Michigan Real Estate Broker Exam — All Questions

A seller wants to net $188,000 after paying a 6% commission and no other costs. What must the sale price be?

• a.$199,280
• b.$188,000
• c.$200,000✓
• d.$212,000

In a net-to-seller problem the commission is charged on the sale price, so you cannot simply add 6% to the net. Use Sale Price = Desired Net / (1 - commission rate) = $188,000 / (1 - 0.06) = $188,000 / 0.94 = $200,000. Check: 6% of $200,000 is $12,000, and $200,000 minus $12,000 equals the $188,000 net. Adding 6% to $188,000 (giving $199,280) is the classic wrong answer the exam includes as a trap.

A property sells for $250,000 with a 6% total commission, split equally between the listing and cooperating brokerages. If the listing agent's brokerage pays that agent 70% of its share, how much does the listing agent receive?

• a.$7,500
• b.$5,250✓
• c.$9,000
• d.$3,750

Work in steps. Total commission = 6% of $250,000 = $15,000. Split equally between the two brokerages gives each $7,500. The listing agent then receives 70% of the listing brokerage's $7,500 share = 0.70 x $7,500 = $5,250 (the brokerage keeps the remaining $2,250). The $7,500 answer forgets the agent's split, and $9,000 or $3,750 come from splitting the wrong figure. Brokers must know these layered commission splits because they set the office compensation plan.

An income property has a net operating income of $60,000 and sold for $750,000. What is the indicated capitalization rate?

• a.12.5%
• b.6%
• c.10%
• d.8%✓

The capitalization rate is found by rearranging Value = NOI / cap rate into cap rate = NOI / value = $60,000 / $750,000 = 0.08, or 8%. This is the same relationship used to value income property, just solved for the rate instead of the value. Any two of the three variables (NOI, value, cap rate) let you solve for the third. Brokers working with investors use this constantly to compare properties, since a higher cap rate signals a lower price relative to income.

A property sells for $500,000 with a 6% total commission divided equally between the listing and cooperating firms. The listing firm deducts an 8% franchise fee from its share, then pays the listing agent 60% of the remainder. What does the agent receive?

• a.$9,000.00
• b.$8,280.00✓
• c.$5,520.00
• d.$13,800.00

Work from the top down. Total commission = 6% of $500,000 = $30,000. Split equally, the listing firm's share is $15,000. The franchise fee comes off that share first: 8% of $15,000 = $1,200, leaving $13,800 of company dollar. The agent's share = 0.60 x $13,800 = $8,280. Taking 60% of $15,000 and skipping the franchise fee gives $9,000. Taking the firm's 40% instead of the agent's 60% gives $5,520. Stopping at the post-franchise figure gives $13,800. Check: $8,280 + $5,520 = $13,800, and $13,800 + $1,200 = the firm's $15,000 share.

A seller wants to net $915,000 after paying a 6% commission and $25,000 of closing costs. What must the property sell for? Round to the nearest dollar.

• a.$940,000
• b.$996,400
• c.$973,404
• d.$1,000,000✓

The commission is a percentage of the unknown sale price, so add the fixed costs to the net first and then divide. Sale price = (net + closing costs) / (1 - commission rate) = ($915,000 + $25,000) / 0.94 = $940,000 / 0.94 = $1,000,000. Adding 6% to $940,000 instead of dividing gives $996,400, the classic trap, because 6% of the smaller number is not 6% of the price. Dividing $915,000 by 0.94 and ignoring the closing costs gives $973,404. Simply adding the costs to the net gives $940,000 and omits the commission. Check: 6% of $1,000,000 = $60,000, and $1,000,000 - $60,000 - $25,000 = $915,000.

A brokerage closed 40 sides last quarter at an average price of $300,000, earning 3% on each side. Agents keep an average of 65% of the firm's commission. What is the office's company dollar?

• a.$360,000
• b.$126,000✓
• c.$234,000
• d.$252,000

Gross commission income is everything the firm collects: 40 x $300,000 x 0.03 = $360,000. Company dollar is what remains after agent splits are paid: $360,000 x (1 - 0.65) = $360,000 x 0.35 = $126,000. Reporting $360,000 confuses gross commission income with company dollar. The $234,000 figure is the agents' side, not the firm's. Applying a full 6% commission to the $12,000,000 of volume gives $720,000 of gross commission income, and $720,000 x 0.35 = $252,000. Check: agents receive $234,000, and $234,000 + $126,000 = the $360,000 of gross commission income. Company dollar, not gross commission income, is what covers office rent and overhead.

