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National practice guide

Real estate calculations practice

A $6,000 deposit has already been paid. If you add it to the buyer’s remaining funds instead of subtracting it, the arithmetic can be flawless and the answer still wrong. These examples make you choose the party, base and time period before calculating.

Last reviewed:

The short answer

Set up each real estate math problem by identifying the requested amount, its units and the applicable assumptions. Use the loan amount for points, annual NOI for a cap rate, and the stated value base for LTV. For closing questions, record each charge, deposit and credit once on the correct party’s side. For prorations and transfer taxes, apply the stated day-count or statutory unit rule before rounding the final result.

Reviewed October 26, 2026. PSI’s National XI, Real Estate Calculations, contains 7 of the 100 scored national broker questions; the instructor allocation is 6. Its named topics include seller proceeds, buyer funds, prorations, transfer fees, PITI, equity, rate of return or capitalization rate, LTV, points and origination fees. Other exam areas can use arithmetic too. These are original teaching problems, with hypothetical amounts and stated assumptions, not PSI questions or current loan quotes.

A setup you can check before calculating

  1. Write the requested result and unit. Seller proceeds, buyer remaining funds, loan amount, a property value and a percentage are different outputs. Mark whose money you are calculating. An answer in dollars cannot substitute for a requested percentage.
  2. Choose the base and rate. Convert 5% to 0.05 and 2.5 points to 0.025 of the loan. Identify whether the problem gives price, appraised value, a permitted lending base or initial cash invested. A similar-looking number is not a substitute.
  3. Match the periods. Convert annual taxes and homeowners insurance to monthly amounts before adding them to monthly principal and interest. Use annual NOI with an annual cap rate. For a day-based adjustment, identify both the denominator and the actual or assumed days.
  4. Build a closing ledger. Start with the relevant amounts owed and available funds, then account for each deposit, payoff, charge and credit once. A seller credit to the buyer ordinarily has opposite effects on their ledgers. An existing mortgage balance is not necessarily its dated payoff amount.
  5. Apply the problem’s convention. State who gets the closing day, who has already paid and who will pay the bill. For transfer tax, first determine the covered taxable base and applicable government layers. A $500-or-fraction rule requires whole taxable units rounded upward, not ordinary nearest-dollar rounding.
  6. Calculate with the stated precision, then reverse-check. Add deductions back to seller proceeds; multiply a cap rate by value to recover NOI; multiply LTV by its base to recover the loan. Keep intermediate precision unless a required convention or instruction says otherwise. Label a negative result and interpret it instead of silently changing its sign.
  7. After checking an answer, name the cause of any miss: wrong party, wrong base, wrong period, missing item, duplicate item, arithmetic or rounding. Use the linked math drill for another set; this page’s worked cases are a separate teaching resource, not a claim that the drill’s question bank has changed.
Choose the relationship, then insert the numbers
Requested resultSetup for the stated factsCheck before using it
Seller proceedsSeller credits − seller debitsInclude each dated payoff, fee and adjustment once
Buyer remaining fundsPrice + included buyer charges − loan funds − credited deposit − applicable creditsDo not subtract a deposit again if already reflected in the supplied figure
ProrationAmount ÷ stated period days × responsible daysState advance or arrears, closing-day ownership and the party charged
Transfer taxTaxable $500 units, rounded up × applicable tax per unitStart with the correct nonexempt taxable base; local rules can differ
Monthly PITIMonthly principal and interest + annual taxes ÷ 12 + annual homeowners insurance ÷ 12Identify any separate mortgage insurance or association charge
EquityCurrent value − relevant secured debtEquity is not sale proceeds or an automatic borrowing limit
Capitalization rateAnnual NOI ÷ property value or price usedNOI is before mortgage debt service
Value by direct capitalizationAnnual NOI ÷ decimal cap rateThis is a stipulated model, not a completed appraisal
LTVLoan amount ÷ required value basePrice and the accepted appraisal can differ
Points or percentage origination feeLoan amount × stated percentageCheck that the items are separate rather than duplicate descriptions of a fee

