Learning Objectives

• Calculate simple interest using principal, rate, and time.
• Convert annual interest into monthly or daily amounts when the problem requires it.
• Calculate loan-to-value ratio, loan amount, equity, and down payment.
• Calculate discount points and distinguish points from the interest rate.
• Apply assessed value, exemptions or deductions, tax rates, and mills in property-tax problems.
• Prorate taxes, rents, association charges, and other expenses using the day-count and ownership rules stated in the question.
• Classify settlement entries as buyer debits, buyer credits, seller debits, or seller credits.
• Calculate cash needed from a buyer and estimated proceeds to a seller.
• Perform basic depreciation calculations when the problem supplies the method, basis, and recovery period.
• Separate national calculation principles from partially verified Indiana tax and closing rules and the fact-specific issues still awaiting authority review.

Key Vocabulary

Term	Meaning
Principal	The unpaid amount on which interest is calculated.
Simple Interest	Interest calculated on principal using a stated rate and period.
Loan-to-Value Ratio (LTV)	Loan amount divided by the property's value or price used by the lender.
Equity	Value remaining after subtracting liens or debt from property value.
Discount Point	One percent of the loan amount, commonly paid in connection with the loan's pricing.
Mill	One-thousandth of a dollar, or 0.001; one mill equals $1 of tax per $1,000 of taxable value.
Assessed Value	Value assigned for property-tax purposes under the applicable assessment system.
Taxable Value	The value to which the applicable tax rate is applied after authorized adjustments.
Proration	Allocation of an income or expense between parties according to time or another stated basis.
Debit	An amount charged to a party on a settlement statement.
Credit	An amount entered in favor of a party on a settlement statement.
Earnest Money Credit	The buyer's previously deposited funds credited toward the amount due at closing.
Mortgage Payoff	Amount required to satisfy an existing loan, generally charged to the seller when seller-owned debt is paid at closing.
Depreciable Basis	Portion of property basis eligible for depreciation under the method supplied; land itself is generally not depreciated.
PITI	Principal, interest, taxes, and insurance—the common components of a total housing payment.

Chapter Opening

Chapter 29 established the math language. This chapter applies that language to financing and settlement. These problems are rarely difficult because of arithmetic. They become difficult when a student uses the wrong base, ignores the time period, or treats every closing entry as though it affects both parties the same way.

The professional habit is simple: label the amount, identify who owns or owes it, determine the time period, write the formula, and calculate one step at a time. A settlement calculation is an accounting story. Every number must answer: What is it, whose amount is it, and why is it here?

Core Lesson

1. Simple Interest: I = P × R × T

Simple interest uses three inputs: principal, annual rate, and time expressed as part of a year. Convert the percentage to a decimal before multiplying.

When solving for a missing value, divide by the other factors. Rate = Interest ÷ (Principal × Time). Principal = Interest ÷ (Rate × Time). Always ensure the time and rate use compatible annual units.

2. Monthly and Daily Interest

For a monthly interest estimate, annual interest may be divided by 12. For a daily calculation, use the number of days the question directs—commonly 360 or 365. Do not choose a convention silently. Licensing questions normally state the convention.

In an amortized loan payment, the interest portion is based on the outstanding balance for the period. The remainder of the principal-and-interest payment reduces principal. As principal declines, the interest portion generally declines and the principal portion generally increases, assuming a standard fixed-rate amortization schedule.

3. Loan-to-Value Ratio

If a lender makes a $306,000 loan on a $360,000 value, the LTV is $306,000 ÷ $360,000 = 0.85, or 85%. If the permitted LTV is 80% on a $500,000 value, the maximum loan is $400,000.

Read carefully to determine whether the lender uses sale price, appraised value, or the lower of the two. The exam may supply the controlling value. Do not assume every transaction uses the same underwriting rule.

4. Down Payment, Equity, and Leverage

When purchase price equals the value used by the lender, the down-payment percentage is commonly 100% minus the LTV percentage. At 85% LTV, the price-based down payment is 15%. Dollar down payment = price × down-payment rate.

Equity is value minus debt. A property worth $420,000 with a $294,000 loan has $126,000 in equity. Equity is not always cash available to the owner because sale expenses, junior liens, taxes, and market changes may affect actual proceeds.