A buyer contracts to pay $355,000 for a home that appraises at $340,000. The lender lends 80% of the lesser of price or appraised value. What are the loan amount and the buyer's cash down payment?

• a.Loan $272,000; down payment $68,000
• b.Loan $272,000; down payment $83,000✓
• c.Loan $284,000; down payment $71,000
• d.Loan $272,000; down payment $71,000

The loan-to-value ratio is applied to the lesser of contract price or appraised value, so the loan is 80% of $340,000 = $272,000. The buyer still owes the full contract price, so the cash down payment is $355,000 - $272,000 = $83,000, which absorbs the $15,000 appraisal gap. Applying 80% to the $355,000 price gives a $284,000 loan and a $71,000 down payment, but the lender will not fund that amount. Taking 20% of the appraised value gives $68,000, and 20% of the price gives $71,000; both ignore the gap. Check: $272,000 + $83,000 = $355,000.

A buyer pays $400,000 for a home appraised at $425,000, financing it with a $300,000 first mortgage plus a $40,000 second lien. The lender measures loan-to-value against the lesser of price or appraised value. What is the combined loan-to-value ratio?

• a.85.0%✓
• b.80.0%
• c.75.0%
• d.10.0%

Combined loan-to-value adds every lien and divides by the lesser of price or appraised value: ($300,000 + $40,000) / $400,000 = $340,000 / $400,000 = 0.85, or 85.0%. Dividing by the $425,000 appraisal gives 80.0%, but the lower of price and value governs when the price is less. Counting only the first mortgage gives 75.0%, which is that loan's own ratio rather than the combined figure. Measuring only the second lien gives 10.0%. Check: 85% of $400,000 = $340,000, the total debt. Brokers watch this ratio because it drives mortgage insurance and secondary-market eligibility.

A buyer purchases at $325,000 with an 80% loan-to-value first mortgage and agrees to pay 2.5 discount points to buy down the rate. What do the points cost in dollars?

• a.$8,125.00
• b.$6,500.00✓
• c.$1,625.00
• d.$2,600.00

Points are charged against the loan amount, never the purchase price. The loan is 80% of $325,000 = $260,000. One point equals 1% of the loan, so 2.5 points = 0.025 x $260,000 = $6,500. Charging 2.5% against the $325,000 price gives $8,125, the most common error on this problem. Counting a single point gives $2,600. Applying the 2.5% to the $65,000 down payment gives $1,625. Check: 1% of $260,000 = $2,600, and $2,600 x 2.5 = $6,500. Points are prepaid interest and count as a finance charge, so a broker should confirm in writing who pays them.

A buyer pays $400,000 with a 75% loan, 1.5 discount points, and $3,800 of other closing costs. A $6,000 earnest money deposit is credited at settlement. How much cash must the buyer bring?

• a.$102,300✓
• b.$108,300
• c.$103,800
• d.$97,800

Build the requirement in steps. The loan is 75% of $400,000 = $300,000, so the down payment is $100,000. Points cost 1.5% of the $300,000 loan = $4,500. Adding the $3,800 of other costs gives $108,300 of total buyer charges. Earnest money already on deposit is a credit, so the buyer brings $108,300 - $6,000 = $102,300. Forgetting that credit leaves $108,300. Charging the points against the $400,000 price instead of the loan gives $103,800. Omitting the points entirely gives $97,800. Check: $102,300 + $6,000 = $108,300 = $100,000 + $4,500 + $3,800.

A $240,000 loan at 6% annual interest carries a monthly principal-and-interest payment of $1,438.92, with interest accruing on the outstanding balance. What is the first month's interest, and the balance after that payment?

• a.Interest $1,438.92; balance $240,000.00
• b.Interest $1,200.00; balance $239,761.08✓
• c.Interest $14,400.00; balance $225,600.00
• d.Interest $1,200.00; balance $238,561.08

Monthly interest = balance x annual rate / 12 = $240,000 x 0.06 / 12 = $1,200. Whatever is left of the payment reduces principal: $1,438.92 - $1,200 = $238.92, so the new balance is $240,000 - $238.92 = $239,761.08. Subtracting the whole payment from the balance gives $238,561.08 and ignores that most of an early payment is interest. Treating the entire payment as interest leaves the balance at $240,000. Using a full year's interest of $14,400 gives $225,600. Check: $1,200 + $238.92 = the $1,438.92 payment. Early amortization is nearly all interest, which is why the balance falls so slowly.