The distinctions that matter

Real Estate Calculations: key distinctions
DistinctionHow it worksWhat to notice
Equity and seller proceedsEquity compares value with relevant secured debt. Proceeds depend on the sale amount, dated payoffs, costs and credits.Selling costs can reduce available proceeds without changing the starting equity definition.
Down payment and remaining buyer fundsThe buyer’s price contribution is price less financing credited toward it. Remaining funds also account for charges, deposits and credits.A deposit already paid is a funding source, not a new charge.
Amount financed and loan fundsThe federal amount-financed disclosure can deduct prepaid finance charges. A closing problem must specify the actual funds available.Do not replace a supplied loan-funding amount with a different disclosure number.
Advance and arrearsA prepaid item can require the buyer to reimburse the seller for the buyer’s period. An unpaid seller-period item can require a seller debit and buyer credit when the buyer will pay it.Identify who paid or will pay before choosing the sign.
30/360 and actual/360Both can use a 360-day denominator. The numerator can still be assumed 30-day months or actual calendar days.A denominator alone does not tell you every day-count convention.
Cap rate and cash-on-cash returnCap rate relates annual NOI to the property’s value or price. A defined cash-on-cash return relates annual cash flow after the specified adjustments to investor cash.Debt service and the denominator change the calculation.
PITI and all housing costsThe PITI examples here use principal, interest, property taxes and homeowners insurance. Broader totals can add separately stated mortgage insurance, association dues or other charges.Answer the requested total and identify the named insurance component.
LTV and the buyer’s price percentageThey add to 100% in a simple case only when the denominators and included amounts match. A lower appraisal can change the relationship.Write the denominator on both fractions.
Discount points and interest-rate reductionOne point costs 1% of the loan amount. It does not promise a one-percentage-point reduction in the loan’s interest rate.Cost arithmetic is separate from lender pricing.
A commission example and a required rateA stated commission can be an input to the problem. The sample percentage is a hypothetical agreement term, not a mandatory or standard rate.Use the given agreement; do not invent a commission.

Work through the facts

Seller proceeds after a stated commission

A property sells for $310,000. The stated hypothetical agreement requires a 5% commission. A dated mortgage payoff is $184,000 and other seller charges total $4,300. There are no other debits or credits.

  1. Commission: $310,000 × 0.05 = $15,500.
  2. Total deductions: $184,000 + $15,500 + $4,300 = $203,800.
  3. $310,000 − $203,800 = $106,200.

Answer: Seller proceeds are $106,200 on these facts. The 5% figure is supplied for the exercise, not a required commission rate.

Buyer funds after a credited deposit

Price is $360,000; loan funds credited toward it are $288,000. Buyer charges are $7,200 and a $6,000 deposit already paid is credited at closing. No other amounts apply.

  1. Price contribution: $360,000 − $288,000 = $72,000.
  2. Add $7,200 of charges and subtract the $6,000 deposit once.

Answer: The remaining buyer funds are $73,200. Adding the deposit would incorrectly require the buyer to pay it again.

Unpaid property-tax proration

For a math-only closing on October 26, 2026, the parties stipulate $7,300 as the annual tax amount for the year, a 365-day basis and buyer ownership of the closing day. The seller owes January 1 through October 25; the buyer will pay the whole unpaid bill. Ignore every other item.

  1. The seller’s stated period has 298 calendar days.
  2. $7,300 ÷ 365 × 298 = $5,960.
  3. The seller owes the buyer for the seller’s unpaid period.

Answer: Debit the seller $5,960 and credit the buyer $5,960. This stipulated calculation does not establish a universal Illinois proration convention or predict a final tax bill.

Prepaid association dues

The seller paid $3,100 of October dues in advance. Closing is October 26, 2026; the buyer gets the closing day. Use actual October days, and assume this is a reimbursable periodic charge with no other adjustment.

  1. October has 31 days; the buyer owns October 26 through 31, or 6 days.
  2. $3,100 ÷ 31 × 6 = $600.

Answer: Debit the buyer $600 and credit the seller $600. The seller already paid for the buyer’s stipulated period.

State transfer tax on a partial unit

A nonexempt Illinois transfer has an already determined, whole-dollar state taxable base of $300,001. No further base adjustment applies. Calculate only the state tax under 35 ILCS 200/31-10.

