Mortgage math for the NMLS exam

Know the conventions before you calculate

Real questions state their own assumptions: the day-count basis for interest, which value to use for LTV, which debts and housing costs go into a ratio. Read the stem for them. Lender and program limits for ratios, loan size and fees change over time and by program, so this guide teaches the method and gives no limits. When a question needs a limit, it will state it.

Loan-to-value (LTV)

LTV = loan amount divided by the property value. For a purchase, the usual convention is the lower of the sales price and the appraised value.

• Price $400,000, appraisal $390,000, loan $320,000.
• Lower value: $390,000. LTV = 320,000 / 390,000 = 0.8205, or 82.05%.
• Down payment from the buyer: 400,000 - 320,000 = $80,000, which is 20% of the price.

The down payment and the LTV use different bases, and that is a common trap. Combined LTV (CLTV) adds the balances of all liens to the numerator: loan plus a second lien, divided by value.

Debt-to-income (DTI)

DTI = monthly debt payments divided by gross monthly income. The front-end ratio uses housing costs only. The back-end ratio uses housing costs plus other monthly debts.

• Gross monthly income $6,000. Housing payment (principal, interest, taxes, insurance) $1,500. Other monthly debts (car, cards, student loan) $500.
• Front-end: 1,500 / 6,000 = 25.00%.
• Back-end: (1,500 + 500) / 6,000 = 2,000 / 6,000 = 33.33%.

Use gross income, not take-home pay, and include any debt the borrower owes, even if it is not on the credit report.

Monthly payment on a fixed-rate loan

For a fully amortizing loan, payment = P x r / (1 - (1 + r)^-n), where P is the loan, r is the monthly rate (annual rate divided by 12) and n is the number of monthly payments. The exam may give you a factor or a table instead. The part you must know is the interest and principal split.

• Loan $300,000 at 6.00% for 30 years. r = 0.005, n = 360.
• Payment of principal and interest: $1,798.65.
• First month's interest: 300,000 x 0.005 = $1,500.00.
• First month's principal: 1,798.65 - 1,500.00 = $298.65. The new balance is about $299,701.35.

Interest each month is the balance times the monthly rate, so more of each payment goes to principal as the balance falls.

Interest-only. An interest-only payment is just the interest: $300,000 x 0.06 / 12 = $1,500.00 a month, and the balance does not fall during the interest-only period. Payments rise when amortization begins.

Discount points and origination charges

One point is 1% of the loan amount. Points are paid at closing, usually to lower the rate.

• 2 points on a $250,000 loan: 250,000 x 0.02 = $5,000.
• A 1% origination charge on the same loan is $2,500.

To judge whether paying points makes sense, divide the points cost by the monthly savings to find the break-even in months. Each lender's rate sheet gives the monthly saving, so a question that asks for it will state both inputs.

Prepaid interest and accrued interest

Mortgage interest is paid in arrears, so the first payment covers the period before it. At closing, the borrower usually prepays interest from the closing date to the end of that month, so the first full payment starts clean one month later. Simple daily interest = loan x annual rate / days in the year (365 unless the question says 360).

• Loan $240,000 at 6.00%, 365-day year. Daily interest = 240,000 x 0.06 / 365 = $39.45.
• If the stem says 10 days of prepaid interest, the charge is 240,000 x 0.06 x 10 / 365 = $394.52.

The number of days is stated in the stem, because conventions on whether the closing day counts differ.

ARM adjustments

An adjustable-rate mortgage rate at an adjustment date = the index plus the margin, the fully indexed rate, limited by the caps. The initial adjustment cap, periodic cap and life-of-loan cap (often called the life cap) limit how far the rate can move.

• Current rate 5.00%. At the adjustment the index is 4.50% and the margin is 2.75%. The fully indexed rate is 4.50 + 2.75 = 7.25%.
• Periodic cap: 2.00 percentage points. The most the rate can rise is 5.00 + 2.00 = 7.00%.
• New rate: the lower of 7.25% and 7.00%, so 7.00%.
• The life cap is a ceiling above the starting rate. If it were 5 points above 5.00%, the ceiling would be 10.00% and would not bind here.

Then recompute the payment on the remaining balance and remaining term at the new rate, the same way as above.

Closing costs and cash to close

Add up the borrower's costs and prepaids, subtract what they have already paid or been credited, and add the down payment. The method is a sum of stated items, so read each line for whether it is a credit or a charge. A lender credit or a seller concession reduces cash needed. For how tolerances treat each kind of charge, see the TRID timing cheat sheet.

A drill routine

1. Write the formula, then the inputs, then the answer. Most slips happen in the setup, not the division.
2. Check the units: annual or monthly, percent or decimal, price or appraised value.
3. Estimate first. 82% LTV should land between 80% and 85%.
4. Practice 10 mixed problems a day in the last two weeks. The study guide puts math in the Origination week, and the NMLS practice test has a worked LTV item.

Take the free 10-question check and see your score by content area in minutes. It needs no signup and explains every answer.

The Rate Lock course has lessons for each content area, original practice questions with every answer worked, and timed practice exams. Your scores come back by content area. It is test prep only and is no substitute for the 20 hours of pre-licensure education from a provider NMLS lists. See the course.

Not affiliated with or endorsed by NMLS, CSBS or Prometric. NMLS, CSBS and Prometric are named only to identify the exam, its owner and its test vendor. This is study material, not financial advice, and every example uses invented numbers.

Sources

Show the list

• SAFE MLO National Test with Uniform State Test Content Outline, the Financial Calculations list, NMLS Resource Center. Read 7 Nov 2026.
• 8.0 Test Center Policies, on the basic calculator, NMLS Resource Center. Read 7 Nov 2026.