Colorado Real Estate Broker Exam — All Questions

A home sells for $340,000 with a total commission of 6%. The listing brokerage receives 50% of the total commission, and the listing agent receives 60% of the listing brokerage's share. How much does the listing agent earn?

• a.$10,200
• b.$6,120✓
• c.$4,080
• d.$20,400

First find the total commission: $340,000 x 6% = $20,400. The listing brokerage's share is 50%: $20,400 x 0.50 = $10,200. The listing agent then receives 60% of that: $10,200 x 0.60 = $6,120. The $20,400 figure is the total commission and $10,200 is the brokerage's full share, not the agent's; $4,080 mistakenly takes 40% instead of 60%.

A seller wants to net $200,000 from a sale after paying a 6% commission (and no other costs). Rounded to the nearest dollar, what must the sale price be?

• a.$212,000
• b.$200,600
• c.$212,766✓
• d.$188,000

After a 6% commission the seller keeps 94% of the sale price, so Sale Price x 0.94 = $200,000, giving Sale Price = $200,000 / 0.94 = $212,765.96, which rounds to $212,766. A common error is to add 6% to $200,000 (getting $212,000), but you cannot simply add the rate back because the commission is charged on the higher sale price, not on the net.

A rectangular parcel measures 200 feet by 217.8 feet. Given that one acre equals 43,560 square feet, how many acres does the parcel contain?

• a.2 acres
• b.1.5 acres
• c.1 acre✓
• d.0.5 acre

Area = length x width = 200 ft x 217.8 ft = 43,560 square feet. Since one acre is exactly 43,560 square feet, the parcel is 43,560 / 43,560 = 1 acre. The other answers result from dividing or multiplying the area incorrectly; memorizing that an acre equals 43,560 square feet makes this a one-step conversion.

A property sells for $425,000 at a 6% commission that is split equally between the listing and selling brokerages. How much does each brokerage receive?

• a.$6,375
• b.$2,550
• c.$12,750✓
• d.$25,500

Total commission = $425,000 x 0.06 = $25,500. Split equally, each brokerage receives $25,500 / 2 = $12,750. The $25,500 is the full commission, and $6,375 would be a further half of one brokerage's share.

A $310,000 sale pays a 7% total commission. The listing brokerage keeps 50%, and the listing agent receives 70% of the brokerage's half. How much does the agent earn?

• a.$15,190
• b.$6,510
• c.$10,850
• d.$7,595✓

Total commission = $310,000 x 0.07 = $21,700. The brokerage's half = $10,850. The agent's 70% share = $10,850 x 0.70 = $7,595. The $10,850 is the brokerage's full half, and using 60% would give $6,510.

A seller wants to net $150,000 after paying a 5% commission and $3,000 in other closing costs. Rounded to the nearest dollar, what sale price is required?

• a.$161,053✓
• b.$161,000
• c.$160,500
• d.$157,500

The seller must net $150,000 plus $3,000 in costs = $153,000 after commission, and keeps 95% of the price: Price = $153,000 / 0.95 = $161,052.63, which rounds to $161,053. You cannot simply add 5% to the net, because the commission is charged on the higher sale price.

Annual property taxes are $3,650, paid in arrears. Using a 365-day year, closing is on the 90th day of the year and the seller is responsible through the day before closing (89 days). What is the seller's share credited to the buyer?

• a.$890✓
• b.$900
• c.$875
• d.$1,000

Daily tax = $3,650 / 365 = $10 per day. The seller owes for 89 days through the day before closing: 89 x $10 = $890, credited to the buyer since taxes are paid in arrears. Charging the seller for 90 days would give $900.

A loan of $240,000 carries a 5% annual interest rate. What is the interest portion of the first month's payment?

• a.$1,000✓
• b.$1,200
• c.$100
• d.$12,000

Annual interest = $240,000 x 0.05 = $12,000. One month's interest = $12,000 / 12 = $1,000. The $12,000 figure is the full year's interest, and the other options come from misplacing the decimal.

A home appraises at $360,000 and the buyer obtains a $288,000 loan. What is the loan-to-value (LTV) ratio?

