Florida real estate math practice
About 10 of the 100 questions on the Florida Real Estate Sales Associate Exam are math. They reward a handful of formulas used carefully, so the fastest way to improve is to work problems and check every step. Try each one below before opening the solution.
Formulas to know cold
| Calculation | Formula |
|---|---|
| Commission | Sales price × commission rate |
| Price needed to net an amount | (Desired net + seller costs) ÷ (1 − commission rate) |
| Percent profit | (Sale price − cost) ÷ cost |
| Maximum loan | Lower of price or appraised value × loan-to-value ratio |
| Discount points | Loan amount × 1% per point |
| Monthly interest | Loan balance × annual rate ÷ 12 |
| Deed stamps (Florida) | $0.70 per $100 of price, rounded up to the next $100 |
| Note stamps (Florida) | $0.35 per $100 of the new note, rounded up to the next $100 |
| Intangible tax (Florida) | New mortgage amount × 0.002 |
| Daily proration, 365-day method | Annual amount ÷ 365, times the actual days |
| Daily proration, 360-day method | Annual amount ÷ 12 ÷ 30, with every month counted as 30 days |
Florida tax rates: Fla. Stat. 201.02 (deeds), 201.08 (notes) and 199.133 (intangible tax). Some counties, such as Miami-Dade, use a different deed rate for some property.
Practice problems
- section acreage
How many acres are in the NE 1/4 of the SW 1/4 of Section 12?
Show the answer and solution
Answer: B. 40 acres
- A section contains 640 acres
- SW 1/4: 640 x 1/4 = 160 acres
- NE 1/4 of that: 160 x 1/4 = 40 acres
Multiply the 640 acres in a section by each fraction. A quarter of a quarter is 1/16 of a section, or 40 acres. 160 acres is only a single quarter, and 10 acres would need a third quarter.
Source: Bureau of Land Management, Module 2: The Public Land Survey System Study Guide
- acreage conversion
A rectangular tract measures 330 feet by 660 feet. How many acres is it?
Show the answer and solution
Answer: A. 5 acres
- Area: 330 x 660 = 217,800 square feet
- Acres: 217,800 / 43,560 = 5 acres
Multiply length by width for square feet, then divide by 43,560 square feet per acre. 2.5 acres is the answer for a triangle with those dimensions, not a rectangle.
Source: NIST Handbook 44, Appendix C: General Tables of Units of Measurement
- price per front foot
A lot has 75 feet of frontage on the street and is 150 feet deep. It sells for $120,000. What is the price per front foot?
Show the answer and solution
Answer: A. $1,600
- Price per front foot = sale price / front feet
- $120,000 / 75 = $1,600 per front foot
Price per front foot divides the price by the frontage only: $120,000 / 75 = $1,600. $800 divides by the depth, $10.67 is the price per square foot (11,250 square feet), and $533.33 divides by frontage plus depth.
Source: NIST Handbook 44, Appendix C: General Tables of Units of Measurement
- pmi cancellation
A buyer pays $250,000 for a home that appraises at $245,000 and takes a conventional loan with borrower-paid PMI. Under the Homeowners Protection Act, at what scheduled principal balance does the PMI terminate automatically (assuming the borrower is current)?
Show the answer and solution
Answer: D. $191,100
- Original value = lesser of $250,000 price and $245,000 appraisal = $245,000
- Automatic termination point = 78% of original value
- $245,000 × 0.78 = $191,100
Original value is the lesser of the sales price or the appraised value, so it is $245,000, not $250,000. Automatic termination is at 78% of that, $191,100. $195,000 is 78% of the sales price, $196,000 is 80% of the appraisal (the borrower-request point), and $200,000 is 80% of the price.
Source: 12 U.S.C. 4901(12), (18) (Homeowners Protection Act definitions)
- qualifying ratios
A buyer earns $90,000 a year and pays $650 a month on a car loan and student loans. The lender in this question limits total monthly debt, including housing, to 36% of gross monthly income. What is the largest housing payment that fits within that limit?
Show the answer and solution
Answer: B. $2,050
- Gross monthly income: $90,000 ÷ 12 = $7,500
- Total debt allowed: $7,500 × 0.36 = $2,700
- Housing payment allowed: $2,700 − $650 = $2,050
Convert to monthly income, apply the 36% debt ratio, then subtract the other debts: $7,500 × 0.36 = $2,700, and $2,700 − $650 = $2,050. $2,700 forgets to subtract the existing debts, $2,100 is 28% of monthly income (a housing ratio the question did not give), and $2,600 is not the result of any correct step.
- Commissions
A home sells for $385,000 with a 6% commission. The listing and selling brokerages split the commission 50/50, and the listing sales associate receives 60% of the listing brokerage's share. How much does the listing sales associate earn?