A lender quotes an amortization factor of $6.65 per $1,000 borrowed for a 30-year fixed loan at 7%. On a $285,000 loan, what is the monthly principal-and-interest payment?

• a.$1,579.38
• b.$1,662.50
• c.$1,895.25✓
• d.$1,995.00

A payment factor is quoted per $1,000 of loan, so divide the loan by 1,000 and multiply by the factor: $285,000 / $1,000 = 285 units, and 285 x $6.65 = $1,895.25. Charging interest only at 7% gives $285,000 x 0.07 / 12 = $1,662.50, a payment that repays no principal at all. Treating the 6.65 as an annual percentage rate gives $1,579.38. Rounding the factor up to $7.00 per $1,000 gives $1,995.00. Check: 285 x $6 = $1,710 and 285 x $0.65 = $185.25, which sum to $1,895.25. The factor already blends principal and interest for the stated term and rate.

A lender uses a 28% front-end housing ratio. A loan applicant's stable gross monthly income is $7,200. Under that ratio alone, what is the maximum monthly PITI payment the applicant qualifies for?

• a.$1,800.00
• b.$2,880.00
• c.$2,592.00
• d.$2,016.00✓

The front-end ratio caps housing expense at a percentage of gross monthly income, not take-home pay: $7,200 x 0.28 = $2,016. PITI means principal, interest, taxes, and insurance, plus any association dues the lender counts. Applying 36%, which is a common back-end total-debt ratio, gives $2,592 and overstates the housing allowance. Using an older 25% guideline gives $1,800, and using a 40% total-debt figure gives $2,880. Check: $2,016 / $7,200 = 0.28. A broker who pre-screens buyers with the wrong ratio sends them shopping in the wrong price range and wastes everyone's time.

A lender applies a 36% back-end ratio to total monthly debt. An applicant earns $8,400 gross monthly and pays $480 on a car, $220 on a student loan, and $100 in minimum card payments. Maximum PITI?

• a.$2,224.00✓
• b.$2,352.00
• c.$1,552.00
• d.$3,024.00

The back-end ratio limits housing plus recurring debt together. Total allowable debt = $8,400 x 0.36 = $3,024. Recurring obligations total $480 + $220 + $100 = $800. Maximum PITI = $3,024 - $800 = $2,224. Reporting $3,024 forgets to subtract the existing obligations. Using the 28% front-end ratio produces $2,352, which ignores the debts entirely. Subtracting the $800 from that front-end figure gives $1,552 and mixes the two tests. Check: ($2,224 + $800) / $8,400 = 0.36. Underwriting runs both ratios and qualifies the borrower at whichever produces the lower payment.

A broker reports that comparable sales support a 6.25% capitalization rate. The seller of an office building is asking $1,600,000. What annual net operating income must the building produce to justify that asking price?

• a.$256,000
• b.$160,000
• c.$96,000
• d.$100,000✓

Rearranging Value = NOI / cap rate gives NOI = value x cap rate = $1,600,000 x 0.0625 = $100,000. Dividing the price by 6.25 instead of multiplying by 0.0625 produces $256,000 and badly inflates the income the property would need. Slipping the decimal and using 10% gives $160,000. Rounding the cap rate down to 6% gives $96,000, which understates the requirement. Check: $100,000 / 0.0625 = $1,600,000. Knowing all three directions of this formula lets a broker show an investor precisely how far the building's actual income falls short of the price being asked.

A building produces a stable $120,000 net operating income. Investors who once accepted an 8% capitalization rate for this property type now demand 10%. What happens to the indicated value?

• a.It falls $150,000, from $1,500,000 to $1,350,000
• b.It rises $300,000, from $1,200,000 to $1,500,000
• c.It falls $300,000, from $1,500,000 to $1,200,000✓
• d.It stays at $1,500,000, since NOI did not change

Value = NOI / cap rate. At 8% the building is worth $120,000 / 0.08 = $1,500,000; at 10% it is worth $120,000 / 0.10 = $1,200,000, a decline of $300,000. Value and cap rate move inversely, so a higher required return cannot raise value, and the reversed pairing has the direction backwards. Subtracting 10% of the old value gives $1,350,000, treating the two-point shift as a discount on price rather than a change in the divisor. Value is not fixed by income alone: identical NOI is worth less when buyers demand more. Check: 10% of $1,200,000 = $120,000.