  1. $300,001 ÷ $500 = 600.002 taxable units.
  2. The statute taxes each $500 or fraction, so use 601 units.
  3. 601 × $0.50 = $300.50.

Answer: The state tax is $300.50. Do not round 600.002 down to 600 units or call this a combined local-tax total.

Monthly PITI from a supplied payment

Monthly principal and interest are $1,640. Annual property taxes are $5,400 and annual homeowners insurance is $1,440. The question asks only for these PITI components.

  1. Monthly taxes: $5,400 ÷ 12 = $450.
  2. Monthly insurance: $1,440 ÷ 12 = $120.
  3. $1,640 + $450 + $120 = $2,210.

Answer: Monthly PITI is $2,210. Separately stated mortgage insurance or association dues would enter a broader requested total, not be silently ignored.

Include the junior lien in equity

Current value is $400,000. The specified existing secured debt consists of a $230,000 first mortgage balance and a $25,000 second mortgage balance. No other relevant debt applies.

  1. Total specified debt is $255,000.
  2. $400,000 − $255,000 = $145,000.

Answer: Equity is $145,000 before any sale-cost or dated-payoff adjustment. This does not promise a $145,000 cash-out loan.

Build NOI before calculating cap rate

Annual potential income is $120,000, vacancy and collection loss are $6,000, and other property income is $3,000. The problem gives $57,000 in annual operating expenses, including property taxes and the specified reserve treatment. No other operating adjustment applies. Price is $750,000.

  1. Effective gross income: $120,000 − $6,000 + $3,000 = $117,000.
  2. NOI: $117,000 − $57,000 = $60,000.
  3. Cap rate: $60,000 ÷ $750,000 = 0.08.

Answer: The cap rate is 8%. Do not subtract mortgage debt service, book depreciation or the owner’s income taxes in this NOI calculation.

Solve for value using the stated cap rate

A direct-capitalization exercise stipulates $60,000 annual NOI and an appropriate 8% cap rate. No further adjustment is required by the problem.

  1. Convert 8% to 0.08.
  2. $60,000 ÷ 0.08 = $750,000.
  3. Reverse-check: $750,000 × 0.08 = $60,000.

Answer: The indicated value under the stated model is $750,000. Selecting a rate and completing an actual appraisal require more than this arithmetic.

Different denominators explain the appraisal gap

Price is $400,000 and the accepted appraisal is $380,000. The hypothetical eligible purchase uses a stated 80% loan cap on the lower figure, with no other adjustment. Ignore costs, deposits and credits.

  1. Loan: $380,000 × 0.80 = $304,000.
  2. Buyer price contribution: $400,000 − $304,000 = $96,000.
  3. LTV is 80%; $96,000 ÷ $400,000 = 24% of price.

Answer: An 80% LTV does not mean the buyer contributes only 20% of price here. The $20,000 price gap is in addition to $76,000 of base equity.

Points and a separate origination fee

A $280,000 loan has 2.5 discount points and a separate 0.75% origination fee. The question expressly says these are distinct charges, both based on the loan, with no other fees.

  1. Points: $280,000 × 0.025 = $7,000.
  2. Origination: $280,000 × 0.0075 = $2,100.
  3. Combined specified charges: $7,000 + $2,100 = $9,100.

Answer: The two stated charges total $9,100. Do not use the purchase price or add a fee twice because its description also appears elsewhere.

Balance the simplified closing

Price is $300,000; loan funds are $240,000. The seller has a $170,000 dated payoff and $18,000 in other seller charges. Buyer charges are $6,000; a $10,000 deposit remains available in escrow. The charges are distinct, all loan funds are available, and no other item applies.

  1. Buyer still brings $300,000 + $6,000 − $240,000 − $10,000 = $56,000.
  2. Seller receives $300,000 − $170,000 − $18,000 = $112,000.
  3. Cash sources: $56,000 + $10,000 + $240,000 = $306,000. Disbursements: $112,000 + $170,000 + $18,000 + $6,000 = $306,000.

Answer: Both sides balance at $306,000. The deposit is a funding source once, not another seller charge or another buyer payment.