Show the answer and solution
Answer: B. $6,930
- Total commission: $385,000 × 0.06 = $23,100
- Listing brokerage share: $23,100 × 0.50 = $11,550
- Associate's share: $11,550 × 0.60 = $6,930
The associate's 60% applies to the listing brokerage's half of the commission, not to the whole commission. $13,860 takes 60% of the full commission, and $4,620 is the brokerage's 40%.
Source: FREC Sales Associate Pre-Licensing Course (Course I) syllabus, Unit 14
- Commissions
A sales associate's brokerage earned a $14,700 commission at a 7% rate. What was the sales price?
Show the answer and solution
Answer: A. $210,000
- Price = commission ÷ rate
- $14,700 ÷ 0.07 = $210,000
The commission is 7% of the price, so the price is the commission divided by 0.07.
Source: FREC Sales Associate Pre-Licensing Course (Course I) syllabus, Unit 14
- Loan-to-value
A buyer contracts to pay $290,000 for a home that appraises for $300,000. The lender makes 80% loan-to-value loans. What is the largest loan the buyer can get?
Show the answer and solution
Answer: D. $232,000
- Lower of price and appraisal: $290,000
- Loan: $290,000 × 0.80 = $232,000
Lenders apply the LTV to the lower of the price or the appraised value. Here that is the $290,000 price.
Source: FREC Sales Associate Pre-Licensing Course (Course I) syllabus, Unit 14
- Discount points
A buyer is paying $300,000 for a home with an 80% loan. The lender charges 2.5 discount points. How much do the points cost?
Show the answer and solution
Answer: B. $6,000
- Loan: $300,000 × 0.80 = $240,000
- Points: $240,000 × 0.025 = $6,000
A point is 1% of the loan amount, not the price. Find the loan first, then take 2.5% of it. $7,500 is 2.5% of the price.
Source: FREC Sales Associate Pre-Licensing Course (Course I) syllabus, Unit 14
- Documentary stamps
A Florida home sells for $350,000. Ignoring any county exceptions, how much is the documentary stamp tax on the deed?
Show the answer and solution
Answer: C. $2,450
- Hundreds: $350,000 ÷ 100 = 3,500
- Tax: 3,500 × $0.70 = $2,450
Deed stamps are $0.70 per $100 of the price. $1,225 uses the $0.35 note rate.
Source: Fla. Stat. 201.02
- Documentary stamps
A buyer signs a note for a new $240,000 mortgage. How much is the documentary stamp tax on the note?
Show the answer and solution
Answer: D. $840
- Hundreds: $240,000 ÷ 100 = 2,400
- Tax: 2,400 × $0.35 = $840
Note stamps are $0.35 per $100 of the loan. $1,680 uses the $0.70 deed rate, and $480 is the intangible tax.
Source: Fla. Stat. 201.08
- Intangible tax
A buyer takes out a new $240,000 mortgage. How much is the nonrecurring intangible tax?
Show the answer and solution
Answer: B. $480
- Tax: $240,000 × 0.002 = $480
The intangible tax is 2 mills, or 0.002, times the new mortgage amount. $840 is the note stamp tax.
Source: Fla. Stat. 199.133
- Prorations
A home closes on June 10 in a non-leap year. This year's property taxes of $4,380 have not been paid. Using the 365-day method, with the buyer owning the day of closing, how does the tax proration appear on the closing statement?
Show the answer and solution
Answer: C. Debit seller, credit buyer $1,920
- Daily rate: $4,380 ÷ 365 = $12
- Seller's days: Jan 31 + Feb 28 + Mar 31 + Apr 30 + May 31 + June 9 = 160
- Seller owes: 160 × $12 = $1,920, a debit to the seller and a credit to the buyer
Florida taxes are paid in arrears, so the buyer will pay the whole bill. The seller owes the buyer for January 1 through June 9, which is 160 days.
Source: FREC Sales Associate Pre-Licensing Course (Course I) syllabus, Unit 14
- Prorations
A rental home closes on September 20. The seller collected $1,800 rent on September 1 for the month. Using a 30-day month, with the buyer owning the day of closing, how is the rent prorated?
Show the answer and solution
Answer: A. Debit seller, credit buyer $660
- Daily rent: $1,800 ÷ 30 = $60
- Buyer's days: September 20 through 30 = 11
- Buyer's share: 11 × $60 = $660, a debit to the seller and a credit to the buyer
The seller collected rent for days the buyer will own, so the seller passes the buyer's share to the buyer. The buyer owns September 20 through 30, which is 11 days.
Source: FREC Sales Associate Pre-Licensing Course (Course I) syllabus, Unit 14
- Closing statements
A buyer is paying $350,000. The buyer has a new $280,000 loan, gave a $10,000 earnest money deposit, owes $6,400 in closing costs, and receives a $1,150 credit for the seller's share of property taxes. How much cash must the buyer bring to closing?