5. Discount Points

One point equals one percent of the loan amount, not the sale price. Two points on a $275,000 loan equal $275,000 × 0.02 = $5,500. Points may affect loan pricing, but a math question asking only for the dollar amount does not require a conclusion about whether the points are deductible, refundable, or beneficial.

6. Property-Tax Framework

Property-tax systems begin with a value assigned under state law. Adjustments such as exemptions, deductions, classifications, assessment ratios, or caps may affect the taxable amount or final bill. The exam problem controls: use only the adjustments stated.

If a problem gives an assessed value of $240,000, an allowed $40,000 deduction, and a 1.25% rate, taxable value is $200,000 and tax is $2,500. Do not subtract an exemption twice or apply a percentage to the wrong base.

7. Proration: Allocate by Ownership

Proration allocates an item between buyer and seller. The calculation requires four decisions:

1. Is the item paid in advance or in arrears?
2. What annual, monthly, or daily amount applies?
3. Who owns the day of closing?
4. Which party has already paid or still owes the outside party?

Use the problem's day-count convention. Annual amount ÷ 360 or 365 produces a daily rate. Monthly amounts may be divided by the actual number of days in the month or by 30 when instructed.

8. Paid in Arrears Versus Paid in Advance

For an expense paid in arrears, the party who benefited before closing may owe the other party a credit because the other party will pay later. For an item paid in advance, the party who prepaid may receive reimbursement for the other party's period.

Do not memorize “taxes are always seller debit/buyer credit” as a universal truth. The direction depends on whether the bill is paid, the period covered, the local billing system, and the contract or problem instructions.

9. Debits and Credits at Settlement

Item	Typical entry when stated facts apply	Reason
Purchase price	Buyer debit; seller credit	Buyer owes price; seller receives it
New loan proceeds	Buyer credit	Funds applied for buyer
Earnest money already deposited	Buyer credit	Buyer has already supplied funds
Seller's mortgage payoff	Seller debit	Seller's lien is satisfied
Seller-paid commission	Seller debit	Charge deducted from seller proceeds
Buyer closing cost	Buyer debit	Charge owed by buyer
Proration	One debit and one credit	Allocates one item between parties

A debit is not automatically “bad,” and a credit is not automatically cash in hand. The columns show accounting treatment for each party.

10. Buyer Cash to Close

A simplified exam calculation may use:

For a $320,000 price with an 80% loan, $10,000 earnest-money credit, and $8,000 in buyer closing costs: loan = $256,000. Cash = $320,000 + $8,000 − $256,000 − $10,000 = $62,000.

Actual lender disclosures include additional items and regulatory calculations. Follow the facts supplied rather than inventing a cost.

11. Seller Net Proceeds

A simplified seller estimate begins with the sale-price credit and subtracts the stated commission, mortgage payoff, seller closing costs, and seller-side prorations. Never call an early estimate guaranteed proceeds; payoff interest, liens, tax figures, repairs, concessions, and closing changes can alter it.

12. Depreciation Fundamentals

Depreciation is an accounting and tax concept that allocates the cost of eligible improvements over a recovery period. Land is generally separated from the depreciable improvement basis. On an exam, use the basis, method, and recovery period stated in the question.

If a problem gives $270,000 of depreciable improvement basis and a 27-year recovery period, annual straight-line depreciation is $10,000. This is a math exercise—not tax advice. Current federal rules, property classifications, placed-in-service dates, improvements, recapture, and Indiana tax treatment require qualified tax guidance.

13. Complete Calculation Workflow

1. Circle the requested answer.
2. List facts with units and party labels.
3. Convert rates to decimals.
4. Identify the correct base and time period.
5. Write one formula per step.
6. Carry full precision until the final rounding step.
7. Classify the result as buyer or seller debit/credit when required.
8. Estimate and test whether the final amount is reasonable.

Learn It

Build a four-column scratch sheet: Amount · Unit · Party · Treatment. For a financing question, write principal, annual rate, and time. For a tax question, write assessed value, allowed adjustment, taxable value, and rate. For a closing question, maintain separate buyer and seller columns. This structure prevents a correct number from being placed on the wrong side.