Estimate PITI from loan rate and term

Assume a $240,000 fully amortizing fixed-rate loan at a hypothetical 6% annual note rate, with 360 equal end-of-month payments, a monthly rate of annual rate divided by 12, and no odd first period. Annual taxes are $4,800 and annual homeowners insurance is $1,200. No other payment component applies.

  1. For this schedule, monthly P&I = P × r ÷ [1 − (1 + r)^(−n)], where P is $240,000, r is 0.06 ÷ 12 = 0.005 and n is 360.
  2. The unrounded P&I result is about $1,438.92126. Add $400 monthly tax and $100 monthly insurance.
  3. Round the final $1,938.92126 amount to cents.

Answer: Estimated monthly PITI is $1,938.92 for this stipulated schedule. Using principal × annual rate ÷ 12 gives first-month interest, not the fully amortizing P&I payment.

Cap rate and a defined investor return

Use $60,000 annual NOI and a $750,000 price. The same teaching case stipulates $30,000 annual debt service, $300,000 total investor cash and no other cash-flow adjustments.

  1. Cap rate: $60,000 ÷ $750,000 = 8%.
  2. Defined annual cash flow: $60,000 − $30,000 = $30,000.
  3. Defined cash-on-cash return: $30,000 ÷ $300,000 = 10%.

Answer: The property cap rate is 8%; the defined cash-on-cash return is 10%. They use different numerators and denominators. Neither number predicts a guaranteed future return.

Mistakes to avoid

  • Using every number in the story. Choose the requested output before deciding which facts enter the formula.
  • Multiplying by 5 for 5%. Use 0.05, then estimate whether the result makes sense.
  • Treating a credited deposit as money still due. Count it once as already available funding.
  • Using equity as seller cash. Seller proceeds also reflect actual sale terms, dated payoffs and costs.
  • Giving the same proration sign to advance and arrears. Ask who has paid, who will pay and whose period is involved.
  • Treating every 360-day method as 30-day months. Actual/360 and 30/360 can count different numerator days.
  • Rounding transfer-tax units to the nearest integer. Each $500 or fraction means round the taxable units upward.
  • Subtracting every payoff from the transfer-tax base. A loan paid off at closing is different from a qualifying transfer subject to an outstanding mortgage.
  • Calling every expense an NOI deduction. Exclude mortgage debt service, book depreciation and the owner’s income taxes; property operating taxes are different.
  • Using NOI divided by investor cash for cap rate. The cap-rate denominator is the identified property value or price.
  • Assuming LTV and the buyer’s price percentage always add to 100%. Check whether their denominators match.
  • Treating one point as one percentage point off the note rate. One point is a cost of 1% of the loan; rate reduction depends on pricing.
  • Promising readiness from a fixed practice score. Review setup, units and explanations. A practice percentage alone does not validate exam readiness.

Check your understanding

These are original teaching questions, not recalled or predicted PSI questions. Answer first, then explain why the other choices fail.

1. Price is $300,000. The stated commission is 5% of price, dated payoff is $170,000 and other seller debits are $5,000. No other item applies. Seller proceeds?

  1. $110,000
  2. $130,000
  3. $115,000
  4. $120,000
Show answer and explanation

Answer: A. $110,000

The stated commission is $15,000. $300,000 − $170,000 − $15,000 − $5,000 = $110,000. The sample rate is not a mandatory rate.

2. Price is $360,000, available loan funds are $288,000, buyer charges are $7,200 and a $6,000 deposit is already credited. No other amount applies. What remains for the buyer to bring?

  1. $66,000
  2. $79,200
  3. $85,200
  4. $73,200
Show answer and explanation

Answer: D. $73,200

$360,000 + $7,200 − $288,000 − $6,000 = $73,200. Subtract the already credited deposit once.

3. A simplified closing has $56,000 buyer funds still due, $10,000 available deposit and $240,000 loan funds. Seller cash is $112,000, payoff is $170,000, seller charges are $18,000 and buyer charges are $6,000. Do these stated cash sources and uses balance?