A 24-unit building rents at $1,250 per unit monthly. Vacancy and collection loss runs 5%. Laundry and parking add $9,000 a year. Operating expenses are $148,000, debt service $96,000, and a new roof cost $40,000. NOI?

• a.$221,000
• b.$107,000
• c.$163,000
• d.$203,000✓

Potential gross income = 24 x $1,250 x 12 = $360,000. Subtract 5% vacancy and collection loss of $18,000 and add the $9,000 of other income to get effective gross income of $351,000. Subtract operating expenses only: $351,000 - $148,000 = $203,000. Debt service is financing and the roof is a capital improvement, so neither is an operating expense. Subtracting the $96,000 of debt service gives $107,000, which is pre-tax cash flow rather than NOI. Skipping the vacancy deduction gives $221,000. Deducting the $40,000 roof gives $163,000. Check: $203,000 + $148,000 - $9,000 + $18,000 = $360,000.

Three comparable rentals sold at $360,000 with $4,000 monthly gross rent, $324,000 with $3,600, and $391,500 with $4,350. The subject rents for $3,800 a month. What value does the gross rent multiplier indicate?

• a.$342,000✓
• b.$4,104,000
• c.$28,500
• d.$358,500

Derive the multiplier from the comparables: $360,000 / $4,000 = 90, $324,000 / $3,600 = 90, and $391,500 / $4,350 = 90, a consistent monthly gross rent multiplier. Apply it to the subject: 90 x $3,800 = $342,000. Multiplying the monthly multiplier by annual rent gives $4,104,000, off by a factor of twelve. Using an annual multiplier of 7.5 against monthly rent gives $28,500. Averaging the three comparable prices gives $358,500 and ignores that the subject rents for less than two of them. Check: $342,000 / $3,800 = 90. This shortcut ignores expenses, so comparables must operate similarly.

An investor buys a $1,050,000 property with 20% down, investing $210,000 of cash. The property produces $84,000 of net operating income against $58,800 of annual debt service. What is the cash-on-cash return?

• a.40.0%
• b.8.0%
• c.2.4%
• d.12.0%✓

Cash-on-cash divides pre-tax cash flow by the cash actually invested. Cash flow = NOI - debt service = $84,000 - $58,800 = $25,200. Divide by the $210,000 invested: $25,200 / $210,000 = 0.12, or 12.0%. Dividing NOI by the cash invested without subtracting debt service gives 40.0%. Dividing NOI by the full $1,050,000 price gives 8.0%, which is the capitalization rate, an unleveraged measure that ignores the loan. Dividing cash flow by the total price gives 2.4%. Check: 12% of $210,000 = $25,200. Leverage is exactly why these two returns differ, and investors track both.

An investor bought a rental for $320,000 with $64,000 down and a $256,000 loan. Five years later the property is worth $395,000 and the loan balance is $232,000. How much has the owner's equity grown?

• a.$163,000
• b.$99,000✓
• c.$75,000
• d.$24,000

Equity is value minus debt. Today that is $395,000 - $232,000 = $163,000. At purchase, equity equaled the $64,000 down payment, so the growth is $163,000 - $64,000 = $99,000. Reporting $163,000 gives total equity rather than the increase the question asks for. Counting appreciation alone gives $75,000 and ignores amortization; counting principal paydown alone gives $24,000 and ignores the market. Check the two sources: appreciation of $395,000 - $320,000 = $75,000 plus paydown of $256,000 - $232,000 = $24,000 equals $99,000. Showing owners both engines of equity build is routine investor-listing work.

An apartment property shows potential gross income of $450,000, effective gross income of $420,000, operating expenses of $189,000, and annual debt service of $132,000. What is its operating expense ratio measured against effective gross income?