Live It

Pass It

Use the words in the problem as instructions. “Of the loan” identifies the base for points. “Annual” requires a time conversion when the period is shorter than a year. “Paid in advance” and “paid in arrears” determine who reimburses whom. “Ignoring other costs” means do not invent them. If the question asks for cash to close, combine buyer debits and credits—not seller figures.

Indiana Law Spotlight

Indiana property-tax assessment, deductions, credits, tax caps, billing, delinquency, and proration practices are controlled by current state and local authority. Closing contracts and local practice determine how parties allocate taxes and other charges. A national math formula does not establish an Indiana legal obligation.

Partially verified Indiana framework: Assessed value is the starting point for the annual tax calculation. Deductions reduce assessed value to net or taxable assessed value; credits reduce the tax liability. Indiana's circuit-breaker framework generally limits liability above 1% of gross assessed value for homesteads, 2% for other residential property and agricultural land, and 3% for other real and personal property, but referendum charges, statutory adjustments, classifications, and exceptions can change the result. Indiana real-property taxes are paid in arrears and generally billed in two installments. Assessment information comes from the county or township assessor, deductions and credits are administered through the county auditor, and payment goes to the county treasurer.

For a covered mortgage transaction, federal Regulation Z generally requires the consumer to receive the Closing Disclosure no later than three business days before consummation. That disclosure, the contract, current payoff and tax information, and the lender or settlement provider's figures—not a classroom estimate—control the actual transaction.

Practical brokerage application: Use the current parcel record, tax bill, contract, lender documents, title or settlement statement, and firm procedure. Date every estimate and label its assumptions. A broker should not decide tax eligibility, guarantee a bill, select a proration convention not found in the controlling documents, give tax advice, or independently alter settlement accounting.

Remaining Indiana legal verification queue: Exact assessment and appeal rules, every exemption/deduction/credit, circuit-breaker exceptions, special assessments, delinquency and tax-sale effects, contract proration language, prior-year estimates, closing-day conventions, escrow reserves, closing and document authority, good funds, disbursement, settlement records, federal disclosure exceptions, depreciation and income-tax treatment, broker scope, controlling forms, local procedure, and case law remain queued. No universal proration direction, closing-day convention, cash-to-close amount, or tax result is stated.

National Exam Alert

• Simple interest: I = P × R × T.
• LTV = loan amount ÷ value.
• One point = 1% of the loan amount.
• One mill = 0.001.
• Use the 360- or 365-day year specified by the question.
• Purchase price is commonly a buyer debit and seller credit.
• New loan proceeds and earnest money are commonly buyer credits.
• Seller mortgage payoff and seller-paid commission are seller debits.
• Land is generally excluded from depreciable basis.

Common Exam Trap

• Points trap: applying points to the purchase price instead of the loan amount.
• LTV trap: dividing value by loan rather than loan by value.
• Time trap: using a full year's interest for a six-month period.
• Mill trap: reading 18 mills as 18% instead of 0.018.
• Proration trap: computing the right amount but reversing the debit and credit.
• Cash trap: forgetting to credit earnest money already paid.
• Net trap: subtracting the buyer's new loan from seller proceeds.
• Depreciation trap: depreciating land when the question separates land and improvements.

PASS FIRST Memory Trick

Broker Insight

Use math to explain, not to overpromise. Date every estimate, state its assumptions, identify the source of each figure, and label unknown items. Updated lender and title documents control over a broker's worksheet. When a client questions taxes, deductibility, loan pricing, payoff, or legal responsibility, preserve the deadline and direct the issue to the lender, title professional, tax professional, attorney, or government office with authority.