  1. Yes, each totals $300,000
  2. No, sources exceed uses by $6,000
  3. No, uses exceed sources by $10,000
  4. Yes, each totals $306,000
Show answer and explanation

Answer: D. Yes, each totals $306,000

Sources total $56,000 + $10,000 + $240,000 = $306,000. Uses total $112,000 + $170,000 + $18,000 + $6,000 = $306,000.

4. An unpaid annual tax of $7,300 is prorated on a 365-day basis. The seller is responsible for 298 stated days; the buyer will pay the whole bill. Which adjustment follows?

  1. Both parties credit $5,960
  2. Buyer debit, seller credit $5,960
  3. Seller debit, buyer credit $5,960
  4. Seller debit, buyer credit $6,000
Show answer and explanation

Answer: C. Seller debit, buyer credit $5,960

$7,300 ÷ 365 × 298 = $5,960. The seller owes the buyer for the seller’s unpaid period.

5. The seller prepaid $3,100 of October dues. Under the stated actual-days convention, the buyer owes the last 6 of October’s 31 days. What is the adjustment?

  1. Buyer debit, seller credit $620
  2. Seller debit, buyer credit $600
  3. Buyer debit, seller credit $600
  4. No adjustment because the bill is paid
Show answer and explanation

Answer: C. Buyer debit, seller credit $600

$3,100 ÷ 31 × 6 = $600. The buyer reimburses the seller for the buyer’s stipulated prepaid period.

6. The seller collected $3,100 of October rent in advance. The agreement allocates the last 6 of 31 days to the buyer. No deposit, collection loss or other adjustment applies. What is the rent adjustment?

  1. Both parties debit $600
  2. Seller debit, buyer credit $620
  3. Seller debit, buyer credit $600
  4. Buyer debit, seller credit $600
Show answer and explanation

Answer: C. Seller debit, buyer credit $600

The buyer’s allocated rent is $3,100 ÷ 31 × 6 = $600. Because the seller already collected it, debit the seller and credit the buyer.

7. A nonexempt transfer has an already determined whole-dollar Illinois state taxable base of $300,001, with no further adjustment. State tax only, at $0.50 per $500 or fraction?

  1. $300.01
  2. $450.75
  3. $300.50
  4. $300.00
Show answer and explanation

Answer: C. $300.50

Use 601 units, because 600.002 contains a fraction of another $500. 601 × $0.50 = $300.50; local layers are excluded here.

8. The already determined nonexempt taxable base is $300,001 for both state and county taxes. Assume the county has imposed $0.25 per $500 or fraction; no municipal or other charge applies. What is the combined tax?

  1. $450.75
  2. $300.50
  3. $601.00
  4. $450.00
Show answer and explanation

Answer: A. $450.75

Use 601 units for each stated layer. State $300.50 plus county $150.25 equals $450.75. County adoption and the common base are expressly assumed.

9. A stated Actual/360 interest exercise uses $7,200 annual interest and the actual 59 days from January 1 through February 28, 2026. What is interest for that period?

  1. $1,160
  2. $1,180
  3. $1,440
  4. $1,200
Show answer and explanation

Answer: B. $1,180

$7,200 ÷ 360 = $20 per day; $20 × 59 = $1,180. Do not replace 59 actual days with two assumed 30-day months.

10. Monthly principal and interest are $1,640, annual taxes are $5,400 and annual homeowners insurance is $1,440. What is PITI for these components?

  1. $2,090
  2. $8,480
  3. $1,760
  4. $2,210
Show answer and explanation

Answer: D. $2,210

Monthly tax is $450; monthly insurance is $120. $1,640 + $450 + $120 = $2,210.

11. Value is $400,000, first-mortgage balance is $230,000 and second-mortgage balance is $25,000. No other relevant debt applies. Equity?

  1. $145,000
  2. $375,000
  3. $170,000
  4. $255,000
Show answer and explanation

Answer: A. $145,000

Include both specified secured debts: $400,000 − $230,000 − $25,000 = $145,000. This is not a borrowing approval or seller-net calculation.

