- Official section
- National XI.D: PITI, Equity, LTV, Points, and Origination Fees
- Broker weight
- A named calculation within 7% of the national portion
- Expected scored items
- The current PSI broker outline assigns about 7 of 100 scored national items to Real Estate Math
Real estate math guide
Discount points from one clean percentage relationship
A point is a percentage of the loan amount. That single relationship solves most exam questions, whether the missing number is the charge, the points, or the loan. The harder part is resisting invented rules about how much a point changes the rate. Calculate the dollars first, then use only the pricing facts the question actually gives.
Last updated: August 1, 2026
What calculation do you need to make?
Short answer: One discount point equals 1% of the loan amount. Point cost equals loan amount multiplied by points divided by 100. Number of points equals point cost divided by loan amount, multiplied by 100. Loan amount equals point cost divided by the points percentage written as a decimal. True discount points trade a higher upfront charge for a lower interest rate, while lender credits generally trade a higher interest rate for lower upfront costs. Current federal guidance does not promise that one point changes the rate by a fixed amount. If an exam problem says each point changes lender yield by a stated fraction, treat that fraction as a problem fact, not a market law. Keep discount points separate from down payment, principal, mortgage insurance, prepaid interest, and an origination fee.
This guide teaches exam arithmetic and disclosure recognition, not a recommendation to buy points or accept a lender credit. Actual pricing depends on the lender, loan product, borrower, lock period, and market. A simple break-even calculation omits important financial and tax considerations. Tax treatment can depend on current law and transaction facts, so use current IRS guidance and a qualified tax professional for an actual return. Sources were checked through August 1, 2026.
How do you solve discount-points and lender-yield questions?
- Circle the requested unknown: point cost, number of points, loan amount, rate tradeoff, lender credit, or simplified break-even time.
- Find the loan amount before doing point math, especially when the stem gives a purchase price and down-payment percentage.
- Translate the points figure to a decimal by dividing by 100, so 1.75 points becomes 0.0175.
- Multiply loan by points decimal for cost, or reverse the relationship with division when another number is missing.
- Treat discount points and percentage points of interest as separate units and use only the rate relationship supplied.
- Keep origination fees, lender credits, down payment, prepaids, and mortgage insurance on their own lines.
- Check the result against one percent of the loan and reverse the arithmetic before choosing an answer.
- Label the final result in dollars, points, percent, or months and state any pricing convention the problem required.
- Unknown or clue
- Cost of one point
- Formula or direction
- Loan amount x 0.01
- Exam safeguard
- Use loan, not price
- Unknown or clue
- Cost of several points
- Formula or direction
- Loan amount x points / 100
- Exam safeguard
- Convert percent
- Unknown or clue
- Number of points
- Formula or direction
- Charge / loan amount x 100
- Exam safeguard
- Answer in points
- Unknown or clue
- Loan amount
- Formula or direction
- Charge / points decimal
- Exam safeguard
- Divide by decimal
- Unknown or clue
- Loan from price
- Formula or direction
- Price - down payment
- Exam safeguard
- Then price points
- Unknown or clue
- Lender credit
- Formula or direction
- Lower upfront cost, usually higher rate
- Exam safeguard
- Reverse tradeoff
- Unknown or clue
- Discount points
- Formula or direction
- Higher upfront cost, lower rate
- Exam safeguard
- Reduction varies
- Unknown or clue
- Break-even months
- Formula or direction
- Point cost / monthly P&I savings
- Exam safeguard
- Simplified only
- Unknown or clue
- Yield shortcut
- Formula or direction
- Use stated change per point
- Exam safeguard
- Never assume it
- Unknown or clue
- Origination fee
- Formula or direction
- Loan x stated fee percentage
- Exam safeguard
- Separate purpose
Can you follow the calculation from facts to answer?
Calculate the cost of fractional points
Scenario: A borrower obtains a $320,000 loan and pays 1.5 discount points. What is the charge?
- Convert 1.5 points to 0.015.
- $320,000 x 0.015 = $4,800.
- Check: one point is $3,200, and half a point is $1,600.
Answer: The discount-point charge is $4,800.
Recover the quoted number of points
Scenario: A $350,000 loan shows a $4,375 charge for points. How many points were paid?
