Discount Points: Borrower Cost and Approximate Lender Yield

One discount point costs 1% of the loan amount. That answers a dollar-cost question. A question about an approximate lender yield uses a different calculation and must identify the approximation to use.

Calculate the cost of points

Cost = loan amount × (number of points ÷ 100).

A $240,000 loan with 2.5 points costs $240,000 × 0.025 = $6,000 in points. Use the loan principal, not the property's sale price. If only the price and down payment are supplied, find the loan first.

For example, a $300,000 purchase with a 20% down payment produces a $240,000 loan, assuming no other financed amounts. Two points cost $4,800, not $6,000.

For a real mortgage offer, paying discount points generally reduces the borrower's interest rate compared with the same lender's otherwise comparable zero-point loan. The reduction varies; one point does not automatically reduce the rate by one percentage point. See the CFPB explanation of points and lender credits.

Understand the classroom yield approximation

Some study exercises instruct you to estimate that each discount point increases lender yield by one-eighth of one percentage point. When that convention is specified:

Approximate yield = stated note rate + (points × 0.125 percentage points).

Example: The note rate is 6.25%, with 2.5 points, and the exercise specifies the one-eighth approximation.

1. Yield increment: 2.5 × 0.125 = 0.3125 percentage points.
2. Approximate yield: 6.25% + 0.3125% = 6.5625%.

This is a study convention, not an exact yield calculation, an APR calculation, or a guaranteed mortgage-pricing rule. Exact yield depends on the loan's cash flows, fees, timing, and repayment. Do not infer this shortcut from a real loan offer.

Why can the borrower get a lower rate while the lender receives points?

The comparisons are different. The borrower's discounted rate is compared with an otherwise comparable zero-point offer. The lender receives interest at the agreed note rate and an upfront payment, affecting its return relative to the note rate alone. The word “discount” does not mean the lender subtracts points from every yield calculation.

Do I need the loan amount?

• For the dollar cost: yes. A percentage needs a dollar base.
• For the stated one-eighth yield exercise: no. The note rate and number of points are sufficient for that approximation.
• For the actual rate reduction: points alone are insufficient; use the lender's quoted pricing.

Try three practice questions

1. A loan is $180,000 and the charge is 1.75 points. What is the cost?
2. A study problem explicitly uses the one-eighth approximation. The note rate is 5.5% and the lender charges 3 points. What is the approximate yield?
3. A buyer pays $400,000 with 25% down and no other financed amounts. What do 2 points cost?

Answers and explanations

1. $3,150: $180,000 × 0.0175.
2. 5.875%: 5.5% + (3 × 0.125 percentage points). The answer is a rate, not dollars.
3. $6,000: the loan is $300,000; $300,000 × 0.02.

Keep studying

See how to choose the right math formula and the exam-prep guide. If a practice question does not make its assumptions clear, send support the course, lesson, question number, and your work. These are original practice examples.