Lending Math
Discount Points: The Calculation and the Concept
How far a point moves the rate is set by the lender's pricing on the day the loan is locked, and it moves with the market. The deductibility of points depends on the borrower's circumstances. Neither is a fixed figure to memorize; on an exam, use the values the question supplies.
A discount point is a charge equal to one percent of the loan amount, paid at settlement, in exchange for a lower note rate over the life of the loan. Points are quoted against the amount borrowed, never against the purchase price, and that distinction is the single most common source of wrong answers on these items.
Exam questions come in two shapes. One asks for the dollar cost of a stated number of points. The other asks whether paying them makes sense given how long the borrower expects to hold the loan. Both are arithmetic, and neither is difficult once the base is right.
Computing the Charge
One point equals one percent of the loan amount. To price a quoted number of points, convert the points to a decimal and multiply by the amount borrowed: points divided by one hundred, times loan amount. Half points and quarter points are quoted routinely and are handled the same way.
Where candidates lose the item is the base. If a question gives a sale price and a down payment, the loan amount is what remains after the down payment, and the points apply to that remainder. If it gives a loan-to-value ratio instead, derive the loan amount from the value first, then apply the points to the result.
A worked shape, with round figures to keep the method visible. Suppose the borrower finances an amount and the lender charges two points. Two percent of the financed amount is the cost, due at settlement in cash unless the transaction provides otherwise. Substitute the figures the question gives and the arithmetic is the same every time.
Sanity check as you go. Any single point is one hundredth of the loan, so a point on a six-figure loan lands in the low thousands. If your answer is an order of magnitude off that, you almost certainly multiplied against the sale price or slipped a decimal converting the percentage.
Points That Are Not Discount Points
The word point appears on several lines of a settlement statement, and item writers exploit the overlap. These are the distinctions worth holding.
Discount points buy down the interest rate. They are prepaid interest in substance, which is why their tax treatment differs from that of fees for services.
Origination points compensate the lender for processing and underwriting the loan. They are a fee for work performed and do not lower the rate. An item that pairs both in one scenario is testing exactly this line.
A loan discount fee on a settlement statement is usually the same thing as discount points expressed as a dollar figure rather than a count.
Rate buydowns arranged by a seller or builder may be temporary, reducing the payment for an initial period before the note rate takes over, rather than permanently lowering the rate as discount points do.
Negative points, also called lender credits, run the other direction: the borrower accepts a higher rate and the lender contributes toward closing costs.
Who pays is negotiable. A seller or other interested party may be permitted to pay points on the buyer's behalf, subject to contribution limits the loan program sets. The limits vary by program and are published by the program, not fixed across the market.
The Recovery-Period Question
The second family of items asks whether points are worth paying. The structure is always the same: an upfront cost against a recurring saving, and the answer is how long it takes the saving to repay the cost.
Divide the total cost of the points by the monthly payment reduction the lower rate produces. The result is the number of months the borrower must keep the loan before the decision breaks even. Convert to years if the question frames the holding period that way.
Then compare that period against how long the borrower expects to keep the loan. Hold it longer and the points pay off, with everything past the crossover a straight saving. Sell or refinance before then and the upfront money is not recovered. Where a question tells you the borrower plans to move or refinance within a stated period, that sentence is the answer key.
One refinement worth knowing. This simple comparison ignores what the same money would have earned elsewhere and any tax effect, so a precise analysis would shift the crossover somewhat. Exam items use the straightforward division; be aware of the simplification without importing it into your arithmetic.
Item-Level Traps
Most lost marks on this subject come from a small set of repeated errors rather than from misunderstanding what a point is.
Computing points on the purchase price instead of the loan amount. Read for the down payment or the loan-to-value figure before computing anything.
Mixing the two question types. A question asking for a dollar cost does not need the rate reduction, and a question asking about recovery does not need the sale price. Extra figures are often supplied precisely to see whether you can ignore them.
Converting percentages carelessly. Points to decimal, then multiply. Writing one and a half points as anything other than fifteen thousandths of the loan amount produces an answer that is confidently wrong.
Using a memorized rate reduction instead of the one the question states. How much a point moves the rate is a market variable; on an exam it is whatever the item says it is.
Assuming the points are the buyer's obligation. Contracts and loan programs may permit another party to pay them, and some items turn on exactly that.
Answering the recovery question in the wrong unit. If you divided a dollar cost by a monthly saving, the answer is in months. Options are frequently written in both units.
Two Items, One of Each Shape
Written for practice on this page rather than taken from any licensing examination. Every figure is illustrative, including the payment reduction in the second item, which on a real loan is whatever the lender's pricing makes it.
Question 1
Illustrative figures: a borrower finances $265,000 and the lender charges 2.5 discount points. What do the points cost at settlement?
$6,625, since 2.5 points is 0.025 of the amount borrowed and 0.025 multiplied by $265,000 gives that figure, with the charge due in cash at settlement unless the transaction shifts it to another party.
Question 2
Illustrative figures: a buyer purchases at $350,000 with 20 percent down. The lender offers 1.25 discount points in exchange for a lower rate that cuts the monthly payment by $70. What do the points cost, and roughly how long until the borrower recovers that cost?
$3,500 and about 50 months. The loan is $350,000 less the $70,000 down payment, or $280,000; 1.25 points is 0.0125 of that, which is $3,500; and $3,500 divided by the $70 monthly saving is 50 months, so a borrower expecting to sell or refinance inside roughly four years would not get the money back.
Discount Point Questions Candidates Ask
Is a point always one percent?
One percent of the loan amount, yes, by definition. What is not fixed is how much rate a point buys, which is set by lender pricing at the time of the lock and changes with market conditions. Work from the figure the question gives you.
Can the borrower deduct them?
Because points are treated as prepaid interest, they may be deductible, but whether they are deductible in the year paid or spread across the loan term depends on the borrower's circumstances and the purpose of the loan. This is a tax professional's question, and licensees should refer it rather than answer it.
How do I tell discount points from origination points in a question?
Look at what the charge buys. If it lowers the rate, it is a discount point. If it compensates the lender for making the loan, it is origination. Wording such as buy down the rate or loan discount signals the first; processing or underwriting fee signals the second.
Does paying points reduce the amount borrowed?
No. Points are a settlement charge paid on top of the loan. The principal is unchanged; only the rate applied to it moves. Items sometimes offer a distractor that subtracts the point cost from the loan balance.
Are points ever a bad idea for a borrower?
Whenever the loan is unlikely to survive to the crossover point, which covers borrowers expecting to sell, to refinance, or to need the cash for other closing costs. The arithmetic decides it; advising on the decision itself belongs to the lender.
Will the exam give me a calculator?
Testing centers commonly provide or permit a basic non-programmable calculator, but the policy is set by the vendor your state uses and stated in the candidate handbook for your jurisdiction. Read that before exam day rather than assuming, and practice the arithmetic so you are not dependent on it.
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