• a.72%
• b.20%
• c.80%✓
• d.125%

LTV = loan / value = $288,000 / $360,000 = 0.80, or 80%. The down payment is the remaining 20% ($72,000). Inverting the ratio would give 125%, which is not how LTV is calculated.

With an 80% loan-to-value loan on a $360,000 home, how much is the buyer's down payment?

• a.$72,000✓
• b.$288,000
• c.$90,000
• d.$36,000

An 80% loan covers $288,000, so the down payment is the other 20%: $360,000 x 0.20 = $72,000. The $288,000 figure is the loan amount, not the down payment.

A borrower pays 2 discount points on a $250,000 loan. How much do the points cost?

• a.$50,000
• b.$500
• c.$5,000✓
• d.$2,500

One point equals 1% of the loan, so 2 points = 2% x $250,000 = $5,000. Points are calculated on the loan amount, not the purchase price, and a single point here would be $2,500.

A rectangular lot measures 120 feet by 90 feet and sells for $12 per square foot. What is the total price?

• a.$129,600✓
• b.$2,520
• c.$1,296,000
• d.$12,960

Area = 120 x 90 = 10,800 square feet. Price = 10,800 x $12 = $129,600. Misplacing a decimal, or adding the sides for a 420-foot perimeter, produces the other figures.

A parcel contains 130,680 square feet. How many acres is that, given that one acre equals 43,560 square feet?

• a.4 acres
• b.2 acres
• c.1.5 acres
• d.3 acres✓

Acres = 130,680 / 43,560 = 3 acres. Memorizing that one acre is 43,560 square feet makes this a single division problem.

How many acres are in the NW 1/4 of the SW 1/4 of a section?

• a.80 acres
• b.40 acres✓
• c.160 acres
• d.20 acres

Multiply the fractions by 640 acres: 1/4 x 1/4 x 640 = 40 acres. Each 'quarter of a quarter' is 40 acres, whereas a single quarter-section would be 160 acres.

A home purchased for $280,000 is now worth $322,000. What is the total percent of appreciation?

• a.42%
• b.8.7%
• c.15%✓
• d.13%

Appreciation = gain / original = ($322,000 - $280,000) / $280,000 = $42,000 / $280,000 = 0.15 = 15%. Dividing by the new value instead of the original would give the wrong percentage.

A property has a net operating income of $48,000 and sells for $600,000. What is the capitalization rate?

• a.8%✓
• b.80%
• c.12.5%
• d.0.8%

Cap rate = NOI / value = $48,000 / $600,000 = 0.08 = 8%. Inverting the fraction would give 12.5 (a multiple), which is not the capitalization rate.

A building's net operating income is $75,000 and investors require a 10% capitalization rate. What is the indicated value?

• a.$825,000
• b.$75,000
• c.$750,000✓
• d.$7,500

Value = NOI / cap rate = $75,000 / 0.10 = $750,000. Multiplying by the rate to get $7,500 instead of dividing is a common error.

A rental property sold for $360,000 and rents for $3,000 per month. What is the monthly gross rent multiplier (GRM)?

• a.1,200
• b.12
• c.100
• d.120✓

GRM = price / gross rent = $360,000 / $3,000 = 120, using monthly rent. Using annual rent of $36,000 would instead give a GRM of 10, so the rent period must stay consistent.

Using a monthly gross rent multiplier of 110, a property that rents for $2,500 per month is valued at:

• a.$22,727
• b.$27,500
• c.$2,750,000
• d.$275,000✓

Value = GRM x monthly rent = 110 x $2,500 = $275,000. The GRM multiplies rent to estimate price; dividing instead would misstate the value.

A borrower pays $9,600 in annual interest on a $160,000 interest-only loan. What is the interest rate?

• a.5%
• b.6.7%
• c.6%✓
• d.16%

Rate = interest / principal = $9,600 / $160,000 = 0.06 = 6%. This rearranges the interest formula (Interest = Principal x Rate x Time) for a one-year period.

A home is assessed at $220,000 with a tax rate of $1.25 per $100 of assessed value. What is the annual property tax?

• a.$275
• b.$27,500
• c.$1,760
• d.$2,750✓

Divide the assessed value by 100 and multiply by the rate: ($220,000 / 100) x $1.25 = 2,200 x $1.25 = $2,750. Because the rate is per $100 of value, the scaling matters.