- $4,375 / $350,000 = 0.0125.
- Multiply by 100 to express the decimal as points.
- 0.0125 x 100 = 1.25.
Answer: The borrower paid 1.25 points.
Recover the loan amount
Scenario: Two points cost a borrower $6,000. What is the loan amount?
- Convert 2 points to 0.02.
- $6,000 / 0.02 = $300,000.
- Check: 1% of $300,000 is $3,000, so 2 points cost $6,000.
Answer: The loan amount is $300,000.
Find the point base after a down payment
Scenario: A buyer pays 20% down on a $450,000 property and pays 0.75 points on the loan. What is the point charge?
- The loan is 80% of $450,000, or $360,000.
- Convert 0.75 points to 0.0075.
- $360,000 x 0.0075 = $2,700.
Answer: The point charge is $2,700.
Calculate a simplified break-even period
Scenario: One loan option requires $4,000 in points and produces $80 in stated monthly P&I savings over the zero-point option. What is the simple break-even period?
- $4,000 / $80 = 50 months.
- At that point, nominal monthly savings equal the upfront charge.
- The shortcut omits timing, tax, refinance, sale, and opportunity-cost effects.
Answer: The simplified break-even period is 50 months.
Use a lender-yield convention only when supplied
Scenario: A classroom problem states that each point raises lender yield by 0.125 percentage point. The note rate is 6% and the desired yield is 6.375% on a $280,000 loan. How many points and how many dollars does the stated convention produce?
- The stated yield gap is 6.375% - 6% = 0.375 percentage point.
- Under the supplied convention, 0.375 / 0.125 = 3 points.
- $280,000 x 0.03 = $8,400. The convention is a problem fact, not universal current pricing.
Answer: The supplied convention produces 3 points, or $8,400.
Which math errors cost the most points?
- Trap
- Calculate points from the purchase price.
- Correction
- Use the loan amount unless the question explicitly defines a different fee base.
- Trap
- Multiply by 1.5 when the loan charges 1.5 points.
- Correction
- Convert 1.5% to 0.015 before multiplying.
- Trap
- Divide a charge by the whole number 2 to recover a two-point loan.
- Correction
- Divide by 0.02 because two points mean 2% of the loan.
- Trap
- Assume one point always lowers the note rate by 0.25 percentage point.
- Correction
- Current federal guidance says the rate reduction varies by lender, loan type, and market.
- Trap
- Apply a one-eighth yield shortcut even though the stem never gives it.
- Correction
- Use a yield-per-point convention only when the problem expressly supplies it.
- Trap
- Call every percentage-based lender charge a discount point.
- Correction
- Separate points paid to reduce the rate from origination and other loan charges.
- Trap
- Treat a lender credit as cash paid by the borrower for a lower rate.
- Correction
- A rate-connected lender credit generally lowers upfront cost in exchange for a higher rate.
- Trap
- Subtract points from the loan balance.
- Correction
- Points are an upfront loan cost unless the stated transaction handles payment differently; they are not principal reduction.
- Trap
- Add a point charge to every monthly mortgage payment.
- Correction
- The charge is paid at closing in the basic calculation; monthly P&I changes only through the quoted rate option.
- Trap
- Confuse interest rate with APR.
- Correction
- APR is a broader disclosure measure and cannot be calculated from points alone.
- Trap
- Declare every point charge immediately tax deductible.
- Correction
- Tax treatment depends on current law and transaction facts; consult current IRS guidance for a real return.
- Trap
- Round the points decimal before multiplying.
- Correction
- Carry the quoted precision through the math and round the final currency result as instructed.
Can you solve these original problems?
These questions are original study items aligned to the published outline. They are not copied, recalled, or predicted PSI questions.
1. A borrower pays 1.25 points on a $280,000 loan. What is the point charge?
- $3,500
- $2,800
- $35,000
- $2,240
Show answer and explanation
Answer: $3,500
$280,000 x 0.0125 = $3,500.
2. A $4,800 point charge equals 1.5 points. What is the loan amount?
- $320,000
- $72,000
- $480,000
- $3,200
Show answer and explanation
Answer: $320,000
$4,800 / 0.015 = $320,000.
