Free Montana Math Practice Test — LicenseIQ

Question 1

An investor buys a rental house for $350,000; the land is valued at $75,000. Using straight-line depreciation over 27.5 years, the annual depreciation deduction is:

Accepted Answer

Only the building depreciates: $350,000 - $75,000 = $275,000; $275,000 / 27.5 = $10,000. Using the full price gives $12,727 (wrong).

Question 2

When competing brokerages agree to charge the same commission rate, they commit:

Accepted Answer

Agreeing on commissions among competitors is illegal price fixing under the Sherman Antitrust Act; commissions must be set independently and are always negotiable.

Question 3

A rectangular parcel measures 330 feet by 660 feet. How many acres does it contain?

Accepted Answer

Area = 330 x 660 = 217,800 sq ft; 217,800 / 43,560 = 5 acres.

Question 4

A buyer contracts to buy a home for $300,000, but it appraises at $290,000. The lender offers 75% LTV. What is the maximum loan?

Accepted Answer

LTV is applied to the LESSER of price or appraised value: $290,000 x 0.75 = $217,500. Using the $300,000 price ($225,000) is the common mistake.

Question 5

A 275-gallon heating oil tank costs $168 to fill at $4.20 per gallon. The buyer will credit the seller for the oil remaining in the tank. What is the credit?

Accepted Answer

Gallons needed = $168 / $4.20 = 40; remaining = 275 - 40 = 235 gallons; credit = 235 x $4.20 = $987.

Question 6

The seller of a rental property collected $1,800 rent for the month on the 1st. Closing is on the 10th, and the seller owns the day of closing (30-day month). What is the rent proration?

Accepted Answer

Daily rent = $1,800 / 30 = $60. Buyer owns days 11-30 = 20 days. 20 x $60 = $1,200, credited to the buyer because the seller collected rent for days the buyer will own.

Question 7

On a $250,000 loan, how much is 2 discount points?

Accepted Answer

1 point = 1% of the loan. 2 points = 0.02 x $250,000 = $5,000.

Question 8

A broker's commission becomes due from funds in the trust account. The broker must withdraw it within:

Accepted Answer

ARM 24.210.426(3)(h) requires earned broker money to be withdrawn within ten business days after it becomes due. Leaving it in longer is commingling.

Question 9

A lender approves a $276,000 loan and the buyer wants to keep an 80% LTV. What is the maximum purchase price?

Accepted Answer

Purchase price = loan / LTV = $276,000 / 0.80 = $345,000. ($220,800 wrongly multiplies by 0.80.)

Question 10

Annual taxes are $3,650. Using a 365-day year, what is the daily proration amount?

Accepted Answer

$3,650 / 365 = $10 per day. (The course's default convention is a 360-day year; this question specifies 365.)

Question 11

A lender offers a 95% LTV loan. The buyer has $18,000 for the down payment. What is the maximum purchase price?

Accepted Answer

At 95% LTV the down payment is 5% of price. Price = $18,000 / 0.05 = $360,000; loan = $342,000.

Question 12

A broker earned a $15,750 commission on a $450,000 sale. What was the commission rate?

Accepted Answer

Rate = commission / sale price = $15,750 / $450,000 = 0.035 = 3.5%.

Question 13

A home sells for $520,000 with a 5% commission. The listing broker pays 2.5% to the buyer's broker and splits the listing side 60/40 with the listing salesperson (salesperson gets 60%). How much does the listing salesperson earn?

Accepted Answer

Total = $520,000 x 0.05 = $26,000. Buyer broker gets 2.5% = $13,000, leaving $13,000 for the listing side. Salesperson = $13,000 x 0.60 = $7,800.

Question 14

A buyer forfeits $9,000 of earnest money. The written listing agreement splits forfeited earnest money 50/50 between brokerage and seller, but the brokerage's share may not exceed the commission it would have earned (3% of $280,000). How much does the brokerage receive?

Accepted Answer

Half of $9,000 is $4,500. The would-be commission is $280,000 x 0.03 = $8,400. Because $4,500 is less than $8,400, the cap does not reduce it; the brokerage receives $4,500 and the seller $4,500.

Question 15

On the $20,000 commission above, the listing broker keeps 50% and pays 50% to the buyer's broker. How much does the buyer's broker receive?

Accepted Answer

$20,000 x 0.50 = $10,000 to the buyer's broker.

Question 16

An investment property with NOI of $63,000 sells for $900,000. What is the capitalization rate?

Accepted Answer

Cap rate = NOI / value = $63,000 / $900,000 = 0.07 = 7%.

Question 17

Under the Code of Ethics, commission disputes between REALTORS associated with different firms are generally resolved through:

Accepted Answer

Article 17 requires REALTORS to mediate or arbitrate contractual and specific non-contractual disputes with other REALTORS through the association.

Question 18

A buyer purchases a $300,000 home with a $60,000 down payment. What is the loan-to-value (LTV) ratio?

Accepted Answer

Loan = $300,000 - $60,000 = $240,000; $240,000 / $300,000 = 80% LTV. (20% is the down payment percentage.)