12. Value is $250,000 and relevant secured debts total $270,000. What is the arithmetic equity?

  1. −$20,000
  2. $270,000
  3. $20,000
  4. Zero, because equity cannot be negative
Show answer and explanation

Answer: A. −$20,000

$250,000 − $270,000 = −$20,000. Label the shortfall; do not turn it positive or treat it as a determined sale-closing amount.

13. Annual potential income is $120,000, vacancy and collection loss $6,000, other property income $3,000 and stipulated operating expenses $57,000. No other operating adjustment applies. NOI?

  1. $60,000
  2. $117,000
  3. $63,000
  4. $57,000
Show answer and explanation

Answer: A. $60,000

$120,000 − $6,000 + $3,000 = $117,000 effective gross income. Less $57,000 expenses gives $60,000 NOI, before mortgage debt service.

14. Annual NOI is $60,000 and the identified property price is $750,000. Cap rate?

  1. 12.5%
  2. 8%
  3. 80%
  4. 0.8%
Show answer and explanation

Answer: B. 8%

$60,000 ÷ $750,000 = 0.08 = 8%. The denominator is the property price, not investor cash.

15. A direct-capitalization problem stipulates $60,000 annual NOI and an appropriate 8% rate. No other adjustment applies. Indicated value?

  1. $480,000
  2. $7,500,000
  3. $750,000
  4. $4,800
Show answer and explanation

Answer: C. $750,000

Divide by the decimal rate: $60,000 ÷ 0.08 = $750,000. This is the stated model’s indication, not a complete appraisal.

16. Loan amount is $304,000 and the required value base is $380,000. LTV?

  1. 125%
  2. 80%
  3. 24%
  4. 76%
Show answer and explanation

Answer: B. 80%

$304,000 ÷ $380,000 = 0.80 = 80%. Do not substitute the separately stated purchase price for the specified base.

17. Price is $400,000, accepted appraisal is $380,000 and a stipulated eligible loan is 80% of the lower figure. Ignore costs, deposits and credits. What percentage of price must the buyer contribute?

  1. 24%
  2. 20%
  3. 76%
  4. 80%
Show answer and explanation

Answer: A. 24%

Loan is $304,000. The $96,000 price contribution divided by $400,000 is 24%. The 80% LTV uses the lower $380,000 denominator.

18. A $280,000 loan has 2.5 discount points. Dollar cost of those points?

  1. $7,500
  2. $2,800
  3. $28,000
  4. $7,000
Show answer and explanation

Answer: D. $7,000

$280,000 × 0.025 = $7,000. A point is 1% of loan amount, not a promise about the rate reduction.

19. A separate origination fee is stipulated as 0.75% of a $280,000 loan. Dollar charge?

  1. $7,500
  2. $2,100
  3. $750
  4. $21,000
Show answer and explanation

Answer: B. $2,100

Convert 0.75% to 0.0075. $280,000 × 0.0075 = $2,100. The example specifies the fee’s base and rate.

20. A $280,000 loan has 2.5 discount points and a distinct 0.75% origination fee, both loan-based. No other fee applies. Combined specified charges?

  1. $9,100
  2. $7,000
  3. $2,100
  4. $8,400
Show answer and explanation

Answer: A. $9,100

Points cost $7,000; the separate origination charge is $2,100. Total $9,100. The facts state that these are distinct items, not duplicate labels for one charge.

21. A simplified seller-net problem targets $120,000 proceeds. Dated payoff is $180,000, fixed other charges are $6,000, and the agreed commission is 4% of sale price. No other amount applies. Required sale price?

  1. $312,240
  2. $300,000
  3. $306,000
  4. $318,750
Show answer and explanation

Answer: D. $318,750

Let price be P: 0.96P − $186,000 = $120,000. Thus P = $306,000 ÷ 0.96 = $318,750. Commission is $12,750 and subtracting it, $180,000 and $6,000 recovers the $120,000 target. The commission percentage is hypothetical, not prescribed.

22. A stipulated buyer-funds calculation is $200,000 price + $3,000 costs − $180,000 loan funding − $25,000 available credited deposit, with no other arithmetic item. The signed result is −$2,000. Best interpretation?

