Real estate math is arithmetic on a handful of formulas: area, percentages (commission, LTV, points, cap rate) and daily rates (prorations). Pearson VUE gives it 7 of its 80 scored national questions and PSI 7% of its national portion; the formulas below, five worked examples and 25 practice problems cover it.
Updated Oct 24, 2026 · Not affiliated with any state commission or test provider.
7of 80 scored, Pearson VUE
7%of the PSI national portion
25questions on this page
What the math section looks like
Pearson VUE lists seven math sub-areas with one item each (area, valuation, commission, loan costs, settlement and closing costs, investment, property management), and all seven are application or analysis items, none pure recall (Pearson VUE outline, area VIII). Each item asks you to apply a formula to a short situation rather than recite it.
Pearson VUE’s math notes:Memorize 43,560 sq ft per acre and 5,280 ft per mile; a proration question states 360 or 365 days and who owns the closing day. Where a result needs rounding, standard rounding rules apply.
Real estate math formulas
The cheat sheet, one line per formula family:
Area: rectangle = length × width; triangle = ½ × base × height; acres = square feet ÷ 43,560.
Commission: sale price × rate; then split between brokerages, then between broker and agent.
Net to seller: price needed = (desired net + seller’s costs) ÷ (1 − commission rate).
Loan-to-value: loan ÷ the lower of price or appraised value; down payment = price − loan.
Points: 1 point = 1% of the loan amount, not of the price.
Prorations: annual amount ÷ 360 or 365 (or monthly ÷ days in the month) × days owed.
Income: effective gross income = potential gross − vacancy and collection loss; NOI = effective gross income − operating expenses (no debt service, no depreciation).
Value and cap rate: value = NOI ÷ cap rate; cap rate = NOI ÷ value (I = R × V).
An L-shaped house: a 40 × 30 ft main block and a 20 × 15 ft wing, listed at $337,500. What is the list price per square foot?
Calculation steps
1Main block40 ft × 30 ft1,200 sq ft
2Wing20 ft × 15 ft300 sq ft
3Total living area1,200 + 3001,500 sq ft
=Price per square foot$337,500 ÷ 1,500$225
Split an irregular shape into rectangles and triangles, add the parts, then divide.
A graduated commission
A listing pays 6% on the first $200,000 of the price and 4% on the rest. The home sells for $380,000. What is the total commission?
Calculation steps
1First tier$200,000 × 6%$12,000
2Amount above the tier$380,000 − $200,000$180,000
3Second tier$180,000 × 4%$7,200
=Total commission$12,000 + $7,200$19,200
Apply each rate only to its own slice of the price; 4% of the whole price would be a different, wrong answer.
25 real estate math practice problems
0 of 25 answered · 0 correct
Question 1 of 25 · Real estate math · 7 items
A buyer secures a $360,000 interest-only loan at a fixed annual interest rate of 5% for a 10-year term. What is the borrower's monthly payment amount, excluding any property taxes and insurance premiums?
Answer and explanations
Incorrect: $18,000 is the whole year's interest, not the monthly payment.
Incorrect: $4,500 is not the result of any correct step; monthly interest is $1,500.
Incorrect: $3,000 doubles the correct monthly interest.
Correct: An interest-only payment is the yearly interest divided by 12: $360,000 × 5% = $18,000 a year, or $1,500 a month.
Incorrect: $1,932 is roughly a 30-year amortizing payment; an interest-only loan pays no principal.
Calculation steps
1Annual interest$360,000 × 5%$18,000
2Monthly payment$18,000 ÷ 12$1,500
=Interest-only payment$1,500 a month
Question 2 of 25 · Real estate math · 7 items
A buyer purchases a property for $400,000 and secures an 80% loan-to-value (LTV) mortgage. To secure a lower interest rate, the buyer agrees to pay 2 discount points at closing. What is the upfront dollar cost of these discount points?
Answer and explanations
Incorrect: $14,400 does not match any step; 2 points on a $320,000 loan is $6,400.