3. A $400,000 loan has a $3,000 percentage-based origination fee and a separate $4,000 discount-point charge. Which statement is correct?
- The charges use similar math but have different purposes
- Both charges are down payment
- The origination fee necessarily reduces the rate
- Only the purchase price matters
Show answer and explanation
Answer: The charges use similar math but have different purposes
The origination fee is 0.75% of the loan and the points equal 1%, but only the true discount-point line is connected to reducing the interest rate.
4. Points cost $3,600 and the stated monthly P&I savings are $75. What is the simplified break-even period?
- 48 months
- 27 months
- 75 months
- 360 months
Show answer and explanation
Answer: 48 months
$3,600 / $75 = 48 months.
5. A problem gives no rate sheet and no rate-change convention. What rate reduction should you assume for one discount point?
- No fixed rate reduction
- Exactly 0.25 percentage point
- Exactly 1 percentage point
- Exactly 0.125 percentage point
Show answer and explanation
Answer: No fixed rate reduction
The dollar definition is fixed at 1% of the loan, but the rate effect varies. Use only pricing facts supplied by the problem.
Which numbers and formulas are easy to confuse?
- Terms
- Discount point vs. percentage point of interest
- Difference
- A discount point is 1% of the loan amount in dollars. A percentage point of interest describes a rate change, and the two are not interchangeable.
- Question cue
- Dollar charge versus interest-rate unit.
- Terms
- Loan amount vs. purchase price
- Difference
- The loan amount is the borrowed principal used as the point base. Purchase price includes the portion financed and the buyer's equity contribution.
- Question cue
- Borrowed amount versus property consideration.
- Terms
- Discount points vs. down payment
- Difference
- Discount points are a loan cost paid for interest-rate pricing. Down payment is the buyer's price contribution that reduces the amount financed.
- Question cue
- Pricing charge versus equity contribution.
- Terms
- Discount points vs. origination fee
- Difference
- True discount points are connected to a reduced interest rate. An origination fee pays for originating or extending credit and does not automatically buy a lower rate.
- Question cue
- Rate discount versus loan-origination charge.
- Terms
- Discount points vs. lender credits
- Difference
- Borrower-paid points increase upfront cost for a lower rate. Lender credits generally reduce upfront cost in exchange for a higher rate.
- Question cue
- Pay now versus receive credit now.
- Terms
- Interest rate vs. APR
- Difference
- The interest rate prices borrowed principal. APR is a broader federal comparison measure that incorporates applicable credit costs under its rules.
- Question cue
- Note rate versus disclosed cost measure.
- Terms
- Point cost vs. monthly savings
- Difference
- Point cost is paid upfront. Monthly savings is the difference between payments on two quoted loan options.
- Question cue
- One-time dollars versus recurring difference.
- Terms
- Break-even period vs. loan term
- Difference
- Break-even is the time for stated monthly savings to equal the upfront cost in a simplified comparison. Loan term is the scheduled repayment period.
- Question cue
- Recovery horizon versus maturity horizon.
- Terms
- Current pricing fact vs. classroom yield convention
- Difference
- Current pricing comes from a lender's actual offer and market conditions. A classroom yield convention is usable only because the question expressly supplies it.
- Question cue
- Quoted transaction fact versus conditional shortcut.
- Terms
- Exam calculation vs. tax conclusion
- Difference
- An exam calculation finds the dollar charge. A tax conclusion requires current law and facts about the loan, home, proceeds, payment, and deduction rules.
- Question cue
- Arithmetic result versus return treatment.
What does the outline expect you to calculate?
- Topic
- One-point definition
- What to know
- One percent, loan amount, mortgage amount, point cost, percentage, decimal, fee, closing, and borrowed principal
- Best exam move
- Anchor every calculation to the loan amount and translate one point to 0.01.
- Topic
- Point-cost formula
- What to know
- Loan amount, number of points, decimal conversion, multiplication, dollar charge, fraction of a point, percentage, and closing cost
- Best exam move
- Multiply the loan by points divided by 100 and label the result in dollars.
- Topic
- Reverse number-of-points formula
- What to know
- Known charge, known loan, division, decimal, percent conversion, quoted points, rate sheet, and verification
- Best exam move
- Divide charge by loan and multiply by 100 to recover the points quote.