  1. The buyer must bring positive $2,000
  2. A negative result proves the lender approved an unrestricted refund
  3. The stated funding exceeds the stated uses by $2,000; actual treatment needs review
  4. The deposit must be charged a second time
Show answer and explanation

Answer: C. The stated funding exceeds the stated uses by $2,000; actual treatment needs review

The stated uses are $203,000 and funding is $205,000, a $2,000 arithmetic surplus. Retain the negative sign. Whether funds may actually be returned, reduced or otherwise applied depends on the transaction and applicable program rules.

23. Annual NOI is $60,000, price is $750,000, annual debt service is $30,000 and total investor cash is $300,000. No other cash-flow adjustment applies. What are cap rate and the defined cash-on-cash return, respectively?

  1. 20% and 10%
  2. 8% and 20%
  3. 10% and 8%
  4. 8% and 10%
Show answer and explanation

Answer: D. 8% and 10%

Cap rate = $60,000 ÷ $750,000 = 8%. Defined cash flow is $30,000 after stated debt service; dividing by $300,000 cash gives 10%. Investor cash is not the cap-rate denominator.

24. A $240,000 fixed-rate loan has a hypothetical 6% annual rate and 360 equal end-of-month amortizing payments, monthly rate annual ÷ 12, with no odd period. Add annual taxes $4,800 and homeowners insurance $1,200; no other component applies. Approximate monthly PITI to cents?

  1. $1,938.92
  2. $6,438.92
  3. $1,438.92
  4. $1,700.00
Show answer and explanation

Answer: A. $1,938.92

P&I = $240,000 × 0.005 ÷ [1 − (1.005)^(−360)] ≈ $1,438.92126. Add $400 tax and $100 insurance, then round the $1,938.92126 total to $1,938.92. First-month interest alone does not include principal repayment.

Common questions

How much math is on the Illinois real estate exam?

PSI’s national broker outline assigns 7 of 100 scored questions to National XI, Real Estate Calculations. It names transaction and general calculation topics. Financing, valuation, ownership and Illinois material can also require arithmetic. Do not interpret the domain allocation as a guarantee that only seven questions anywhere on the exam involve numbers.

Which calculation topics should I practice?

Practice seller proceeds, buyer funds, real-property taxes and other prorations, transfer fees, PITI, equity, rate of return or capitalization rate, LTV, discount points and origination fees. The current outline also specifies PITI payment estimation given loan rate and term. Learn the base and units for each relationship rather than memorizing a list of answer patterns.

Are commission splits or debt ratios separate current math headings?

Commission splits are not a standalone heading in National XI, although a stated commission can enter proceeds or compensation arithmetic. General underwriting, including debt ratios, appears in Financing. An outline label tells you where PSI organizes a topic; it does not make supporting arithmetic irrelevant.

What is the difference between buyer down payment and cash to close?

Price less loan funding gives the basic buyer price contribution in a simple purchase. Buyer charges, prepaids, deposits and credits change the remaining amount needed. Identify whether a supplied figure is total contribution, remaining funds, amount financed or actual loan proceeds. Do not count a deposit or prepaid fee twice.

How do I know whether a proration is a debit or credit?

First identify whose period is involved and who paid or will pay. For an unpaid seller-period expense the buyer will pay, the seller generally owes the buyer: seller debit, buyer credit. For the seller’s prepaid charge covering the buyer’s period, the buyer generally reimburses the seller. Advance rent collected by the seller is different because it is income allocated to the buyer’s period. Use the agreement and exact facts.

Does Illinois always require 360 days or a 105% tax credit?

No universal 360-day basis, 105% multiplier or closing-day allocation follows from the IDOR closing guidance cited here. It describes existing-home seller responsibility and credits according to the contract, separately from a lender’s escrow requirements. New construction can involve a reproration agreement. If the exercise gives a percentage, day basis or annual tax estimate, use it and keep those instructions visible.

Are Actual/360 and 30/360 the same?

No. Both can divide an annual amount by 360, but Actual/360 counts actual calendar days in its numerator, while a 30/360 method uses assumed month days under its convention. The Fannie Mae source is a loan-interest example, not a statewide Illinois tax-proration requirement. State the exact convention before calculating.

What is the Illinois state real estate transfer-tax rate?

