Math Concept
Loan-to-Value Ratio: Definition, Denominator, and Worked Problems
All figures on this page are illustrative and chosen to divide cleanly. Insurance thresholds, minimum down payments and cancellation rules belong to individual loan programs and to federal servicing law, and they are revised periodically. Verify any specific percentage against the current guidelines of the program in question rather than memorizing a number from a study aid.
Loan-to-value states a loan amount as a percentage of what the collateral is worth. One division and one shift of the decimal produce it. Candidates almost never miss the arithmetic on these items; they miss the denominator.
This page defines the ratio, settles which figure belongs underneath it, shows the relationship between LTV and the cash a buyer brings, and works three problems of the kinds that appear on the exam.
The Ratio and Its Denominator
Loan-to-value is the loan amount divided by the value of the property, expressed as a percentage. In one line: LTV = loan / value, then multiply by 100. Everything difficult about the topic is contained in the second word of the denominator.
Lenders use the lesser of the appraised value and the contract price. The reason is credit risk rather than arithmetic. A lender's security is the property, not the negotiation, so an agreement to pay above the appraised figure does not enlarge the collateral and cannot enlarge the loan. When an appraisal comes in below the contract price, the loan is sized off the appraisal and the buyer covers the gap in cash or the parties renegotiate.
One more relationship is worth holding in memory because it saves a step on roughly half of these items: on a purchase, the down payment percentage and the LTV percentage add to 100. A buyer contributing one fifth of the purchase price is financing four fifths, so the ratio is 80 percent. Read a problem that gives you a down payment as a problem that has already given you the LTV.
Be careful transplanting that shortcut onto a refinance. There is no purchase price and no down payment, so the denominator is the appraised value alone and the numerator is the new loan. A cash-out refinance raises the numerator against an unchanged denominator, which is exactly why lenders cap it.
Three Problems Worked in Full
Original practice items written for this page. The dollar amounts are illustrative. None of these is taken from any licensing examination.
Question 1
Illustrative figures: a property is under contract at $250,000 and the appraisal supports that amount. The lender approves a loan of $200,000. What is the loan-to-value ratio?
Price and appraised value agree, so the denominator is $250,000. Divide the loan by the value: 200,000 / 250,000 = 0.80. Shift the decimal two places and the ratio is 80 percent. Cross-check with the buyer's cash: the down payment is $50,000, which is 20 percent, and 20 plus 80 returns 100.
Question 2
Illustrative figures: a buyer agrees to pay $420,000. The appraisal returns $400,000. The lender writes a loan of $360,000. What is the loan-to-value ratio, and how much cash does the buyer bring?
Use the lesser of price and appraised value, so the denominator is $400,000, not the contract figure. 360,000 / 400,000 = 0.90, a ratio of 90 percent. The cash requirement is measured against the price the buyer actually agreed to pay: 420,000 - 360,000 = $60,000. Note that the cash is not 10 percent of anything here, because the low appraisal pushed the shortfall onto the buyer.
Question 3
Illustrative figures: a lender will finance at a maximum 75 percent loan-to-value. The property appraises for $480,000 and the contract price is $470,000. What is the largest loan available?
Reverse the formula: loan = value x LTV. The value to use is the lesser figure, $470,000. Multiply: 470,000 x 0.75 = $352,500. That is the ceiling, and the remaining $117,500 of the price must come from the buyer or from another source the lender permits. Using the $480,000 appraisal would have produced $360,000, which is the distractor this item is built to catch.
What the Ratio Controls
LTV is the lender's shorthand for how much cushion stands between the loan balance and a loss. Each item below follows from that single idea.
Equity cushion. A lower ratio means the borrower has more of their own money at stake and the lender has more room between the balance and a forced-sale price. That is the entire risk story in one sentence.
Mortgage insurance. Conventional lending treats a ratio above 80 percent as requiring private mortgage insurance, a premium the borrower pays to protect the lender. Government-backed programs carry their own insurance or guaranty structures under different names and their own premium schedules.
Cancellation of that premium. Federal servicing law provides for borrower-requested cancellation and for automatic termination of private mortgage insurance once the balance has amortized to specified thresholds on a primary residence. The thresholds, the conditions and the exceptions are statutory, so read the current rule rather than repeating a figure.
Pricing. High-ratio loans commonly carry rate or fee adjustments because the expected loss is larger. The adjustment is set by the investor's pricing grid, not by the license law.
Program eligibility. Each program publishes a maximum ratio and a minimum contribution from the borrower, and government-guaranteed programs for eligible veterans and for qualifying rural buyers can reach full financing. Those maximums are published by the agencies and change.
Piggyback structures. A borrower can hold the first lien at or below the insurance threshold by adding a simultaneous second lien. The combined loan-to-value across both liens is what a lender actually underwrites, which is why the combined figure has its own acronym.
The ratio moves after closing. Amortization lowers the numerator every month and a change in market value moves the denominator in either direction, so the figure a borrower cites years later is not the one written at origination.
Where Candidates Lose These Points
Grabbing the larger number. When a problem supplies both an appraisal and a price, one of them is a distractor, and the option list will contain the answer you get by using it. Underline the smaller figure before doing anything else.
Answering the wrong question. Some items give the ratio and the value and want the loan; some give the ratio and the loan and want the value; some want the cash the buyer brings. Multiply when you are moving from value to loan, divide when you are moving from loan back to value, and subtract only when the item asks for cash.
Confusing the ratio with the combined ratio. If a second lien is described anywhere in the stem, decide whether the question is about the first loan alone or about both together before you divide.
Treating the down payment complement as universal. It holds on a purchase where price and appraisal agree. It fails on a low appraisal, as the second worked problem shows, and it is meaningless on a refinance.
Rounding early. Carry the division to full precision and round once at the end, to whatever precision the option list uses. On a percentage this large, an early round can move the answer past the nearest option.
Loan-to-Value Questions the Exam Returns To
Appraised value or sale price in the denominator?
Whichever is lower. A high appraisal does not let a buyer borrow more than the price, and a low appraisal does not let a buyer borrow against the price. If the item names only one figure, that figure is your denominator and you should not invent the other.
What is the difference between LTV and CLTV?
The plain ratio uses one loan. The combined ratio adds every lien secured by the same property, including a simultaneous second and any home equity line, and divides the total by the same value. A borrower can show a comfortable first-lien ratio and a high combined ratio, and underwriting cares about the combined figure.
How does an 80/10/10 arrangement work?
It is a labeling convention for a piggyback: a first lien at 80 percent of value, a second lien at 10 percent, and 10 percent from the borrower. The first lien sits at the conventional insurance threshold so no private mortgage insurance attaches to it, while the combined ratio is 90 percent. The borrower trades an insurance premium for a second payment, usually at a higher rate.
Does the ratio change over the life of the loan?
Yes, in both directions. Each amortizing payment reduces the balance, which lowers the ratio, while the denominator follows the market. A borrower seeking cancellation of mortgage insurance is arguing that the current ratio has crossed a threshold, and the servicer decides what evidence of current value it will accept.
Does a larger down payment always mean a better loan?
It lowers the ratio, which generally improves pricing and can remove an insurance premium, but the exam wants the tradeoff named rather than a recommendation. Cash placed in equity is cash not held in reserve, and lenders also underwrite reserves, income and credit. Advising a particular borrower on that tradeoff is a lending conversation, not a licensee's call.
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