Correct: Points are charged on the loan amount: 80% of $400,000 is $320,000, and 2 points is 2% of that, $6,400.
Incorrect: $2,000 is not tied to either the loan or the price.
Incorrect: $1,600 applies 2% to the $80,000 down payment.
Incorrect: $8,000 applies the points to the price, not the loan.
Calculation steps
1Loan amount$400,000 × 80%$320,000
2Discount points$320,000 × 2%$6,400
=Cost of 2 points$6,400
Question 3 of 25 · Real estate math · 7 items
A seller wishes to walk away from closing with exactly $183,000 in net proceeds. To do so, they must pay a 6% broker commission and a flat fee of $5,000 in seller closing costs. What is the minimum sales price required to meet this goal?
Answer and explanations
Incorrect: $199,681 is close but does not leave $183,000 after a 6% commission and $5,000.
Correct: Add the flat costs to the desired net, then divide by the share left after commission: ($183,000 + $5,000) ÷ 0.94 = $200,000.
Incorrect: $188,000 adds only the flat costs and forgets the commission.
Incorrect: $198,980 adds 6% to the net alone and then the $5,000.
Incorrect: $199,280 adds 6% to $188,000 instead of dividing by 94%.
Calculation steps
1Net plus flat costs$183,000 + $5,000$188,000
2Share left after 6% commission100% − 6%94%
3Sales price$188,000 ÷ 0.94$200,000
=Minimum price$200,000
Question 4 of 25 · Real estate math · 7 items
A buyer is securing a mortgage for a property with a negotiated purchase price of $320,000. The lender's appraiser subsequently values the property at $305,000. If the lender requires an 80% loan-to-value (LTV) ratio, what is the required down payment from the buyer?
Answer and explanations
Incorrect: $244,000 is the loan, not the down payment.
Incorrect: $256,000 is 80% of the price; the lender uses the lower appraised value.
Incorrect: $61,000 is 20% of the appraisal, but the buyer must also cover the $15,000 gap between price and appraisal.
Correct: The lender lends 80% of the lower of price and appraisal: 80% × $305,000 = $244,000, so the buyer pays $320,000 − $244,000 = $76,000.
Incorrect: $64,000 is 20% of the price, which assumes the loan is based on the price.
Calculation steps
1Lower of price and appraisal$320,000 vs $305,000$305,000
2Loan$305,000 × 80%$244,000
3Down payment$320,000 − $244,000$76,000
=Buyer brings$76,000
Question 5 of 25 · Real estate math · 7 items
A property sells for $125,100. The local real estate transfer tax is $1.50 per $500 of value or fraction thereof. What is the total transfer tax liability for this transaction?
Answer and explanations
Incorrect: $376.00 rounds the units up but then miscounts the tax.
Correct: $125,100 ÷ $500 = 250.2, and "fraction thereof" rounds up to 251 units; 251 × $1.50 = $376.50.
Incorrect: $1,876.50 is not tied to the per-$500 rate correctly.
Incorrect: $375.00 drops the fraction instead of rounding it up.
Incorrect: $375.30 uses 250.2 units without rounding the fraction up.
Calculation steps
1Taxable units$125,100 ÷ $500250.2 → 251 (fraction counts as a full unit)
2Transfer tax251 × $1.50$376.50
=Tax due$376.50
Question 6 of 25 · Real estate math · 7 items
A property closes for $280,000 with a 6% total commission, split evenly between the listing and selling brokerages. The selling agent receives a 60% split from their brokerage, less a $250 transaction fee. What is the selling agent's net payout?
Answer and explanations
Incorrect: $5,040 is the agent's split before the $250 fee.
Incorrect: $8,150 is the selling brokerage's half less the fee, before the agent's split.
Correct: 6% of $280,000 is $16,800; the selling side gets half, $8,400; the agent's 60% is $5,040; minus $250 leaves $4,790.