Show the answer and solution
Answer: A. $65,250
- Buyer's debits: $350,000 + $6,400 = $356,400
- Buyer's credits: $280,000 + $10,000 + $1,150 = $291,150
- Cash to close: $356,400 − $291,150 = $65,250
Cash to close is the buyer's debits minus the buyer's credits. The tax proration is a credit to the buyer, so it reduces the cash needed.
Source: FREC Sales Associate Pre-Licensing Course (Course I) syllabus, Unit 14
- cma adjustments
A comparable sold for $340,000. It has an in-ground pool that the market values at $20,000. The subject property has no pool. What is the comparable's adjusted sale price?
Show the answer and solution
Answer: B. $320,000
- Comp has a pool; subject does not, so the comp is better: subtract
- $340,000 − $20,000 = $320,000
The comparable is better than the subject because it has the pool, so subtract the pool's value from the comparable's price. Adding gives $360,000, which is the classic direction error. Leaving the price unchanged ignores the difference, and $300,000 subtracts the pool twice.
Source: HUD Handbook 4465.1, Chapter 8: Market Comparison Approach to Value
- price per square foot
A comparable home with 1,800 square feet of living area sold for $378,000. Using the comparable's price per square foot, what does a 2,100 square foot subject indicate?
Show the answer and solution
Answer: C. $441,000
- Price per sq ft: $378,000 ÷ 1,800 = $210
- Subject: 2,100 × $210 = $441,000
Find the comparable's price per square foot, then multiply by the subject's area. $324,000 divides by the larger area instead ($378,000 ÷ 2,100 × 1,800). $420,000 and $399,000 use $200 and $190 per square foot, which are not the comparable's rate.
Source: Fannie Mae Selling Guide B4-1.3-08, Comparable Sales
- cost approach
A lot is worth $90,000. The house on it has 2,400 square feet and would cost $150 per square foot to replace new. Accrued depreciation is $54,000. What is the value by the cost approach?
Show the answer and solution
Answer: B. $396,000
- Cost new of the building: 2,400 × $150 = $360,000
- Depreciated building: $360,000 − $54,000 = $306,000
- Add land: $306,000 + $90,000 = $396,000
Value = land + (cost new − depreciation). $450,000 forgets to subtract depreciation, $306,000 forgets to add the land, and $360,000 is only the cost new of the building.
Source: California DRE Reference Book, Ch. 15: Appraisal and Valuation
- net operating income
An apartment building has potential gross income of $180,000. Vacancy and collection loss is 5%. Operating expenses are $61,000, and the owner's annual mortgage payments total $45,000. Using an 8% capitalization rate, what is the building's value?
Show the answer and solution
Answer: B. $1,375,000
- Vacancy and collection loss: $180,000 × 0.05 = $9,000
- EGI: $180,000 − $9,000 = $171,000
- NOI: $171,000 − $61,000 = $110,000 (debt service is not deducted)
- Value: $110,000 ÷ 0.08 = $1,375,000
Build NOI first: PGI minus vacancy gives EGI, then subtract operating expenses. Mortgage payments are debt service, not an operating expense. $1,487,500 skips the vacancy loss, $812,500 wrongly subtracts the mortgage payments, and $2,250,000 capitalizes gross income instead of NOI.
Source: California DRE Reference Book, Ch. 15: Appraisal and Valuation
- gross rent multiplier
A comparable rental home sold for $270,000 while renting for $1,800 a month. The subject is similar and rents for $2,000 a month. Using a gross rent multiplier, what is the subject's estimated value?
Show the answer and solution
Answer: C. $300,000
- GRM = sale price ÷ monthly rent: $270,000 ÷ $1,800 = 150
- Subject value: $2,000 × 150 = $300,000
First derive the GRM from the comparable, then apply it to the subject's monthly rent. $243,000 applies the subject's rent backwards, $3,600,000 multiplies annual rent by a monthly-rent GRM, and $270,000 ignores the subject's higher rent.
- effective gross income
A 10-unit apartment building rents for $1,500 per unit per month. The owner allows 5% for vacancy and collection loss. What is the effective gross income?
Show the answer and solution
Answer: C. $171,000
- Potential gross income: 10 units × $1,500 × 12 months = $180,000
- Vacancy and collection loss: $180,000 × 0.05 = $9,000
- Effective gross income: $180,000 − $9,000 = $171,000
Potential gross income assumes every unit is rented all year; effective gross income subtracts the expected vacancy and collection loss. $180,000 is PGI before the loss is taken out, and $189,000 adds the 5% instead of subtracting it.