For a covered nonexempt transfer, 35 ILCS 200/31-10 imposes $0.50 for each $500 of taxable value or fraction. County law allows a separate $0.25-per-$500-or-fraction tax where imposed. Municipal rules can add another layer with their own requirements. Determine the taxable base, exemption and applicable layers before calculating. The worked questions expressly stipulate an already determined base.

Can I subtract the seller’s mortgage payoff from the transfer-tax base?

Do not do so automatically. A loan paid off at closing is different from a qualifying transfer subject to an outstanding mortgage under the statutory language. The transferring-document and remaining-mortgage conditions matter. A seller-proceeds deduction does not, by itself, become a transfer-tax-base deduction.

What does PITI include?

Principal, interest, property taxes and insurance. The examples identify homeowners insurance expressly. Convert annual tax and insurance amounts to monthly before adding them to monthly principal and interest. If asked for a broader payment or housing total, include other specified items such as mortgage insurance or association dues. Do not count the same insurance twice.

How do I estimate a payment when the problem gives rate and term?

For the positive-rate, fully amortizing monthly schedule stated in the worked example, use M = P × r ÷ [1 − (1 + r)^(−n)]. P is loan principal, r is the monthly rate in decimal form and n is the number of monthly payments. For an otherwise matching zero-interest schedule, the principal payment is P divided by n. A supplied payment factor can be used with its stated units instead. Then add monthly taxes and the specified insurance for PITI. Interest-only, balloon, adjustable-rate, odd-period and other schedules need their own terms; do not apply this formula without identifying the schedule.

What goes into NOI for a cap-rate question?

Use the defined effective property income less the stated operating expenses. Ordinary property taxes can be operating expenses; the owner’s income taxes are different. Standard NOI is before mortgage debt service and book depreciation. Reserve and capital-item treatment can differ across models, so use consistent stated assumptions in the NOI and the selected cap rate.

How are cap rate and investor cash return different?

Cap rate uses annual NOI divided by property price or value. A defined cash-on-cash return uses the stated annual cash flow after applicable adjustments divided by investor cash. Financing can change the second measure without changing the same underlying NOI-to-price ratio. Neither is a guaranteed total investment return.

Why is an 80% LTV not always a 20% down payment?

The denominators may differ. In the stated purchase example, the loan is 80% of a $380,000 accepted appraisal while price is $400,000. The $304,000 loan leaves $96,000 toward price, or 24% of price, before costs and credits. The Fannie Mae purchase rule has program and transaction qualifications; the exercise is not a universal lending maximum or approval.

Do discount points and origination fees use the sale price?

One point is 1% of the loan amount. A percentage origination fee uses the base the problem or actual fee agreement specifies; the examples stipulate the loan amount. Points and an origination charge can be separate, but do not add one fee twice if the figures already include it. A point’s dollar cost does not fix how much the lender reduces the interest rate.

What does a negative closing-funds result mean?

Keep the sign and check the setup. Negative seller proceeds indicate a shortfall under the stated items. A negative buyer-funds result can indicate that the stated credits and funding exceed the stated uses. Neither result independently approves a refund, fee allocation or loan. Review the underlying figures and applicable requirements before deciding how real funds are handled.

What score means I am ready, and when should I round?

A practice score alone cannot validate readiness. Check whether you can explain the setup, units and wrong options on fresh problems, including after a delay. Keep intermediate precision unless an instruction or required convention says otherwise. Rounding up a statutory taxable unit is different from rounding a final money amount to cents. If a question omits a convention that changes the answer, identify the missing assumption rather than inventing a universal local custom.

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Official sources and scope

Reviewed October 26, 2026. The current PSI outline and identified official tax, consumer-finance and mortgage materials support the distinctions above. Prior actual ledger, equity, lending, income-analysis and competition readings are identified in the review record. The older DRE chapter is used for foundational income arithmetic. All example rates, prices, credits and day conventions are hypothetical or expressly stipulated. No private closing, filing, appraisal or loan approval is determined.

This is exam preparation, not advice for a specific transaction. State law and the applicable facts control. Our editorial and corrections process explains how to report an issue.

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