Loan-to-Value and Discount Points, Without the Decimal Slips
LTV problems are ratio problems; points problems are percent problems on the LOAN, not the price. Both are one step each — and the exam builds its distractors from applying the right percentage to the wrong base.
The formula
LTV = Loan ÷ Value (lesser of price or appraisal) · 1 point = 1% of the LOAN amount
- LTV
- loan amount as a share of value
- Value
- lenders use the LESSER of sale price and appraised value
- Point
- 1% of the loan — never 1% of the price
Try it live
Every intermediate step is shown — the goal is that on exam day you can run the same chain on paper.
LTV & points calculator
- Lending baselesser of $250,000 and $240,000
- $240,000
- Loan amount$240,000 × 80%
- $192,000
- Down paymentprice − loan
- $58,000
- Cost of 2 points$192,000 × 2% — points price off the LOAN
- $3,840
The method, worked in exam style
A buyer pays $250,000 for a home that appraises at $240,000, with an 80% LTV loan. The lender charges 2 discount points. Find the loan, the down payment, and the cost of the points.
- The lender lends on the lesser value: $240,000.
- Loan: 240,000 × 0.80 = $192,000.
- Down payment: price − loan = 250,000 − 192,000 = $58,000 (note: more than 20% of price, because the appraisal came in low).
- Points: 192,000 × 0.02 = $3,840.
Answer: Loan $192,000 · down payment $58,000 · points $3,840
The classic trap
The classic distractors: a loan of $200,000 (used the price instead of the lower appraisal) and points of $5,000 (charged on the price instead of the loan). Circle which number is the base before touching the calculator.
Practice problems
Work each on paper first, then open the solution. If your setup differs from the solution's first line, that — not arithmetic — is what to fix.
1. A home sells for $400,000 and appraises at $400,000. The buyer puts 10% down. What is the LTV and the loan amount?
Show the solution
- Down payment: 400,000 × 0.10 = 40,000; loan = 360,000.
- LTV = 360,000 ÷ 400,000 = 90%.
Answer: 90% LTV; $360,000 loan
2. A lender quotes 3 points on a $284,000 loan. What do the points cost?
Show the solution
- 3 points = 3% of the loan: 284,000 × 0.03 = 8,520.
Answer: $8,520
3. A buyer has a $57,000 down payment and the lender requires 75% LTV on a purchase where price equals appraisal. What is the maximum price?
Show the solution
- If LTV is 75%, the down payment is 25% of value.
- Price = 57,000 ÷ 0.25 = 228,000.
Answer: $228,000
Math is one domain — the diagnostic measures all of them
The free 24-question adaptive diagnostic finds the difficulty level where your setup breaks down — in math and every other blueprint domain — and reports a Readiness Score with a stated confidence range.
Keep going: The T-method · Financing & settlement on the exam · Real Estate Math on the exam
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