Free Michigan Math Practice Test — LicenseIQ

Question 1

A new highway interchange built next to a residential subdivision lowers home values. This is:

Accepted Answer

Loss in value caused by factors outside the property boundaries is external obsolescence.

Question 2

A buyer purchases a $275,000 home with an 80% LTV loan and pays 2.5 discount points. What do the points cost?

Accepted Answer

Loan = $275,000 x 0.80 = $220,000; points = $220,000 x 0.025 = $5,500. ($6,875 wrongly applies points to the price.)

Question 3

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 4

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 5

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 6

Annual taxes of $5,400 are paid in arrears at year-end. Closing is June 15, and the seller owns the day of closing. Using a 360-day year, what is the proration?

Accepted Answer

Daily = $5,400 / 360 = $15. Seller owned Jan 1-Jun 15 = 5 months + 15 days = 165 days. 165 x $15 = $2,475. Because the buyer will pay the whole bill later, the seller is debited and the buyer credited.

Question 7

A house is L-shaped: one section is 40 ft by 30 ft and the other is 20 ft by 15 ft. At $185 per square foot, what is the estimated cost to build?

Accepted Answer

Area = (40 x 30) + (20 x 15) = 1,200 + 300 = 1,500 sq ft; 1,500 x $185 = $277,500.

Question 8

A listing agreement in which the broker earns a commission regardless of who sells the property is a(n):

Accepted Answer

In an exclusive right-to-sell listing, the listing broker earns a commission no matter who procures the buyer, even the owner. (Reclassified to section 6 / CORE.)

Question 9

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 10

One discount point equals what percentage of the loan amount?

Accepted Answer

One point = 1% of the loan amount (not the purchase price), paid to lower the interest rate.

Question 11

Monthly rent is $1,850. What is the largest security deposit the landlord may collect?

Accepted Answer

1.5 x $1,850 = $2,775. $3,700 would be two months' rent, which exceeds the cap.

Question 12

A borrower pays $4,500 for 1.5 discount points. What is the loan amount?

Accepted Answer

Loan = cost of points / points as a percentage = $4,500 / 0.015 = $300,000.

Question 13

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 14

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 15

A listing where the seller may sell themselves without owing commission, but only the listing broker among agents is protected, is:

Accepted Answer

In an exclusive agency listing, the seller pays no commission on a self-sale, but the listing broker is protected if any broker sells it. (Reclassified to section 6 / CORE.)

Question 16

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 17

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 18

A Michigan broker may lawfully pay part of a commission to which of the following?

Accepted Answer

MCL 339.2512(1)(h) allows a licensed Michigan broker to pay a commission to a broker licensed in another state who does not negotiate in Michigan. Every other choice is an unlicensed (for real estate) person being paid for real estate-related activity.

Question 19

In October 2026, under the schedule then in effect, how many parcels may a 50-acre parent parcel be divided into (before any bonus parcels)?

Accepted Answer

From March 24, 2026 to March 24, 2027, the first 10 acres allow 4 parcels, plus 1 for each whole 10 acres beyond the first 10: 40 / 10 = 4 more. 4 + 4 = 8. Fourteen would apply the 10-parcel base that takes effect March 24, 2027.

Question 20

A home in Oakland County sells for $275,000. Using the state rate of $3.75 per $500 and the county rate of $0.55 per $500, what is the total transfer tax?

Accepted Answer

$275,000 / 500 = 550 units. State: 550 x $3.75 = $2,062.50. County: 550 x $0.55 = $302.50. Total = $2,365.00. $2,062.50 is the state tax alone.

Question 21

A home sells for $189,900. What is the Michigan state transfer tax at $3.75 per $500 or fraction thereof?

Accepted Answer

$189,900 / 500 = 379.8, which rounds up to 380 units because any fraction of $500 is taxed. 380 x $3.75 = $1,425.00. $1,424.25 multiplies the unrounded 379.8 units.

Question 22

A home's taxable value is $140,000 and the school operating levy is 18 mills. How much does the Principal Residence Exemption save the owner each year?

Accepted Answer

Savings = $140,000 x 18 / 1,000 = $2,520. $1,260 incorrectly applies the millage to half the taxable value (taxable value is already the base).

Question 23

A division creates a 45-acre accessible parcel from a parent parcel. For counting purposes under MCL 560.108, the 45-acre parcel:

Accepted Answer

MCL 560.108(4) provides that an accessible parcel of 40 acres or more is not counted toward the limits and is not subject to section 109.

Question 24

Under Michigan's statute of frauds, an agreement to pay a real estate commission:

Accepted Answer

MCL 566.132(1)(e) expressly lists agreements to pay a commission for the sale of an interest in real estate among those that must be in writing and signed.

Question 25

To sue a seller for a commission in Michigan, a broker generally must show:

Accepted Answer

MCL 339.2512a requires the plaintiff to prove licensure, and MCL 566.132(1)(e) requires the commission promise to be in a signed writing. Procuring cause alone is not enough without the writing.

Michigan real estate math practice test

1. A new highway interchange built next to a residential subdivision lowers home values. This is:

2. A buyer purchases a $275,000 home with an 80% LTV loan and pays 2.5 discount points. What do the points cost?

3. 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?

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

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

6. Annual taxes of $5,400 are paid in arrears at year-end. Closing is June 15, and the seller owns the day of closing. Using a 360-day year, what is the proration?

7. A house is L-shaped: one section is 40 ft by 30 ft and the other is 20 ft by 15 ft. At $185 per square foot, what is the estimated cost to build?

8. A listing agreement in which the broker earns a commission regardless of who sells the property is a(n):

9. 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?

10. One discount point equals what percentage of the loan amount?

11. Monthly rent is $1,850. What is the largest security deposit the landlord may collect?

12. A borrower pays $4,500 for 1.5 discount points. What is the loan amount?

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

14. 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?

15. A listing where the seller may sell themselves without owing commission, but only the listing broker among agents is protected, is:

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

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

18. A Michigan broker may lawfully pay part of a commission to which of the following?

19. In October 2026, under the schedule then in effect, how many parcels may a 50-acre parent parcel be divided into (before any bonus parcels)?

20. A home in Oakland County sells for $275,000. Using the state rate of $3.75 per $500 and the county rate of $0.55 per $500, what is the total transfer tax?

21. A home sells for $189,900. What is the Michigan state transfer tax at $3.75 per $500 or fraction thereof?

22. A home's taxable value is $140,000 and the school operating levy is 18 mills. How much does the Principal Residence Exemption save the owner each year?

23. A division creates a 45-acre accessible parcel from a parent parcel. For counting purposes under MCL 560.108, the 45-acre parcel:

24. Under Michigan's statute of frauds, an agreement to pay a real estate commission:

25. To sue a seller for a commission in Michigan, a broker generally must show:

Sources