wunder beta🏠 How Mortgages Work
Demystify the biggest loan most people take. You'll see where the payment number comes from, why early payments are almost all interest, and who bears which risk — mechanics, not advice.
What you’ll learn
- A Loan Wearing a LeashSeparate the loan from the purchase, and see why the lien is what makes the money cheap.A mortgage is two documents doing two jobs: a promissory note (the debt and its schedule) and a security instrument (the lien that lets the lender take the house if the promise fails). The lien is not predation — it is why a stranger will lend you six figures for thirty years at single-digit rates. Every later clause is a variation on the same bargain: someone bears a risk, and someone pays for it.
- Where the Number Comes FromDerive the monthly payment yourself and understand interest as rent on the outstanding balance.Interest is rent charged on whatever you still owe: $300,000 × (6.5%/12) = $1,625 in month one. The level payment M = P·r·(1+r)ⁿ ