Mortgage Calculation Questions, Set Up and Solved
All figures here are invented for illustration. Program requirements, qualifying standards and disclosure rules are set by lenders, loan programs and regulators and change over time, so verify any specific threshold against its own published source rather than an example.
Loan questions punish a careless setup more than a slow calculation. Most of them supply a balance, a rate and a period, and the whole task is deciding which of the three the item wants back and on what time basis.
This page works through the setup checkpoints, then gives eight original problems with full solutions and a way to classify whatever you miss.
Where Loan Problems Actually Go Wrong
Three failures account for most missed loan items, and none of them is arithmetic. The first is answering a different question than the one asked, usually returning a loan amount when the item wanted a payment component. The second is a time-basis mismatch, pairing an annual rate with a monthly figure. The third is confusing two loan structures, so a correct calculation is run on the wrong instrument.
Each failure is caught at setup rather than at the calculator. Naming the unknown in words, converting the rate to the period being asked about, and identifying the structure before computing removes the whole group.
Checkpoints Before You Compute
Run these in order on every loan item. They take seconds and they catch the errors that cost points.
Name the unknown in plain words. Loan amount, cash required, a period's interest, a remaining balance, a ratio, a dollar cost of points: the wording of the last line decides which relationship applies.
Match the time basis. An annual rate must be divided by twelve before it touches a monthly figure, and a monthly figure must be multiplied by twelve before it meets an annual rate. Decide which direction to convert before substituting.
Move every percentage to decimal form first, whether it is an interest rate, a ratio or a point.
Identify the structure. Interest-only, fully amortizing, adjustable and balloon instruments behave differently, and the structure decides whether the balance falls, holds or comes due in a lump.
Separate the loan from the property. Value, price and appraised amount belong to the sale; balance, rate and term belong to the note. Items mix them on purpose.
Check the size of the answer before you commit. A month's interest that rivals the balance, or a payment smaller than the interest it must cover on an amortizing loan, is a conversion error announcing itself.
Eight Loan Problems, Solved in Full
Original practice written for this page, not drawn from any official examination. Work each on paper and compare your setup line, not just the final figure.
Question 1
A lender will finance 70 percent of a value it places at $410,000. What is the loan amount, and what cash does the buyer bring if the contract price is also $410,000?
Loan = 410,000 x 0.70 = $287,000. Cash = 410,000 - 287,000 = $123,000. The relationship is value times ratio; the second half is the remainder. Where the appraised amount and the contract price differ, the lender applies the ratio to the lower of the two and the buyer covers the gap in cash.
Question 2
A note carries a balance of $246,000 at 6 percent annual interest. What interest accrues in one month?
Convert the rate to the period being asked about: 0.06 / 12 = 0.005. Then 246,000 x 0.005 = $1,230. Multiplying the balance by 0.06 returns the annual figure of $14,760, which is the single most common miss in this family and is caught by asking whether a month's interest should be that large.
Question 3
An interest-only loan of $180,000 carries a 7 percent annual rate. What is the monthly payment, and what happens to the balance?
Monthly interest = 180,000 x 0.07 / 12 = $1,050, and on an interest-only note that is the entire payment. The balance stays at $180,000 because nothing is applied to principal, which is the structural point the item is usually testing.
Question 4
An amortizing loan has a balance of $220,000 at 6 percent, with a monthly payment of $1,400 covering principal and interest. How much of this month's payment reduces the balance, and what is the new balance?
Interest first: 220,000 x 0.06 / 12 = $1,100. Principal = 1,400 - 1,100 = $300. New balance = 220,000 - 300 = $219,700. Next month's interest is computed on the smaller balance, so the interest share falls and the principal share rises with every payment while the payment itself stays level.
Question 5
A borrower pays 2 discount points on a $265,000 loan. What is the dollar cost, and what is the borrower buying?
A point is one percent of the loan amount, so 265,000 x 0.02 = $5,300. The points are paid at closing to obtain a lower note rate over the life of the loan. Note the base: points are computed on the loan, not on the sale price, and an item supplying both is checking which one you use.
Question 6
One item gives a payment and asks for a rate; another gives a rate and asks for a payment. Why does recognizing the direction matter more than knowing the formula?
Because the same three quantities appear in both, and only the unknown tells you whether to multiply or divide. Naming the unknown before inventorying the figures is what keeps a familiar relationship from being run on the wrong variable, and that classification step is scored at least as often as the arithmetic.
Question 7
A loan is described as amortizing on a long schedule but due in full after a short term. What does that structure mean for the calculation?
Payments are computed as though the loan ran the longer schedule, so each one covers interest and a modest amount of principal. Because the term ends first, a substantial balance remains and comes due as a balloon payment. Identify the structure before computing: the payment question and the balance-at-maturity question are different questions about the same note.
Question 8
You missed a loan item on a practice set. What is the fastest way to find out why?
Rebuild the solution line by line with each variable labeled, then compare it to your own work and find the first line that differs. That line names the cause: a rate left annual, a base taken from the price instead of the loan, a structure misread, or an unknown misidentified. Re-solving without locating that line teaches nothing.
Turning Misses Into a Shorter List
Sort every missed loan item into one of four causes: conversion, base, structure or unknown. Conversion is a time basis or a percentage handled wrong. Base is a rate applied to the wrong figure, usually the price rather than the loan. Structure is a misread instrument. Unknown is answering something the item did not ask.
The causes call for different work. Conversion and base respond to short repetitive drills and clear quickly. Structure is a vocabulary gap, so the fix is the finance concepts themselves: amortization, the note and its security instrument, acceleration, subordination and release. Unknown is a reading habit, corrected by reading to the final line before gathering figures.
Pair calculation drills with the terminology rather than running them separately. A candidate who can compute a month's interest but cannot say what acceleration does will be beaten by an item that describes the structure in words and asks for a number. Track which cause keeps reappearing; your PassPulse Score shows whether the improvement is holding across attempts, and PassMap™ puts the stubborn cause ahead of the ones already settled.
Questions About Loan Math on the Exam
Will I have to compute a full amortized payment from scratch?
Items generally supply the payment and ask what it is composed of, or supply a factor to apply, because deriving a payment requires tools a basic calculator does not provide. What matters is knowing that interest is charged on the current balance first and the remainder reduces it.
Are points calculated on the price or the loan?
On the loan amount. One point equals one percent of that amount, paid at closing. An item that supplies both a sale price and a loan amount is testing exactly this, so read which figure the points attach to before multiplying.
How do qualifying ratios come up?
Usually as a relationship between a housing or debt figure and income. The thresholds themselves belong to individual loan programs and lenders, change over time, and are published by those programs, so learn the structure of the ratio and take any specific cutoff from the question or the program's own guidelines.
Is the note the same as the mortgage?
No, and items exploit the confusion. The note is the promise to repay, carrying the amount, rate and term your calculation uses. The mortgage or deed of trust is the instrument pledging the property as security. Which document a jurisdiction uses, and the procedure that follows a default, are matters of state law.
What should I do first if loan math is my weak area?
Take a diagnostic cold and let it show whether the problem is conversion, base, structure or reading. Each has a different remedy, and guessing at which one you have is how candidates spend a week on arithmetic they already had.
Where to go next: Related Pages
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