• a.42.0%
• b.76.4%
• c.55.0%
• d.45.0%✓

The operating expense ratio divides operating expenses by effective gross income: $189,000 / $420,000 = 0.45, or 45.0%. Dividing by the $450,000 of potential gross income gives 42.0% and flatters the property by ignoring vacancy. Adding debt service to expenses gives 76.4%, but loan payments are financing rather than operations and vary with each buyer's terms. The 55.0% figure is the complement, the share of income surviving as NOI. Check: 45% of $420,000 = $189,000, leaving $231,000 of NOI. Comparing this ratio against market norms tells a broker whether a seller's reported expenses look understated.

A property's potential gross income is $500,000, operating expenses are $180,000, and annual debt service is $195,000. What occupancy level does the property need just to cover expenses and the loan payment?

• a.25.0%
• b.75.0%✓
• c.36.0%
• d.39.0%

Break-even occupancy = (operating expenses + debt service) / potential gross income = ($180,000 + $195,000) / $500,000 = $375,000 / $500,000 = 0.75, or 75.0%. The 25.0% figure is break-even vacancy, the cushion before the property runs a deficit, not the occupancy required. Using operating expenses alone gives 36.0% and omits the mortgage. Using debt service alone gives 39.0%. Check: 75% of $500,000 = $375,000, exactly the cash needed. Unlike NOI, this measure deliberately includes debt service, because a lender wants to know the occupancy at which the loan stops being paid.

A county assesses property at 40% of market value and levies 28 mills. One mill equals $0.001 of assessed value, or $1 per $1,000. What is the annual tax on a home with a $475,000 market value?

• a.$5,320.00✓
• b.$53,200.00
• c.$133,000.00
• d.$13,300.00

Two steps, in order. Assessed value = $475,000 x 0.40 = $190,000. Convert the levy: 28 mills x $0.001 = 0.028, so the tax is $190,000 x 0.028 = $5,320. Applying the mill rate to the full $475,000 market value gives $13,300 and skips the assessment ratio entirely. Treating 28 mills as 28 percent of assessed value gives $53,200, off by a factor of ten. Making both errors at once, 28 percent of market value, gives $133,000. Check: $190,000 / $1,000 = 190 thousand-dollar units, and 190 x $28 = $5,320. Assessment ratios and mill rates are set locally, so both figures must come from the tax bill.

A state charges a documentary transfer tax of $0.55 for each $500 of sale price or any fraction of $500. A property sells for $384,250. What is the transfer tax?

• a.$422.68
• b.$211.75
• c.$422.95✓
• d.$422.40

Count the taxable increments, then round up. $384,250 / $500 = 768.5 increments, and because any fraction of $500 counts as a whole increment, the taxable number is 769. Tax = 769 x $0.55 = $422.95. Multiplying the raw 768.5 by $0.55 gives $422.68 and ignores the fraction rule. Rounding down to 768 increments gives $422.40. Treating the rate as $0.55 per $1,000 gives $211.75. Check: 769 x $500 = $384,500, the first full increment at or above the price. Transfer tax rates and rounding rules differ by jurisdiction, so a broker applies the local rule as written.

The seller prepaid the full $4,320 calendar-year property tax. Closing is June 15. Use a 360-day year with 30-day months and charge the day of closing to the buyer. How is the tax prorated?

• a.Debit the buyer and credit the seller $2,352.00✓
• b.Debit the buyer and credit the seller $1,968.00
• c.Debit the seller and credit the buyer $2,352.00
• d.Debit the seller and credit the buyer $1,968.00

The seller already paid for the entire year, so the buyer reimburses the seller for the days the buyer will own the property. Daily tax = $4,320 / 360 = $12. The seller owns January 1 through June 14, which is five 30-day months plus 14 days, or 164 days. The buyer's share is 360 - 164 = 196 days x $12 = $2,352, entered as a debit to the buyer and a credit to the seller. Using the seller's 164 days gives $1,968. Reversing the entries is right only when the tax is still unpaid at closing. Check: $1,968 + $2,352 = $4,320.

The seller of an income property collected $18,600 of April rent on the first of the month. Closing is April 20. Use 30-day months and give the buyer the day of closing. How is the rent prorated?

• a.Credit the buyer and debit the seller $6,200.00
• b.Credit the buyer and debit the seller $11,780.00
• c.Credit the buyer and debit the seller $6,820.00✓
• d.Credit the seller and debit the buyer $6,820.00

Rent collected in advance belongs to whoever owns the property on the days it covers, so the seller passes the unearned part to the buyer. Daily rent = $18,600 / 30 = $620. The buyer owns April 20 through April 30, which is 11 days: 11 x $620 = $6,820, credited to the buyer and debited to the seller. Counting only 10 days gives $6,200 and hands the closing day to the seller. The $11,780 figure is the seller's own earned share. Reversing the entries would make the buyer pay for money the seller is already holding. Check: $11,780 + $6,820 = $18,600.