A property is assessed at $180,000 and taxed at 20 mills. What is the annual tax (one mill equals $0.001)?

• a.$3,600✓
• b.$36,000
• c.$360
• d.$900

One mill is $0.001, so 20 mills = $0.020 per dollar of value: $180,000 x 0.020 = $3,600. Equivalently, 20 mills is $20 per $1,000 of assessed value.

Monthly rent is $1,800 and closing is on the 16th of a 30-day month, with the buyer owning the property from the closing day forward. How much of the collected rent must the seller credit the buyer?

• a.$900✓
• b.$1,050
• c.$960
• d.$840

Daily rent = $1,800 / 30 = $60. The buyer owns from the 16th through the 30th = 15 days, so the seller, who collected the full month, credits the buyer 15 x $60 = $900. Counting 16 days would give $960.

A seller paid $18,000 in commission on a $300,000 sale. What commission rate is that?

• a.5%
• b.6.6%
• c.16.7%
• d.6%✓

Rate = commission / sale price = $18,000 / $300,000 = 0.06 = 6%. This rearranges Commission = Sale Price x Rate to solve for the rate.

An investor wants a 20% profit over a $250,000 purchase price. At what price must the property be sold?

• a.$270,000
• b.$290,000
• c.$312,500
• d.$300,000✓

Selling price = cost x (1 + profit rate) = $250,000 x 1.20 = $300,000. Adding only $20,000, or dividing instead of multiplying, produces the other answers.

A 2,400-square-foot home is listed at $384,000. What is the price per square foot?

• a.$16
• b.$150
• c.$1,600
• d.$160✓

Price per square foot = $384,000 / 2,400 = $160. Dividing the total price by the living area gives the per-square-foot figure used to compare homes.

A seller wants to net $250,000 in cash after paying a 5% brokerage commission and $3,000 in other closing costs. Rounded to the nearest dollar, what must the sale price be?

• a.$266,316✓
• b.$265,650
• c.$265,500
• d.$263,158

The commission is charged on the sale price, so you must gross up. Add the fixed costs to the desired net, then divide by (1 - commission rate): ($250,000 + $3,000) / (1 - 0.05) = $253,000 / 0.95 = $266,315.79, which rounds to $266,316. Simply adding 5% back to the net understates the price because the commission is figured on the larger sale price, not on the net.

A property sells for $425,000 with a 6% total commission. The listing and selling brokerages split the commission 50/50, and the listing agent receives 70% of the listing brokerage's share. How much does the listing agent earn?

• a.$25,500
• b.$8,925✓
• c.$12,750
• d.$17,850

Total commission = $425,000 x 0.06 = $25,500. The listing brokerage's half is $25,500 x 0.50 = $12,750. The listing agent's 70% cut is $12,750 x 0.70 = $8,925. The $12,750 is the brokerage's full share and $25,500 is the total commission, neither of which is the agent's take-home.

A broker earned a $14,400 commission on the sale of a $240,000 home. What commission rate did the broker charge?

• a.4.8%
• b.6.25%
• c.5.5%
• d.6%✓

Rate = commission / sale price = $14,400 / $240,000 = 0.06 = 6%. This is the basic Part = Total x Rate formula solved for the rate by dividing the part (commission) by the total (sale price).

Annual property taxes are $2,920, prorated on a 365-day year. What is the daily proration amount?

• a.$8.00 per day✓
• b.$243.33 per day
• c.$8.11 per day
• d.$80.00 per day

Daily proration on a 365-day year = annual amount / 365 = $2,920 / 365 = $8.00 per day. The $243.33 figure is the monthly amount ($2,920 / 12), and $8.11 wrongly uses a 360-day year.

Using a 365-day proration year and a daily tax rate of $8.00, what is the seller's share of taxes if the seller owned the property for 150 days of the tax year?

• a.$1,720
• b.$1,320
• c.$1,200✓
• d.$1,168

Seller's share = daily rate x days owned = $8.00 x 150 = $1,200. Multiplying the per-day amount by the exact number of days each party owns the property is the essence of a proration.