Incorrect: $9,830 subtracts the fee from 60% of the whole commission.
Incorrect: $10,080 is 60% of the whole commission, not of the selling side's half.
Calculation steps
1Total commission$280,000 × 6%$16,800
2Selling side$16,800 ÷ 2$8,400
3Agent's 60%$8,400 × 60%$5,040
4Less transaction fee$5,040 − $250$4,790
=Net payout$4,790
Question 7 of 25 · Real estate math · 7 items
A property has a market value of $400,000 and is assessed at 80% of that value. The local tax rate is 25 mills. What is the annual property tax liability?
Answer and explanations
Incorrect: $10,000 applies the mills to market value, not assessed value.
Incorrect: $12,500 is not produced by any correct step.
Incorrect: $80,000 treats 25 mills as 25%.
Incorrect: $1,000 treats 25 mills as a tenth of its real size.
Correct: Assessed value is 80% of $400,000 = $320,000; 25 mills is $25 per $1,000, so $320,000 × 0.025 = $8,000.
Calculation steps
1Assessed value$400,000 × 80%$320,000
2Tax rate25 mills = 25 ÷ 1,0000.025
3Annual tax$320,000 × 0.025$8,000
=Property tax$8,000
Question 8 of 25 · Real estate math · 7 items
A buyer purchases a $100,000 home with a 5% down payment. The lender charges 2 discount points. Escrow prepaids total $1,100. If the buyer already submitted a $2,000 earnest money deposit, how much additional cash is required at closing?
Answer and explanations
Incorrect: $10,100 is not produced by the correct steps.
Incorrect: $8,000 is the total before crediting the $2,000 earnest money.
Correct: Down payment $5,000 plus points on the $95,000 loan ($1,900) plus $1,100 prepaids is $8,000; less the $2,000 deposit leaves $6,000.
Incorrect: $10,000 adds the deposit instead of subtracting it.
Incorrect: $6,200 overstates the cash; the correct total is $8,000 less the $2,000 deposit.
Calculation steps
1Down payment$100,000 × 5%$5,000
2Discount points$95,000 × 2%$1,900
3Total due$5,000 + $1,900 + $1,100$8,000
4Less earnest money$8,000 − $2,000$6,000
=Cash at closing$6,000
Question 9 of 25 · Real estate math · 7 items
An appraiser is valuing a warehouse using the cost approach. The estimated replacement cost new of the structure is $800,000. Total accrued depreciation is estimated at 20%. The site value is estimated at $250,000. What is the indicated value of the property?
Answer and explanations
Incorrect: $1,210,000 adds depreciation instead of subtracting it.
Incorrect: $640,000 is the depreciated building alone, without the land.
Incorrect: $840,000 subtracts depreciation from cost plus land, but land does not depreciate.
Correct: Depreciation is 20% of $800,000, leaving $640,000; adding the $250,000 site value gives $890,000.
Calculation steps
1Depreciation$800,000 × 20%$160,000
2Depreciated building$800,000 − $160,000$640,000
3Add site value$640,000 + $250,000$890,000
=Indicated value$890,000
Question 10 of 25 · Real estate math · 7 items
A seller prepaid a $1,095 annual hazard insurance policy on January 1. The closing is scheduled for August 15. Using an actual/365-day calendar, what is the correct settlement statement entry for this policy if the buyer assumes it? (Assume the closing day belongs to the seller).
Answer and explanations
Correct: The seller paid for the whole year and used January 1 through August 15 (227 days), so the buyer pays for the 138 unused days at $3 a day: credit seller, debit buyer $414.
Incorrect: Debiting the seller the full premium reverses who paid.
Incorrect: $681 is the seller's used portion (227 days), not the unused part.
Incorrect: The buyer pays only for the unused days, not the full premium.
Incorrect: The seller paid in advance, so the seller is credited, not debited.
