on 30-day months (360-day year) or calendar days (365-day year) — the question will specify
Double-check your decimal placement — a misplaced decimal in a commission or tax calculation will always produce a wrong answer

For more Pennsylvania exam math practice, visit [CARealestate.com/states/pennsylvania](https://carealestate.com/states/pennsylvania).