Tables & Comparison Charts

Calculation	Formula	Primary base
Simple interest	P × R × T	Principal
LTV	Loan ÷ Value	Property value used
Loan amount	Value × LTV	Property value used
Points	Loan × points rate	Loan amount
Property tax	Taxable value × tax rate	Taxable value
Daily proration	Annual amount ÷ stated days × allocated days	Annual item
Buyer cash	Buyer debits − buyer credits	Buyer columns
Seller net	Seller credits − seller debits	Seller columns
Straight-line depreciation	Depreciable basis ÷ recovery period	Eligible improvement basis

Chapter Summary

• Simple interest equals principal times rate times time.
• LTV divides the loan by the value used in the problem.
• One discount point equals 1% of the loan amount.
• Property tax applies the stated rate to taxable value; one mill equals 0.001.
• Prorations require the payment status, time convention, closing-day ownership, and responsible party.
• Buyer cash is generally buyer debits minus buyer credits.
• Seller net is generally seller credits minus seller debits.
• Earnest money and new loan proceeds are commonly buyer credits; seller payoff and seller-paid commission are seller debits.
• Depreciation normally applies to eligible improvements rather than land and follows the method supplied.
• Indiana assessment, deduction/credit, circuit-breaker, arrears-billing, installment and federal Closing Disclosure principles are partially verified; transaction-specific tax and closing issues remain queued.

Quick Review

• I = P × R × T.
• LTV = Loan ÷ Value.
• Loan = Value × LTV.
• Points = Loan × points percentage.
• 1 mill = 0.001.
• Daily amount = annual amount ÷ stated days per year.
• Classify every closing entry by party and debit or credit.
• Use only costs supplied in the problem.
• Keep full precision until final rounding.
• Estimate before accepting the result.

Practice Questions

1. A $240,000 principal balance bears 6% simple annual interest for six months. How much interest accrues?
   1. $14,400
   2. $1,200
   3. $7,200
   4. $6,000
2. A lender makes a $306,000 loan on a property value of $360,000. What is the LTV?
   1. 85%
   2. 80%
   3. 88%
   4. 118%
3. What is the cost of two discount points on a $275,000 loan?
   1. $2,750
   2. $4,125
   3. $27,500
   4. $5,500
4. A buyer makes a 15% down payment on a $425,000 purchase. What is the down payment?
   1. $60,000
   2. $63,750
   3. $72,250
   4. $361,250
5. What is one month's simple interest on $192,000 at 7.5% annual interest?
   1. $1,200
   2. $14,400
   3. $1,440
   4. $960
6. Taxable value is $210,000 and the tax rate is 18 mills. What is the annual tax?
   1. $378
   2. $37,800
   3. $3,780
   4. $11,667
7. Assessed value is $240,000, an allowed deduction is $40,000, and the tax rate is 1.25%. What is the tax?
   1. $3,000
   2. $2,500
   3. $2,400
   4. $3,500
8. Annual taxes are $4,380 on a 365-day basis. The seller owns 100 days, and the unpaid taxes will later be paid by the buyer. What is the seller's share?
   1. $438
   2. $1,000
   3. $1,460
   4. $1,200
9. An annual association charge of $1,200 was paid in advance by the seller. Closing is April 1, and the buyer owns April through December. Using whole months, what should the buyer reimburse the seller?
   1. $300
   2. $900
   3. $1,000
   4. $1,200
10. A property sells for $480,000. The seller's mortgage payoff is $286,000, commission is $24,000, and other seller costs are $5,000. What are estimated seller proceeds?
    1. $189,000
    2. $170,000
    3. $175,000
    4. $165,000
11. A home costs $320,000. The buyer receives an 80% loan, has a $10,000 earnest-money credit, and owes $8,000 in buyer closing costs. What simplified cash amount is due from the buyer?
    1. $62,000
    2. $54,000
    3. $72,000
    4. $64,000
12. A problem supplies a $270,000 depreciable improvement basis and a 27-year straight-line recovery period. What is annual depreciation?
    1. $7,500
    2. $27,000
    3. $10,000
    4. $12,500
13. Which item is most commonly a seller debit when the seller's existing loan is paid at closing?
    1. Buyer earnest money
    2. Buyer loan proceeds
    3. Purchase price
    4. Seller mortgage payoff
14. A borrower pays $9,000 simple interest on $150,000 principal for one year. What annual rate was charged?
    1. 5%
    2. 6%
    3. 7.5%
    4. 9%
15. A monthly principal-and-interest payment is $1,600, and $950 is the interest portion. How much reduces principal?
    1. $550
    2. $950
    3. $650
    4. $1,600
16. A lender permits an 80% LTV on a $500,000 value. What is the maximum loan amount under that assumption?
    1. $400,000
    2. $100,000
    3. $420,000
    4. $625,000
17. Which information is essential before assigning a tax proration debit and credit?
    1. Only the property's listing price
    2. Only the buyer's loan amount
    3. Whether the tax is paid, the allocation period, and who owns the closing day
    4. The commission split between brokerages
18. Three discount points equal what percentage of the loan amount?
    1. 3%
    2. 0.3%
    3. 30%
    4. 0.03%
19. Annual taxes of $6,240 were paid in full in advance by the seller. The buyer will own exactly half of the covered year. Ignoring other facts, what reimbursement is due to the seller?
    1. $520
    2. $6,240
    3. $2,080
    4. $3,120
20. A lender will loan no more than 75% of a $200,000 appraised value. What is the maximum loan?
    1. $50,000
    2. $150,000
    3. $175,000
    4. $266,667