Calculation steps
1Daily cost$1,095 ÷ 365$3
2Seller's days (Jan 1 – Aug 15, closing day to seller)31+28+31+30+31+30+31+15227 days
3Unused days365 − 227138 days
4Proration138 × $3$414
=Credit seller, debit buyer$414
Question 11 of 25 · Real estate math · 7 items
A property produces $120,000 in gross scheduled income. The market vacancy rate is 10%. Operating expenses total $45,000 annually. What is the net operating income if calculations follow standard pro forma order of operations?
Answer and explanations
Incorrect: $108,000 is effective gross income before expenses.
Incorrect: $75,000 skips the vacancy deduction.
Incorrect: $87,000 is not produced by the correct steps.
Incorrect: $67,500 takes vacancy after expenses, which is out of order.
Correct: Effective gross income is $120,000 less 10% vacancy = $108,000; subtracting $45,000 of expenses gives NOI of $63,000.
Calculation steps
1Vacancy loss$120,000 × 10%$12,000
2Effective gross income$120,000 − $12,000$108,000
3Net operating income$108,000 − $45,000$63,000
=NOI$63,000
Question 12 of 25 · Real estate math · 7 items
A residential duplex sold for $450,000. It generates a gross scheduled monthly rent of $3,000. The property experiences a 5% vacancy rate and incurs $8,000 in annual operating expenses. What is the indicated annual Gross Rent Multiplier?
Answer and explanations
Incorrect: 150.00 is the monthly multiplier, not the annual one.
Incorrect: 13.16 uses rent after vacancy; a GRM uses gross scheduled rent.
Incorrect: 17.18 deducts expenses, which a GRM ignores.
Incorrect: 15.00 does not match the price-to-annual-rent ratio.
Correct: An annual GRM is price divided by gross scheduled annual rent: $450,000 ÷ $36,000 = 12.50.
Calculation steps
1Annual gross rent$3,000 × 12$36,000
2Annual GRM$450,000 ÷ $36,00012.50
=GRM12.50
Question 13 of 25 · Real estate math · 7 items
A primary borrower has a monthly gross income of $4,000, a proposed PITI payment of $2,000, and a $500 auto loan payment, resulting in a back-end DTI ratio that exceeds lender limits. A co-borrower is added who earns a monthly gross income of $3,000 and has a $300 student loan payment. What is the newly combined back-end DTI ratio?
Answer and explanations
Incorrect: 62.5% is the primary borrower's ratio alone before the co-borrower is added.
Correct: Back-end DTI adds all monthly debts ($2,000 + $500 + $300 = $2,800) and divides by combined income ($7,000): 40.0%.
Incorrect: 38.5% leaves out part of the debt.
Incorrect: 43.0% does not divide combined debts by combined income.
Incorrect: 55.0% is not produced by combined debts over combined income.
Calculation steps
1Monthly debts$2,000 + $500 + $300$2,800
2Combined income$4,000 + $3,000$7,000
3Back-end DTI$2,800 ÷ $7,00040.0%
=DTI40.0%
Question 14 of 25 · Real estate math · 7 items
A borrower closes on a 5/1 ARM with an initial interest rate of 4.5% and standard 2/2/5 caps. What is the absolute maximum interest rate the borrower could face at the first adjustment period in year six?
Answer and explanations
Correct: In 2/2/5 caps the first number is the first-adjustment cap: 4.5% + 2% = 6.5%.
Incorrect: 5.5% adds only 1%, but the first cap allows 2%.
Incorrect: 9.5% is the lifetime cap (4.5% + 5%), which cannot be reached at the first adjustment.
Incorrect: 8.5% would need a 4% increase, twice the first-adjustment cap.
Incorrect: 11.5% exceeds even the lifetime cap.
