How the drill works
Pick a drill type or leave it on all types. A mixed set covers all 6 types before it repeats any, and a single-type set gives you 10 problems of that type. Type a number and check it. A dollar sign, commas and a % sign are fine, and the key accepts a small rounding difference, so 82.1 passes for 82.05%.
You score one point per problem. At the end you see your score by type, weakest first, your longest streak and a link to the part of the math guide that fixes your weakest type. Hit New set for fresh numbers, and quote the set number if you report an error.
What each type drills
- LTV and CLTV. LTV = loan ÷ value, and CLTV adds every lien to the top. Each problem tells you which value to use. Some ask the other way round: the loan amount for a target LTV.
- Front-end and back-end DTI. Front-end = monthly housing ÷ gross monthly income. Back-end adds the other monthly debts. Taxes and insurance come as yearly figures, so divide by 12 first.
- Fixed-rate payment and interest. Payment = P × r ÷ (1 − (1 + r)^−n), with r the monthly rate and n the number of payments. You also split a first payment into interest and principal, and work an interest-only payment.
- Discount points. One point is 1% of the loan amount. You find the cost, sometimes from a price and a down payment, and the break-even month when a monthly saving is given.
- Prepaid interest. Loan × rate × days ÷ 360 or 365. Each problem states the basis and either the days or how to count them from the closing date.
- ARM rate adjustments. Index + margin gives the fully indexed rate. The periodic cap limits the move from the current rate, and the lifetime cap sets a ceiling above the start rate.
Worked examples
Example 1: payment and the first month's split
A $250,000 loan at 6.50% for 30 years. Step 1: r = 0.065 ÷ 12 = 0.0054167 and n = 360. Step 2: 1 − (1 + r)^−360 = 0.856975. Step 3: the first month's interest is 250,000 × 0.065 ÷ 12 = $1,354.17. Step 4: payment = 1,354.17 ÷ 0.856975 = $1,580.17, so $226.00 of the first payment goes to principal. Keep r at full precision on the calculator; the rounded figures here are for reading.
Example 2: when the lifetime cap binds
An ARM started at 4.50% and now carries 8.50%. The index is 7.00%, the margin 2.75%, the periodic cap 2 points and the lifetime cap 5 points. Step 1: fully indexed rate = 7.00 + 2.75 = 9.75%. Step 2: the periodic cap allows up to 8.50 + 2 = 10.50%. Step 3: the lifetime ceiling is 4.50 + 5 = 9.50%. Step 4: the new rate is the lowest of the three, 9.50%. The ARM section of the math guide works a case where the periodic cap binds instead.
Calculator habits that save points
- Turn every rate into a decimal before you multiply: 6.50% is 0.065, and the monthly rate is that divided by 12.
- Convert yearly taxes and insurance to monthly before a ratio. Mixing yearly and monthly figures is the most common slip.
- Keep full precision on the screen and round once at the end.
- Estimate first. A loan of 80% of the value should give an LTV near 80%, and points on a $300,000 loan are $3,000 each.
How the problems are made
Each problem is generated from one formula with numbers drawn from short lists of invented prices, loans, incomes and rates. Loan, price and appraisal amounts are round multiples of $5,000, so none is a published loan limit. The same set number always gives the same set, so a set number is enough to report a problem.
NMLS math FAQ
Where do these problems come from?
Every problem is original and written to the Financial Calculations list on NMLS's published SAFE MLO Test outline, plus the LTV, qualifying ratio and discount point terms the outline lists. The numbers are invented and generated for each set. None is an NMLS sample question, and none uses a loan limit, a mortgage insurance rate or any other amount that changes by year.
Should prepaid interest use a 360-day or a 365-day year?
Use the basis the question gives you. Practices differ, so every prepaid interest problem here states its basis and how many days to charge, or how to count them from the closing date. The same loan on a 360-day year costs a little more per day than on a 365-day year, which is why the drill checks to the cent.
How do I work the payment formula on a basic calculator?
A question may give you a payment factor or a table in place of the formula, so first know the split: interest for a month is the balance times the annual rate divided by 12, and the rest of the payment is principal. For the full formula, work 1 + r first, raise it to the power n on a calculator with a power key, and keep every digit until the last step.
How many math questions are on the NMLS exam?
NMLS weights the outline by content area, not by question type, so the outline does not say how many questions are calculations. Financial Calculations is one list under Mortgage Loan Origination Activities, and LTV and qualifying ratios show up under other headings. Be quick on all six types here and a math question is a point you expect to win.