An annual insurance premium of $1,080 is prorated using a 360-day (banker's) year with 30-day months. What are the monthly and daily amounts?

• a.$90 per month and $2.96 per day
• b.$100 per month and $3.33 per day
• c.$108 per month and $3.60 per day
• d.$90 per month and $3 per day✓

On a 360-day year: monthly = $1,080 / 12 = $90, and daily = $1,080 / 360 = $3.00 (equivalently $90 / 30). The banker's year assumes every month has 30 days, which makes the daily figure a clean $3.

A tenant paid $1,500 for a full 30-day month of rent. The property closes and the buyer will own the property for 21 days of that month. Using a 30-day month, how much of the collected rent must be credited to the buyer?

• a.$700
• b.$1,050✓
• c.$1,500
• d.$450

Daily rent = $1,500 / 30 = $50. The buyer owns 21 of the 30 days, so the buyer's share of the already-collected rent = $50 x 21 = $1,050. The seller keeps the $450 for the 9 days the seller owned it; the two shares add back to the full $1,500.

Taxes of $3,650 for the year have already been PAID in full by the seller. Using a 365-day year, the seller owned the property for 100 days before closing. What amount should the buyer reimburse the seller at closing?

• a.$3,650
• b.$1,000
• c.$2,550
• d.$2,650✓

Daily = $3,650 / 365 = $10. The seller prepaid the whole year but only used 100 days ($1,000 worth); the buyer will own the remaining 265 days, so the buyer reimburses the seller $10 x 265 = $2,650. When the seller has prepaid, the buyer owes the seller for the days after closing.

A state charges a transfer tax of $0.50 for each $500 of the sale price. On a $180,000 sale, what is the transfer tax?

• a.$180✓
• b.$360
• c.$900
• d.$90

Divide the price into $500 increments: $180,000 / $500 = 360 increments. Multiply by the per-increment rate: 360 x $0.50 = $180. Keeping the units straight (dollars of tax per $500 of price) prevents off-by-a-factor errors.

A documentary transfer tax is $0.75 per $500 of value. What is the tax on a $256,000 sale?

• a.$768
• b.$512
• c.$192
• d.$384✓

$256,000 / $500 = 512 increments; 512 x $0.75 = $384. The $512 answer forgets to multiply by the $0.75 rate, and $192 uses $0.50 by mistake.

A recording jurisdiction levies a documentary stamp of $1.00 per $1,000 of the sale price, rounding the price UP to the next full $1,000 when it is not an even thousand. What is the stamp tax on a $349,400 sale?

• a.$349
• b.$349.40
• c.$700
• d.$350✓

Round $349,400 up to the next $1,000, giving $350,000. Then $350,000 / $1,000 = 350 increments x $1.00 = $350. Rounding up to the next taxable increment is a common convention worth watching for.

A fully amortizing loan of $200,000 has a 6% annual interest rate and a monthly principal-and-interest payment of $1,199.10. How much of the FIRST monthly payment is applied to principal?

• a.$199.10✓
• b.$1,000.00
• c.$1,000.90
• d.$1,199.10

Month-1 interest = balance x monthly rate = $200,000 x (0.06 / 12) = $200,000 x 0.005 = $1,000. Principal = payment - interest = $1,199.10 - $1,000 = $199.10. In an amortizing loan, early payments are mostly interest and only a small part reduces principal.

Continuing the prior loan (original $200,000 at 6%, payment $1,199.10; month-1 principal was $199.10), how much of the SECOND payment goes to principal?

• a.$199.10
• b.$999.00
• c.$1,000.00
• d.$200.10✓

New balance = $200,000 - $199.10 = $199,800.90. Month-2 interest = $199,800.90 x 0.005 = $999.00. Principal = $1,199.10 - $999.00 = $200.10. As the balance shrinks, interest falls slightly and the principal portion grows each month.

A straight (interest-only) note of $160,000 carries a 6% annual rate. What is the monthly interest payment?

• a.$666.67
• b.$9,600
• c.$960
• d.$800✓

Annual interest = $160,000 x 0.06 = $9,600. Monthly = $9,600 / 12 = $800. On an interest-only (straight) loan the payment covers only interest, and the full principal is due at maturity in a balloon.