Question 1

A home sells for $400,000 with a 6% total commission. If the commission is split 50/50 between listing and buyer sides, and the listing agent has a 70/30 broker split, how much does the listing agent receive?

Accepted Answer

Total commission = $400,000 × 6% = $24,000. Listing side = $24,000 × 50% = $12,000. Agent's share at 70% = $12,000 × 70% = $8,400.

Question 2

Annual property taxes of $5,475 are paid in arrears. The property closes on September 1. Using a 365-day year, how much does the seller owe the buyer at closing for prorated taxes?

Accepted Answer

Daily rate = $5,475 / 365 = $15/day. From January 1 through August 31 = 243 days (31+28+31+30+31+30+31+31). Seller owes = 243 × $15 = $3,645. The closest answer is $3,650, accounting for rounding conventions used in practice.

Question 3

A seller wants to net $250,000 after paying a 5% commission. What must the property sell for?

Accepted Answer

If commission is 5%, the seller nets 95% of the sale price. Sale price = Net ÷ (1 - commission rate) = $250,000 ÷ 0.95 = $263,157.89, rounded to $263,158. A common mistake is to multiply $250,000 × 1.05 = $262,500, which does not account for the fact that the commission is 5% of the sale price, not of the net.

Question 4

A rectangular parcel measures 330 feet by 660 feet. How many acres is this parcel? (1 acre = 43,560 sq ft)

Accepted Answer

Area = 330 ft × 660 ft = 217,800 sq ft. Acres = 217,800 ÷ 43,560 = 5 acres. Knowing that 1 acre = 43,560 sq ft is essential for real estate math. Also useful: 1 mile = 5,280 ft; a section = 640 acres; a quarter-section = 160 acres.

Question 5

A property is purchased for $180,000. Three years later it is sold for $207,000. What is the percentage of appreciation?

Accepted Answer

Appreciation = (Sale Price - Purchase Price) ÷ Purchase Price = ($207,000 - $180,000) ÷ $180,000 = $27,000 ÷ $180,000 = 0.15 = 15%. This measures total appreciation over the 3-year period, not annual appreciation.

Question 6

A borrower's gross monthly income is $7,500. Using a maximum front-end (housing) debt-to-income ratio of 28%, what is the maximum allowable monthly housing payment?

Accepted Answer

Maximum housing payment = $7,500 × 28% = $2,100. The front-end ratio (also called the housing ratio) compares the monthly housing expense (principal, interest, taxes, and insurance — PITI) to gross monthly income. Conventional lenders often use 28% as the front-end ratio and 36% as the back-end (total debt) ratio.

Question 7

A comparable sale recently closed at $310,000. The comp has a pool valued at $15,000 that the subject property lacks. After adjusting for the pool, what is the adjusted sale price of the comparable?

Accepted Answer

In the sales comparison approach, adjustments are made to the comparable, not the subject. Because the comp has a feature (pool) the subject lacks, the comp is superior — so we subtract the adjustment from the comp's sale price. Adjusted price = $310,000 - $15,000 = $295,000. The rule: if the comp is better, subtract; if the comp is inferior, add.

Question 8

A property is assessed at 80% of its market value of $350,000. The tax rate is $2.50 per $100 of assessed value. What is the annual property tax?

Accepted Answer

Assessed value = $350,000 × 80% = $280,000. Tax = $280,000 ÷ $100 × $2.50 = 2,800 × $2.50 = $7,000. Property taxes are calculated on assessed value (which may be a percentage of market value) multiplied by the mill rate or tax rate. Be sure to divide by $100 (or $1,000 for mill rates) before multiplying by the rate.

Question 9

A lender requires a 20% down payment on a home. If the buyer has saved $65,000 for a down payment, what is the maximum purchase price the buyer can afford?

Accepted Answer

If down payment = 20% of purchase price, then purchase price = down payment ÷ 20% = $65,000 ÷ 0.20 = $325,000. The loan amount would be $325,000 - $65,000 = $260,000, representing an 80% LTV. This is a straightforward division problem using the part/whole relationship.

Question 10

An investment property generates $36,000 in annual gross rent. After vacancy and collection losses of 5% and operating expenses of $14,000, what is the net operating income (NOI)?

Accepted Answer

Effective gross income = $36,000 × (1 - 0.05) = $36,000 × 0.95 = $34,200. NOI = EGI - Operating Expenses = $34,200 - $14,000 = $20,200. NOI excludes debt service (mortgage payments) and income taxes. It is the starting point for income approach valuation and cap rate calculations.

Real Estate Math Practice Questions

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