Detailed Answer Explanations

1. C. I = P × R × T. $240,000 × 0.06 × 0.5 = $7,200. Choice A incorrectly uses a full year.
2. A. LTV = $306,000 ÷ $360,000 = 0.85, or 85%. Loan belongs in the numerator.
3. D. One point is 1% of the loan. Two points are $275,000 × 0.02 = $5,500.
4. B. $425,000 × 0.15 = $63,750. The remaining $361,250 would equal 85% of price.
5. A. Annual interest is $192,000 × 0.075 = $14,400. Divide by 12 to obtain $1,200 for one month.
6. C. Eighteen mills is 0.018. $210,000 × 0.018 = $3,780.
7. B. Taxable value is $240,000 − $40,000 = $200,000. $200,000 × 0.0125 = $2,500.
8. D. $4,380 ÷ 365 = $12 per day. $12 × 100 days = $1,200. Because the buyer will pay the unpaid bill later, this is commonly a seller debit and buyer credit under the stated facts.
9. B. The monthly charge is $1,200 ÷ 12 = $100. The buyer owns nine months, so reimbursement is $900.
10. D. $480,000 − $286,000 − $24,000 − $5,000 = $165,000. Use only the seller charges supplied.
11. A. Loan is $320,000 × 0.80 = $256,000. Buyer cash = $320,000 + $8,000 − $256,000 − $10,000 = $62,000.
12. C. Straight-line annual depreciation = $270,000 ÷ 27 = $10,000. The problem supplies the eligible basis and period.
13. D. The seller's existing mortgage payoff is charged to the seller. Buyer loan proceeds and earnest money are commonly buyer credits; purchase price is commonly a seller credit.
14. B. Rate = Interest ÷ (Principal × Time). $9,000 ÷ ($150,000 × 1) = 0.06, or 6%.
15. C. $1,600 payment − $950 interest = $650 applied to principal.
16. A. Loan = Value × LTV. $500,000 × 0.80 = $400,000.
17. C. A proration cannot be assigned correctly without knowing the payment status, allocation period, closing-day treatment, and responsible party. Price, loan, and commission split do not answer those questions.
18. A. Each point is 1% of the loan amount, so three points equal 3%.
19. D. Half of $6,240 is $3,120. Because the seller prepaid the covered year, the buyer reimburses the seller for the buyer's half under the stated assumptions.
20. B. $200,000 × 0.75 = $150,000. Dividing by 0.75 would solve for value when the loan is known, not the maximum loan here.

Mastery Checklist

• I can calculate simple interest and solve for principal, rate, or time.
• I can calculate a monthly or daily interest amount using the stated convention.
• I can calculate LTV, maximum loan, down payment, and equity.
• I can calculate points using the loan amount as the base.
• I can convert mills to a decimal and calculate tax from taxable value.
• I can identify the facts needed for a valid proration.
• I can distinguish expenses paid in advance from expenses paid in arrears.
• I can classify common buyer and seller debits and credits.
• I can calculate simplified buyer cash to close and seller net proceeds.
• I can calculate straight-line depreciation from a supplied basis and recovery period.
• I can explain why an estimate is not a guaranteed lender, tax, title, or settlement figure.
• I can separate national math principles from partially verified Indiana tax and closing rules and identify what remains queued.
• I can answer at least 80% of this chapter's assessment and explain why each distractor is less appropriate.