Calculation steps
1Initial rate4.5%
2First-adjustment cap (first 2 in 2/2/5)4.5% + 2%6.5%
=Maximum at year six6.5%
Question 15 of 25 · Real estate math · 7 items
A borrower signs a 5/1 adjustable-rate mortgage (ARM) with an initial teaser rate of 3.5% for the first five years. The loan has a margin of 2.25% and is tied to the SOFR index. At the first adjustment period, the SOFR index is at 4.50%. The loan features a 2% initial adjustment cap and a 5% lifetime cap. What is the fully indexed rate (index plus margin, before caps) at the first adjustment?
Answer and explanations
Incorrect: 5.50% is the capped rate the borrower would pay (3.5% + 2%), not the fully indexed rate.
Incorrect: 7.75% is not index plus margin.
Incorrect: 5.75% adds the margin to the teaser rate instead of the index.
Correct: The fully indexed rate is index plus margin: 4.50% + 2.25% = 6.75%; the caps decide how much of it the borrower actually pays.
Incorrect: 8.00% is not index plus margin.
Calculation steps
1Index4.50%
2Fully indexed rate4.50% + 2.25%6.75%
=Fully indexed rate6.75%
Question 16 of 25 · Real estate math · 7 items
A closing takes place on September 20. The annual property taxes are paid in arrears at the end of the year. The settlement statement displays the tax proration as a debit to the buyer and a credit to the seller. Why is this specific entry procedurally incorrect?
Answer and explanations
Incorrect: Arrears taxes are split by days of ownership, not equally.
Incorrect: The seller owes for the time owned; the buyer is not responsible for the whole year.
Incorrect: These taxes are not prepaid; for prepaid items the entry would credit the seller.
Correct: Taxes paid in arrears are still owed for the seller's months, so the seller is debited and the buyer credited; the entry is reversed.
Incorrect: The seller paid nothing yet, so there is nothing to reimburse.
Question 17 of 25 · Real estate math · 7 items
A parcel is legally described under the Public Land Survey System as 'the W½ of the NE¼ and the SE¼ of Section 10, Township 2 North, Range 3 West.' Assuming Section 10 contains exactly 640 acres with no government lot adjustments, what is the total acreage of the described parcel?
Answer and explanations
Correct: W½ of NE¼ is 640 × ¼ × ½ = 80 acres, and SE¼ is 160 acres; together 240 acres.
Incorrect: 320 acres is a half section, larger than the described pieces.
Incorrect: 160 acres counts only the SE¼ and leaves out the W½ of the NE¼.
Incorrect: 180 acres is not a combination of the described parts.
Incorrect: 200 acres does not match either piece or their sum.
Calculation steps
1W½ of NE¼640 × ¼ × ½80 acres
2SE¼640 × ¼160 acres
3Total80 + 160240 acres
=Parcel240 acres
Question 18 of 25 · Real estate math · 7 items
A listing agent receives three offers for a 5.0-acre rectangular parcel. Offer A: $1.10 per square foot; Offer B: $45,000 per acre; Offer C: $215,000 total. Which offer should the seller accept if all other terms are equal?
Answer and explanations
Incorrect: Offer C is $215,000, the lowest of the three.
Incorrect: Offers B and C differ by $10,000.
Incorrect: Offer A at $239,580 is worth more than Offer B at $225,000.
Incorrect: Offer B is $225,000, less than Offer A.
Correct: Five acres is 217,800 square feet, so Offer A is $239,580, more than B's $225,000 or C's $215,000.
Calculation steps
1Square feet5 × 43,560217,800 sq ft
2Offer A217,800 × $1.10$239,580
3Offer B5 × $45,000$225,000
4Offer C$215,000
=Best offerOffer A
Question 19 of 25 · Real estate math · 7 items
An investor is analyzing a small apartment building offered for sale at $800,000. Potential gross income is $120,000 per year; vacancy and collection losses are estimated at 5% and 2% of potential gross income, respectively; and annual operating expenses are $35,000. What is the going-in capitalization rate? Round to two decimal places.
Answer and explanations
Incorrect: 9.88% deducts only the 5% vacancy and forgets collection loss.
