Montana Real Estate Salesperson Exam — All Questions

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.

What is one month of simple interest on a $150,000 loan at a 5% annual rate?

• a.$625✓
• b.$750
• c.$7,500
• d.$600

Annual interest = $150,000 x 0.05 = $7,500; one month = $7,500 / 12 = $625. Interest for a period = Principal x Rate x Time, and here the time is 1/12 of a year.

A borrower pays $9,000 in interest during the first year on a $150,000 interest-only loan. What is the annual interest rate?

• a.9%
• b.6.5%
• c.6%✓
• d.5%

Rate = annual interest / principal = $9,000 / $150,000 = 0.06 = 6%. Dividing the interest paid by the loan balance backs into the rate.

An interest-only loan requires a monthly interest payment of $800 at an annual rate of 6%. What is the loan's principal balance?

• a.$133,333
• b.$16,000
• c.$96,000
• d.$160,000✓

Annualize the payment: $800 x 12 = $9,600 per year. Principal = annual interest / rate = $9,600 / 0.06 = $160,000. Working backward from the payment and rate reveals the balance.

An adjustable-rate mortgage has a margin of 2.5% and is tied to an index currently at 4%. Ignoring any caps, what is the fully indexed rate at the next adjustment?

• a.2.5%
• b.6.5%✓
• c.4%
• d.1.5%

The fully indexed rate = index + margin = 4% + 2.5% = 6.5%. The margin is the lender's fixed markup that stays constant; the index moves with the market. The start (teaser) rate may differ, but the fully indexed rate drives future adjustments.

An ARM currently at 3% has a margin of 2.5%, an index of 4%, and a 2% periodic (per-adjustment) cap. At the first adjustment, what is the new rate?

• a.6.5%
• b.7%
• c.3%
• d.5%✓

The fully indexed rate would be 4% + 2.5% = 6.5%, but the 2% periodic cap limits any single adjustment to a 2-point increase from the current 3%, capping the new rate at 5%. Caps protect the borrower by limiting how fast the rate can climb.

Each discount point equals 1% of the loan amount. How much do 3 discount points cost on a $250,000 loan?

• a.$2,500
• b.$750
• c.$25,000
• d.$7,500✓

One point = 1% of the loan = $250,000 x 0.01 = $2,500. Three points = 3 x $2,500 = $7,500. Points are a one-time, up-front charge calculated on the loan amount, not the sale price.

If a lender's rule of thumb is that each discount point paid raises the lender's yield by about 1/8% (0.125%), roughly how many points must be charged to raise the yield by 0.5%?

• a.8 points
• b.2 points
• c.4 points✓
• d.6 points

Points needed = desired yield increase / yield per point = 0.5% / 0.125% = 4 points. Buyers or sellers 'buy down' the rate by paying points that boost the lender's effective return.

A buyer agrees to pay 2 discount points on a $300,000 loan. What is the dollar cost of the points?

• a.$600
• b.$3,000
• c.$60,000
• d.$6,000✓

Two points = 2% of the loan = $300,000 x 0.02 = $6,000. Points are always a percentage of the loan amount.

An income property produces net operating income (NOI) of $60,000 per year. If investors require an 8% capitalization rate, what is the indicated value?

• a.$666,667
• b.$480,000
• c.$750,000✓
• d.$4,800

Using IRV, Value = Income / Rate = $60,000 / 0.08 = $750,000. A lower cap rate produces a higher value, and vice versa. Multiplying instead of dividing ($60,000 x 0.08) gives the incorrect $4,800.

A commercial building valued at $1,200,000 generates NOI of $96,000. What is the capitalization rate?

• a.9.6%
• b.8%✓
• c.6%
• d.12.5%

Cap rate = NOI / value = $96,000 / $1,200,000 = 0.08 = 8%. The cap rate expresses the property's unleveraged annual return as a percentage of its price.

An investor buys a property for $500,000 at a 7.5% capitalization rate. What annual net operating income does that imply?

• a.$37,500✓
• b.$66,667
• c.$3,750
• d.$46,500

NOI = Value x Rate = $500,000 x 0.075 = $37,500. Rearranging IRV, the income equals the value multiplied by the cap rate.

A rental has potential gross income of $100,000, a 5% vacancy and collection loss, and $35,000 of annual operating expenses. What is its net operating income?

• a.$95,000
• b.$60,000✓
• c.$65,000
• d.$45,000

Effective gross income = $100,000 - (5% x $100,000 = $5,000) = $95,000. NOI = $95,000 - $35,000 operating expenses = $60,000. Note that mortgage debt service is NOT an operating expense and is never subtracted when computing NOI.

A home sold for $240,000 and rents for $2,000 per month. What is its gross rent multiplier (GRM) based on monthly rent?

• a.480
• b.12
• c.10
• d.120✓

Monthly GRM = price / monthly rent = $240,000 / $2,000 = 120. The GRM is a quick screening ratio; dividing by annual rent instead would give the gross income multiplier of 10.

Comparable properties in an area sell at a monthly GRM of 110. A subject property rents for $1,800 per month. What value does the GRM indicate?

• a.$180,000
• b.$237,600
• c.$198,000✓
• d.$16,364

Value = GRM x monthly rent = 110 x $1,800 = $198,000. Once a market-derived GRM is known, multiplying it by the subject's rent gives a fast value estimate.

An investor uses a gross income multiplier (GIM) of 8 based on ANNUAL income. If a property's annual gross income is $48,000, what is its indicated value?

• a.roughly $96,000
• b.about $48,000
• c.$384,000✓
• d.around $6,000

Value = GIM x annual gross income = 8 x $48,000 = $384,000. The GIM works like the GRM but uses annual gross income rather than monthly rent.

For federal income-tax purposes, a residential rental building (excluding land) is depreciated straight-line over 27.5 years. If the depreciable improvement value is $275,000, what is the annual depreciation deduction?

• a.$7,051
• b.$10,000✓
• c.$5,000
• d.$27,500

Straight-line depreciation = improvement value / recovery period = $275,000 / 27.5 = $10,000 per year. Only the improvements are depreciated; land is never depreciated because it is considered to have an unlimited life.

Nonresidential (commercial) real property is depreciated straight-line over 39 years for federal tax purposes. What is the annual depreciation on a commercial building valued at $390,000 (excluding land)?

• a.$9,750
• b.$39,000
• c.$10,000✓
• d.$14,182

Annual depreciation = $390,000 / 39 = $10,000. Commercial improvements use a 39-year recovery period, versus 27.5 years for residential rentals.

An investor pays $400,000 for a residential rental; 25% of the value is allocated to land. Using a 27.5-year period, what is the approximate annual depreciation deduction?

• a.$14,545
• b.$3,636
• c.$10,909✓
• d.$40,000

Land is not depreciable. Improvements = $400,000 x (1 - 0.25) = $300,000. Annual depreciation = $300,000 / 27.5 = $10,909. Allocating value between land and building first is essential, since only the building is written off.