Utah Real Estate Math Practice: Key Formulas and Problems

# Utah Real Estate Math Practice: Key Formulas and Problems

Real estate math questions on the Utah PSI exam test your ability to apply formulas accurately under time constraints. Here are the core formulas and worked practice problems.

Core Formulas

Commission Commission = Sale Price x Rate

Down Payment and Loan Amount Loan Amount = Purchase Price - Down Payment LTV = Loan Amount / Purchase Price x 100

Proration Daily Rate = Annual Amount / 365 (or 360 for banker's year) Party's share = Daily Rate x Days Responsible

Capitalization Rate Cap Rate = Net Operating Income / Value

Gross Rent Multiplier (GRM) GRM = Sale Price / Gross Annual Rent

Monthly Interest (First Payment) Monthly Interest = Loan Balance x Annual Rate / 12

Points Each point = 1% of the loan amount

Practice Problems

Problem 1 — Commission with Split: A Salt Lake City home sells for $520,000. Total commission is 5%. The listing brokerage and the selling brokerage split the commission 50/50. The listing agent receives 55% of her brokerage's share. What does the listing agent earn?

Total commission = 520,000 x 0.05 = $26,000 Each brokerage = 26,000 / 2 = $13,000 Listing agent = 13,000 x 0.55 = $7,150

Problem 2 — LTV and PMI Threshold: A buyer purchases a home for $440,000 with a $55,000 down payment. What is the LTV? Does the buyer need PMI?

Loan = 440,000 - 55,000 = $385,000 LTV = 385,000 / 440,000 = 87.5% Since LTV exceeds 80%, PMI is required.

Problem 3 — Proration (Seller Paid in Advance): Annual property taxes of $3,650 were paid in advance by the seller. Closing is September 15. The buyer takes ownership starting September 16. Using a 365-day year, how much does the buyer owe the seller for the prepaid taxes?

Days remaining after closing (Sept 16 to Dec 31) = 107 days Daily rate = 3,650 / 365 = $10/day Buyer owes seller = 107 x $10 = $1,070

Problem 4 — Capitalization Rate: A Provo commercial property has annual gross income of $96,000. Operating expenses are $36,000. A buyer wants a 7.5% cap rate. What is the maximum price?

NOI = 96,000 - 36,000 = $60,000 Max price = 60,000 / 0.075 = $800,000

Problem 5 — Points on a Loan: A buyer takes a $310,000 mortgage and pays 2 discount points to lower the interest rate. What is the cost of the points?

1 point = 1% of loan amount = $3,100 2 points = $6,200

Calculator Tips

PSI provides an on-screen calculator. Write each step on scratch paper before calculating to avoid entry errors. For proration questions, establish the daily rate first, then multiply. For commission splits, work from the total outward through each level of the split.