Question 19

A broker sells a ranch after an oral agreement with the owner for a 5% commission. The owner refuses to pay. Under Montana law the broker:

Accepted Answer

MCA 28-2-903(1)(e) requires a written agreement, subscribed by the party to be charged, to employ an agent or broker to buy or sell real estate for compensation.

Question 20

Depositing a broker's commission check into the trust account and leaving it there indefinitely is:

Accepted Answer

ARM 24.210.426(3)(q) prohibits commingling trust funds with personal funds, and earned money must be withdrawn within 10 business days.

Question 21

A salesperson earns $6,000 on a $150,000 sale. What was the commission rate?

Accepted Answer

Rate = commission / sale price = $6,000 / $150,000 = 0.04 = 4%.

Question 22

When may a Montana broker take a commission out of earnest money held in trust?

Accepted Answer

ARM 24.210.426(3)(i) prohibits taking commission from earnest money until the transaction closes or terminates.

Question 23

A trust account bank statement shows $52,300. Outstanding checks total $4,100 and a $1,800 deposit is in transit. The transaction ledgers total $50,000. What is the result of the reconciliation?

Accepted Answer

Adjusted bank balance = $52,300 - $4,100 + $1,800 = $50,000, which equals the ledger total, so the account reconciles. Adding outstanding checks instead of subtracting them, or subtracting the deposit in transit, produces the wrong figures.

Question 24

A Montana home sells for $460,000. The listing brokerage's commission is 2.5%, and the listing salesperson receives 65% of it. What is the salesperson's share?

Accepted Answer

Brokerage commission: $460,000 x 0.025 = $11,500. Salesperson's share: $11,500 x 0.65 = $7,475. $11,500 is the brokerage total and $4,025 is the brokerage's retained 35%.

Question 25

A buyer brokerage receives 2.7% of a $395,000 price. The brokerage pays a 25% referral fee to a licensed out-of-area broker, then splits the remainder 70/30 with its salesperson (70% to the salesperson). What does the salesperson receive?

Accepted Answer

Commission: $395,000 x 0.027 = $10,665. After the 25% referral ($2,666.25), $7,998.75 remains. Salesperson: $7,998.75 x 0.70 = $5,599.13 (rounded). The referral is lawful because the recipient is licensed.

Montana real estate math practice test

1. An investor buys a rental house for $350,000; the land is valued at $75,000. Using straight-line depreciation over 27.5 years, the annual depreciation deduction is:

2. When competing brokerages agree to charge the same commission rate, they commit:

3. A rectangular parcel measures 330 feet by 660 feet. How many acres does it contain?

4. A buyer contracts to buy a home for $300,000, but it appraises at $290,000. The lender offers 75% LTV. What is the maximum loan?

5. A 275-gallon heating oil tank costs $168 to fill at $4.20 per gallon. The buyer will credit the seller for the oil remaining in the tank. What is the credit?

6. The seller of a rental property collected $1,800 rent for the month on the 1st. Closing is on the 10th, and the seller owns the day of closing (30-day month). What is the rent proration?

7. On a $250,000 loan, how much is 2 discount points?

8. A broker's commission becomes due from funds in the trust account. The broker must withdraw it within:

9. A lender approves a $276,000 loan and the buyer wants to keep an 80% LTV. What is the maximum purchase price?

10. Annual taxes are $3,650. Using a 365-day year, what is the daily proration amount?

11. A lender offers a 95% LTV loan. The buyer has $18,000 for the down payment. What is the maximum purchase price?

12. A broker earned a $15,750 commission on a $450,000 sale. What was the commission rate?

13. A home sells for $520,000 with a 5% commission. The listing broker pays 2.5% to the buyer's broker and splits the listing side 60/40 with the listing salesperson (salesperson gets 60%). How much does the listing salesperson earn?

14. A buyer forfeits $9,000 of earnest money. The written listing agreement splits forfeited earnest money 50/50 between brokerage and seller, but the brokerage's share may not exceed the commission it would have earned (3% of $280,000). How much does the brokerage receive?

15. On the $20,000 commission above, the listing broker keeps 50% and pays 50% to the buyer's broker. How much does the buyer's broker receive?

16. An investment property with NOI of $63,000 sells for $900,000. What is the capitalization rate?

17. Under the Code of Ethics, commission disputes between REALTORS associated with different firms are generally resolved through:

18. A buyer purchases a $300,000 home with a $60,000 down payment. What is the loan-to-value (LTV) ratio?

19. A broker sells a ranch after an oral agreement with the owner for a 5% commission. The owner refuses to pay. Under Montana law the broker:

20. Depositing a broker's commission check into the trust account and leaving it there indefinitely is:

21. A salesperson earns $6,000 on a $150,000 sale. What was the commission rate?

22. When may a Montana broker take a commission out of earnest money held in trust?

23. A trust account bank statement shows $52,300. Outstanding checks total $4,100 and a $1,800 deposit is in transit. The transaction ledgers total $50,000. What is the result of the reconciliation?

24. A Montana home sells for $460,000. The listing brokerage's commission is 2.5%, and the listing salesperson receives 65% of it. What is the salesperson's share?

25. A buyer brokerage receives 2.7% of a $395,000 price. The brokerage pays a 25% referral fee to a licensed out-of-area broker, then splits the remainder 70/30 with its salesperson (70% to the salesperson). What does the salesperson receive?

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