- Topic
- Reverse loan-amount formula
- What to know
- Known charge, known points, decimal divisor, mortgage amount, principal, reverse calculation, units, and check
- Best exam move
- Divide the dollar charge by the points decimal, not by the whole-number label.
- Topic
- Fractional points
- What to know
- Half point, quarter point, 0.625 points, 1.375 points, decimal, precision, loan pricing, and exact percentage
- Best exam move
- Treat the quoted point figure as a percentage, even when it is not a whole number.
- Topic
- Discount-point purpose
- What to know
- Upfront cost, reduced interest rate, monthly payment, same lender, same loan type, loan pricing, borrower choice, and long-term cost
- Best exam move
- Recognize the tradeoff without inventing a specific rate reduction.
- Topic
- Rate-reduction variability
- What to know
- Lender, loan type, mortgage market, rate sheet, lock period, pricing, comparison, quoted option, and no universal conversion
- Best exam move
- Use the exact rate and points alternatives stated in the problem.
- Topic
- Lender-yield convention
- What to know
- Stated convention, eighth of a percent, desired yield, note rate, rate difference, points required, classroom problem, and explicit fact
- Best exam move
- Apply an old yield shortcut only when the stem expressly defines it, then show both the rate gap and point cost.
- Topic
- Lender credits
- What to know
- Negative points, higher rate, lower upfront cost, closing-cost credit, Loan Estimate, tradeoff, same lender, and comparison
- Best exam move
- Identify the reverse pricing direction and keep the credit separate from borrower-paid points.
- Topic
- Origination fees
- What to know
- Origination charge, loan originator, extending credit, percentage fee, dollar calculation, disclosure label, Section A, and separate purpose
- Best exam move
- Use the same percentage math when stated, but do not call every origination charge a discount point.
- Topic
- Loan Estimate placement
- What to know
- Page 2, Section A, Origination Charges, percentage of loan amount, dollar amount, points label, lender credits, Section J, and disclosure
- Best exam move
- Recognize points as a separately itemized charge connected to reducing the interest rate.
- Topic
- Break-even shortcut
- What to know
- Upfront cost, monthly P&I savings, months, division, keeping period, refinance, sale, time value, and comparison
- Best exam move
- Divide cost by stated monthly savings only when the question requests a simplified break-even period.
- Topic
- Price versus loan amount
- What to know
- Purchase price, down payment, financed balance, LTV, loan amount, point base, borrower cash, and mistaken base
- Best exam move
- Calculate the loan first when the problem gives only price and down payment, then apply the point percentage.
- Topic
- Cash-to-close relationship
- What to know
- Point charge, closing cost, down payment, deposits, credits, prepaids, loan costs, Cash to Close, and ledger
- Best exam move
- Add the calculated point charge only within the fuller closing ledger the question supplies.
- Topic
- APR boundary
- What to know
- Interest rate, annual percentage rate, finance charge, loan costs, disclosure, comparison measure, note rate, and calculation boundary
- Best exam move
- Do not substitute the APR for the note rate or try to derive APR from points alone.
- Topic
- Tax boundary
- What to know
- Mortgage interest deduction, points, secured debt, qualified home, itemizing, acquisition, refinancing, allocation, and current IRS guidance
- Best exam move
- Do not assume every point charge receives the same deduction or timing treatment.
- Topic
- Rounding and labels
- What to know
- Currency, cents, percentage points, basis points, exact points quote, nearest dollar, disclosure precision, and answer choices
- Best exam move
- Carry precision through the calculation, round at the end, and attach the correct unit.
- Topic
- Reasonableness check
- What to know
- One-percent benchmark, proportionality, upper bound, reverse multiplication, loan base, estimate, answer choice, and decimal error
- Best exam move
- Compare the result with one point on the loan before accepting it.
How should you drill this calculation?
- Session
- Session 1
- Focus
- Build the one-point benchmark
- Proof you are ready
- Find one point on 30 loan amounts mentally and explain why purchase price is usually the wrong base.
- Session
- Session 2
- Focus
- Calculate fractional-point costs
- Proof you are ready
- Solve 25 charges from whole and fractional quotes without a percent-to-decimal error.