A buyer assumes a $180,000 loan at 6% interest paid in arrears; the July 1 payment covered interest through June 30. Closing is July 18. Use a 360-day year and charge the closing day to the buyer. What accrued-interest entry is made?

• a.Debit the seller and credit the buyer $510.00✓
• b.Debit the buyer and credit the seller $510.00
• c.Debit the seller and credit the buyer $390.00
• d.Debit the seller and credit the buyer $540.00

Interest paid in arrears means the buyer's next payment will cover interest that accrued before closing, so the seller owes it now. Daily interest = $180,000 x 0.06 / 360 = $30. The seller owns July 1 through July 17, which is 17 days once the closing day goes to the buyer: 17 x $30 = $510, debited to the seller and credited to the buyer. Counting 18 days gives $540 and charges the seller for the buyer's day. Prorating forward over the 13 remaining days gives $390. Reversing the entries makes the buyer fund the seller's interest. Check: $30 x 30 = $900, one full month at 6%.

A buyer purchases the northeast quarter of the southwest quarter of a section of land at $2,300 per acre. A section contains 640 acres. What is the purchase price?

• a.$92,000✓
• b.$184,000
• c.$368,000
• d.$1,472,000

Read the legal description from the back forward and multiply the fractions: 640 acres x 1/4 x 1/4 = 40 acres. Price = 40 x $2,300 = $92,000. Stopping at the first quarter leaves 160 acres and gives $368,000. Adding the denominators, so treating it as 640 / 8 = 80 acres, gives $184,000. Pricing the entire 640-acre section and ignoring both fractions gives $1,472,000. Check: $92,000 / $2,300 = 40 acres, and 40 x 16 = the 640 acres in a section. Every quarter-quarter of a section is 40 acres, a figure worth memorizing for rural land and acreage work.

A rectangular lot has 220 feet of street frontage and is 396 feet deep. Zoning requires 25-foot front and rear setbacks and 10-foot side setbacks on each side. What is the buildable area?

• a.63,920 square feet
• b.87,120 square feet
• c.72,345 square feet
• d.69,200 square feet✓

Subtract each setback from the dimension it actually restricts. Width: 220 - 10 - 10 = 200 feet. Depth: 396 - 25 - 25 = 346 feet. Buildable area = 200 x 346 = 69,200 square feet. The 87,120 figure is the whole lot and ignores the setbacks; note that it equals exactly 2.00 acres at 43,560 square feet per acre. Deducting each setback only once gives 195 x 371 = 72,345. Applying the side setbacks to the depth and the front and rear setbacks to the width gives 63,920. Check: 87,120 - 69,200 = 17,920 square feet consumed by yards.

A warehouse has a footprint of 180 feet by 240 feet plus a second floor covering half the footprint. It is offered at $85 per square foot of gross building area. What is the asking price?

• a.$3,672,000
• b.$7,344,000
• c.$5,508,000✓
• d.$1,836,000

Compute the area before the price. Ground floor = 180 x 240 = 43,200 square feet. The second floor covers half of that, or 21,600 square feet, so gross building area = 64,800 square feet. Price = 64,800 x $85 = $5,508,000. Pricing only the footprint gives $3,672,000. Treating the second floor as full size produces 86,400 square feet and $7,344,000. Pricing only the upper level gives $1,836,000. Check: 64,800 x $80 = $5,184,000 plus 64,800 x $5 = $324,000, which sum to $5,508,000. Commercial pricing per square foot depends on which area measure the listing actually uses.

An investor paid $260,000 for a duplex and spent $40,000 on improvements, then sold it for $375,000. Ignoring transaction costs, what was the profit as a percentage of the investor's total cost? Round to the nearest tenth.

• a.20.0%
• b.28.8%
• c.25.0%✓
• d.44.2%

Percentage of profit divides profit by total cost, not by the sale price. Total cost = $260,000 + $40,000 = $300,000, and profit = $375,000 - $300,000 = $75,000, so $75,000 / $300,000 = 0.25, or 25.0%. Dividing the same $75,000 by the $375,000 sale price gives 20.0%, the single most common error, because the base must be what the investor put in. Leaving the improvements out of the base gives $75,000 / $260,000 = 28.8%. Leaving them out of both the profit and the base gives $115,000 / $260,000 = 44.2%. Check: $300,000 x 1.25 = $375,000.