- before tax cash flow
An 8-unit building rents for $1,250 per unit per month. Vacancy and collection loss is 6%, operating expenses are $41,000 a year, and annual debt service is $36,000. What is the before-tax cash flow?
Show the answer and solution
Answer: A. $35,800
- PGI: 8 × $1,250 × 12 = $120,000
- Vacancy and collection loss: $120,000 × 0.06 = $7,200
- EGI: $120,000 − $7,200 = $112,800
- NOI: $112,800 − $41,000 = $71,800
- Before-tax cash flow: $71,800 − $36,000 = $35,800
Work down the operating statement: PGI, less vacancy, less operating expenses gives NOI, then subtract debt service. $43,000 forgets the vacancy loss, $71,800 is NOI (debt service not yet subtracted), and $76,800 skips the operating expenses.
- leverage
A $500,000 property produces NOI of $40,000. The buyer finances 75% with an interest-only loan at 6% and pays the rest in cash. What is the return on the buyer's cash investment?
Show the answer and solution
Answer: B. 14%
- Loan: $500,000 × 0.75 = $375,000; cash invested: $500,000 − $375,000 = $125,000
- Annual interest: $375,000 × 0.06 = $22,500
- Cash flow: $40,000 − $22,500 = $17,500
- Return on cash: $17,500 ÷ $125,000 = 0.14 = 14%
Borrowing at 6% to buy a property earning 8% is positive leverage, which lifts the return on the buyer's cash above 8%. 8% is the all-cash return. 3.5% divides the cash flow by the full price, and 32% forgets to subtract the interest.
Source: Cornell LII Wex: Leverage
- property tax calculation
A commercial lot has a taxable value of $180,000. The combined millage rate is 22 mills. What is the annual property tax?
Show the answer and solution
Answer: A. $3,960
- 22 mills = 22 ÷ 1,000 = 0.022
- $180,000 × 0.022 = $3,960
One mill is $1 per $1,000 of taxable value, so multiply the taxable value by 22 and divide by 1,000. $396 and $39,600 misplace the decimal, and $3,600 treats 22 mills as if it were 2%.
Source: Fla. Stat. 192.001(10)
- homestead tax calculation
A Florida homestead has an assessed value of $300,000. The school district millage is 6.5 and all other levies total 14.0 mills. Assume a $25,000 homestead exemption that applies to all levies and an additional $25,000 exemption that applies to assessed value above $50,000 for non-school levies only. What is the total tax?
Show the answer and solution
Answer: C. $5,287.50
- School taxable value: $300,000 − $25,000 = $275,000
- School tax: $275,000 × 6.5 ÷ 1,000 = $1,787.50
- Non-school taxable value: $300,000 − $50,000 = $250,000
- Non-school tax: $250,000 × 14.0 ÷ 1,000 = $3,500.00
- Total: $1,787.50 + $3,500.00 = $5,287.50
The first $25,000 comes off for every levy, but the additional $25,000 does not apply to school taxes. So school tax is figured on $275,000 and non-school tax on $250,000. $5,125 wrongly takes $50,000 off the school levy too, $5,637.50 takes only $25,000 off everything, and $6,150 ignores the exemptions.
Source: Fla. Stat. 196.031(1)(a), (1)(b)
- depreciation
An investor buys a single-family rental for $385,000. The land is worth $55,000. Using straight-line depreciation over 27.5 years and ignoring the mid-month convention, what is the annual depreciation deduction?
Show the answer and solution
Answer: A. $12,000
- Building value: $385,000 − $55,000 = $330,000
- Annual depreciation: $330,000 ÷ 27.5 = $12,000
Only the building is depreciated, and residential rental property uses 27.5 years. $14,000 wrongly includes the land, $8,461.54 uses the 39-year nonresidential period, and $2,000 depreciates the land instead of the building.
Source: 26 U.S.C. 168(c)
- home sale exclusion
A married couple filing jointly sells the home they have owned and lived in for 6 years and realizes a $620,000 gain. Neither has used the exclusion in the past 2 years. How much of the gain is taxable?
Show the answer and solution
Answer: D. $120,000
- Joint filers meeting all tests may exclude up to $500,000
- Taxable gain: $620,000 − $500,000 = $120,000
They meet the 2-of-5-year ownership and use test and qualify for the $500,000 joint exclusion, so $620,000 − $500,000 = $120,000 is taxable. $370,000 uses the $250,000 single limit, $0 assumes the exclusion has no cap, and $620,000 ignores the exclusion.
Source: 26 U.S.C. 121(b)(2)
Keep going
- Math drill: shuffled problems by topic with instant feedback. The full bank of 81 math questions is in Pro.
- Unit 14 lessons: Commissions, profit, and net to seller, Loan-to-value, points, and interest, Documentary stamp and intangible taxes, Prorations, Closing statements.
- Timed mock exams weighted like the real test.