Correct: EGI is $120,000 less 7% ($8,400) = $111,600; NOI is $111,600 − $35,000 = $76,600; $76,600 ÷ $800,000 = 9.58%.
Incorrect: 10.63% skips both vacancy and collection loss.
Incorrect: 13.95% uses effective gross income instead of NOI.
Incorrect: 7.33% is not NOI divided by price.
Calculation steps
1Vacancy and collection loss$120,000 × 7%$8,400
2Effective gross income$120,000 − $8,400$111,600
3NOI$111,600 − $35,000$76,600
4Cap rate$76,600 ÷ $800,0009.58%
=Going-in cap rate9.58%
Question 20 of 25 · Real estate math · 7 items
An apartment building has 10 units renting for $1,200 per month each. Vacancy and collection loss is 5%. Annual operating expenses: property taxes $18,000, insurance $6,000, maintenance $12,000, management 6% of effective gross income, and annual mortgage payment $42,000 (includes principal and interest). Calculate annual NOI.
Answer and explanations
Correct: Gross rent $144,000 less 5% = $136,800 EGI; expenses are $36,000 plus 6% management ($8,208) = $44,208; NOI = $92,592. Debt service is not an operating expense.
Incorrect: $50,592 wrongly subtracts the $42,000 mortgage payment.
Incorrect: $136,800 is effective gross income before expenses.
Incorrect: $86,400 is not produced by the correct steps.
5NOI (debt service excluded)$136,800 − $44,208$92,592
=NOI$92,592
Question 21 of 25 · Real estate math · 7 items
A triangular parcel has a street frontage base of 300 feet and a depth of 290.4 feet. What is the area of this parcel expressed in acres?
Answer and explanations
Incorrect: 1.50 acres is not produced by the area formula.
Correct: A triangle's area is ½ × base × height: ½ × 300 × 290.4 = 43,560 square feet, exactly 1.00 acre.
Incorrect: 2.00 acres forgets to halve the base times height.
Incorrect: 4.00 acres is far larger than the triangle.
Incorrect: 0.50 acre halves the area twice.
Calculation steps
1Area½ × 300 × 290.443,560 sq ft
2Acres43,560 ÷ 43,5601.00 acre
=Parcel1.00 acre
Question 22 of 25 · Real estate math · 7 items
A tenant paid the August rent of $1,612 to the seller on August 1. Closing is scheduled for August 12. If the seller is responsible for the day of closing using an actual/actual day count, what is the seller's rent proration credit to the buyer?
Answer and explanations
Incorrect: $1,040.00 gives the buyer 20 days, as if the closing day belonged to the buyer.
Incorrect: $624.00 is the seller's 12 days, not the buyer's credit.
Correct: August has 31 days, so rent is $52 a day; the seller keeps August 1–12 and owes the buyer the other 19 days: 19 × $52 = $988.00.
Incorrect: $967.20 does not use the 19 days the buyer owns.
Incorrect: $859.73 is not produced by the daily rate and the buyer's days.
Calculation steps
1Daily rent$1,612 ÷ 31$52
2Buyer's days (Aug 13–31)31 − 1219 days
3Credit to buyer19 × $52$988.00
=Seller credits buyer$988.00
Question 23 of 25 · Real estate math · 7 items
For the fiscal year July 1, 2023 through June 30, 2024, the annual property taxes are $3,660 and were paid in full by the seller on July 1, 2023. Closing is February 15, 2024, and the buyer is responsible for the day of closing. How much should the seller be credited for the unused portion of the taxes? (2024 is a leap year.)
Answer and explanations
Incorrect: $1,380 adds a day.
Incorrect: $2,290 is the seller's used portion, not the unused part.
Incorrect: $2,300 is not produced by the correct day count.
Incorrect: $1,360 gives the closing day to the seller, but the buyer owns it.
Correct: The leap fiscal year has 366 days, so taxes are $10 a day; the seller owned July 1 through February 14 (229 days), leaving 137 unused days: $1,370.