- Session
- Session 3
- Focus
- Reverse the formula
- Proof you are ready
- Recover 15 points quotes and 15 loan amounts, then verify each answer by multiplication.
- Session
- Session 4
- Focus
- Separate loan-pricing terms
- Proof you are ready
- Classify 30 point, origination, credit, down-payment, prepaid-interest, and mortgage-insurance facts.
- Session
- Session 5
- Focus
- Handle rate and break-even prompts
- Proof you are ready
- Complete 20 quoted-option comparisons while rejecting every unstated rate-change shortcut.
- Session
- Session 6
- Focus
- Complete a mixed points set
- Proof you are ready
- Score at least 90% and label every answer as dollars, points, percent, or months with its assumptions stated.
Do not count recognition as mastery. Close the notes and explain the rule, apply it to a new fact pattern, and identify why each distractor fails.
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Questions students ask about Discount Points and Lender Yield: Illinois Exam Guide
What is one discount point on a mortgage?
One point equals 1% of the loan amount, not 1% of the price or down payment. One point on a $320,000 loan costs $3,200. A borrower may pay a fraction of a point, such as 0.625 points, when that is the quoted option.
What is the discount-points formula?
Point cost equals loan amount multiplied by the points percentage written as a decimal. For 1.5 points, multiply by 0.015. You can also calculate one point first by moving the loan amount's decimal two places left, then multiply by the number of points.
Do discount points lower the mortgage interest rate?
Yes, true discount points are paid in connection with a reduced interest rate. The amount of the rate reduction is not fixed by a universal formula. CFPB guidance says it depends on the lender, loan type, and mortgage market, so use only the pricing or convention supplied in the question.
Does one point always lower the rate by 0.25%?
No. That is a common shortcut, not a universal rule. A real pricing table might show a larger or smaller change. On the exam, calculate a rate change only from facts expressly given in the stem, such as a rate sheet or a stated points-to-yield convention.
How do you find the number of points paid?
Divide the dollar charge by the loan amount, then multiply by 100. A $4,375 charge on a $350,000 loan is $4,375 / $350,000 = 0.0125, or 1.25 points.
How do you find a loan amount from a point charge?
Divide the point charge by the points percentage written as a decimal. If 2 points cost $6,000, divide $6,000 by 0.02. The loan amount is $300,000.
What is the difference between discount points and an origination fee?
Both may be calculated as a percentage of the loan amount, but they describe different charges. Regulation Z separately identifies points paid to reduce the interest rate, while origination charges can include fees for originating and extending credit. Do not assume an origination fee buys a lower rate.
What is a lender credit?
A lender credit generally makes the opposite tradeoff from discount points: the borrower accepts a higher interest rate and receives a credit that reduces upfront closing costs. CFPB guidance notes that lender credits may be described as negative points on a lender worksheet.
How do you calculate the break-even time for points?
In a simplified comparison, divide the upfront point cost by the stated monthly principal-and-interest savings. A $4,000 charge divided by $80 in monthly savings gives 50 months. That shortcut does not account for time value, taxes, refinancing, sale timing, or alternate uses of the cash.
Are these official Illinois broker exam questions?
No. They are original practice calculations aligned to the PSI Illinois broker outline effective June 24, 2026. The current PSI outline, CFPB mortgage guidance, Regulation Z, Freddie Mac definitions, and current IRS publication were checked through August 1, 2026.
Primary sources
- PSI Illinois Candidate Information Booklet dated June 24, 2026
- Consumer Financial Protection Bureau, current points and lender-credits explanation
- Consumer Financial Protection Bureau, current Regulation Z Section 1026.37 Loan Estimate requirements
- Consumer Financial Protection Bureau, current Loan Estimate explainer
- Consumer Financial Protection Bureau, discount-points pricing and consumer break-even discussion
- Freddie Mac Primary Mortgage Market Survey definitions, one-point definition
- Internal Revenue Service Publication 936, current home-mortgage points guidance
The current official outline controls the tested scope. Statutes, regulations, and official agency materials control when a general study rule and a jurisdiction-specific rule differ.
Editorial status
Checked against primary sources
The Pass Illinois editorial team last checked this guide on August 1, 2026. Every practice question is an original study item, and the source links above let you verify the rules that support the lesson.