A property sold for $437,000, which the seller's accountant reports is 115% of what the seller originally paid for it. What was the original purchase price? Round to the nearest dollar.

• a.$514,118
• b.$371,450
• c.$502,550
• d.$380,000✓

When a sale price is expressed as a percentage of cost, divide rather than multiply: cost = $437,000 / 1.15 = $380,000. Taking 85% of $437,000 gives $371,450, which subtracts 15% of the wrong number. Multiplying by 1.15 gives $502,550 and runs the wrong direction, producing a cost above the sale price on a profitable deal. Dividing by 0.85 gives $514,118 and treats the sale as 85% of cost, which would be a loss. Check: 115% of $380,000 = $437,000, a $57,000 gain. Always identify which figure the percentage is measured against before choosing an operation.

A parcel bought for $180,000 has appreciated on a straight-line basis at 4% of its original value per year for six years. What is its indicated value now?

• a.$223,200✓
• b.$216,000
• c.$227,757
• d.$187,200

Straight-line means each year's change is a percentage of the original value, not of a growing balance. Total appreciation = 4% x 6 years = 24% of $180,000 = $43,200, so the value is $180,000 + $43,200 = $223,200. Compounding at 4% for six years gives $180,000 x 1.04 to the sixth power, or $227,757, which answers a different question and is the classic trap. Using five years gives $216,000, and applying a single year gives $187,200. Check: $223,200 / $180,000 = 1.24. Appraisers apply straight-line rates the same way to depreciation over an item's economic life.

Under the cost approach, improvements have a replacement cost new of $480,000, an effective age of 12 years, and a total economic life of 60 years. The land is worth $150,000. What value is indicated?

• a.$504,000
• b.$534,000✓
• c.$384,000
• d.$630,000

Depreciate the improvements only, then add land back. Straight-line depreciation = 12 / 60 = 20% of $480,000 = $96,000, leaving depreciated improvements of $384,000. Adding the $150,000 of land gives $384,000 + $150,000 = $534,000. Depreciating the land along with the building gives 80% of $630,000 = $504,000, but land is never depreciated because it does not wear out. Stopping at $384,000 omits the land entirely, and $630,000 omits the depreciation. Check: $534,000 + $96,000 = $630,000, the undepreciated total. The cost approach carries the most weight for new or special-purpose buildings.

A store's percentage lease sets base rent at $4,000 a month plus 5% of annual gross sales above a $600,000 breakpoint. The tenant's sales for the year were $940,000. What is the total annual rent?

• a.$95,000
• b.$48,000
• c.$65,000✓
• d.$17,000

Base rent comes first: $4,000 x 12 = $48,000. Percentage rent applies only to sales above the breakpoint: $940,000 - $600,000 = $340,000 of overage, and 5% of $340,000 = $17,000. Total rent = $48,000 + $17,000 = $65,000. Charging 5% against all $940,000 of sales produces $47,000 of percentage rent and a $95,000 total, ignoring the breakpoint. Reporting $48,000 counts base rent alone, and $17,000 counts the overage alone. Check: $65,000 - $48,000 = $17,000, which is 5% of the $340,000 excess. Percentage leases let a landlord share in a successful retail tenant's growth.

A seller's property closes at $465,000. The seller pays a 6% commission, pays off a loan balance of $288,400, and owes $6,850 of other closing costs. What are the seller's net proceeds?

• a.$148,700
• b.$141,850✓
• c.$430,250
• d.$169,750

Deduct every seller charge from the sale price in order. Commission = 6% of $465,000 = $27,900, leaving $437,100. Subtract the $288,400 loan payoff to get $148,700, then subtract $6,850 of other costs for net proceeds of $141,850. Stopping before those other costs leaves $148,700. Forgetting the commission gives $169,750, and forgetting the loan payoff gives $430,250, a number no seller with a mortgage will ever receive. Check: $27,900 + $288,400 + $6,850 + $141,850 = $465,000. A broker prepares this seller's net sheet before the listing is signed so the seller can weigh offers realistically.