Calculation steps
1Daily tax$3,660 ÷ 366$10
2Seller's days (Jul 1 – Feb 14)31+31+30+31+30+31+31+14229 days
3Unused days366 − 229137 days
4Credit to seller137 × $10$1,370
=Seller credit$1,370
Question 24 of 25 · Real estate math · 7 items
A seller's property closes on August 31. The gross sales price is $350,000. The seller agreed to pay a 6% broker commission and a flat $500 home warranty fee. The seller's mortgage payoff is $185,000. Annual property taxes are $4,200, unpaid, and prorated through the day of closing (using a 360-day year). What is the seller's final net proceeds?
Answer and explanations
Incorrect: $142,100 deducts only part of the tax proration.
Incorrect: $143,500 omits the tax proration.
Incorrect: $140,704 uses a 365-day year, but the stem says 360 days.
Correct: $350,000 less $21,000 commission, $500 warranty, $185,000 payoff and $2,800 of unpaid taxes (240 days of a 360-day year) leaves $140,700.
Incorrect: $161,700 does not come from the listed deductions.
When preparing a settlement statement, a percentage-based broker commission is calculated based on which of the following amounts?
Answer and explanations
Incorrect: Appraised value does not determine the commission.
Incorrect: Commission is not based on what the seller nets after the payoff.
Correct: A percentage commission is figured on the final gross sales price.
Incorrect: The seller's target net does not set the commission base.
Incorrect: Buyer concessions do not reduce the base unless the listing agreement says so.
Answer every question to see your score
Prorating taxes paid in arrears
Annual taxes of $4,320 are paid at the end of the year. Closing is April 20, the year is 360 days (12 months of 30), and the seller owns the day of closing. How is it entered?
Calculation steps
1Days the seller ownedJan–Mar 3 × 30 + 20 days of April110 days
2Daily rate$4,320 ÷ 360$12.00
3Seller’s share110 × $12.00$1,320
=Settlement entry: debit the seller, credit the buyer$1,320
Taxes in arrears: the buyer will pay the whole bill later, so the seller pays for the days owned now. Taxes paid in advance reverse the entry: credit seller, debit buyer.
The first payment on an amortized loan
A $240,000, 30-year loan at 6% has a monthly principal and interest payment of $1,438.92. How much of the first payment reduces the debt?
Calculation steps
1Interest for month 1$240,000 × 6% ÷ 12$1,200.00
2Principal in payment 1$1,438.92 − $1,200.00$238.92
=Balance after payment 1$240,000 − $238.92$239,761.08
Each month repeats the same two steps on the new balance, so interest shrinks and principal grows while the payment stays fixed.
Value from NOI and a cap rate
A small office building nets $54,000 a year after vacancy and operating expenses. Similar buildings sell at a 7.5% capitalization rate. What is the indicated value?
Calculation steps
1Net operating income$54,000
2Capitalization rate7.5% = 0.075
=Indicated value$54,000 ÷ 0.075$720,000
Value and cap rate move in opposite directions: at 9% the same income indicates $600,000.
Points on the loan, not the price
One discount point is 1% of the loan amount, so on any loan smaller than the price, points computed on the price are too high. LTV has its own trap: divide by the lower of price or appraised value.
Where math shows up besides this section
Valuation, financing and settlement items on other pages use the same formulas without calling themselves math: the approaches to value on valuation, loan types and PMI on financing, closing on transfer of title. State closing statements and transfer taxes follow state rules; the Florida broker exam is the hub’s example.
Arithmetic and percentages: area and acreage, commission, loan-to-value and points, interest and payments, prorations, NOI and cap rate, property tax and net to seller. No algebra beyond rearranging one formula.
Can I use a calculator?
Arizona allows a silent, non-printing calculator without an A–Z keypad; Alabama and Georgia give an on-screen calculator only.
How many math questions are on the national portion?
Pearson VUE: 7 of 80 scored questions. PSI: 7% of the national portion.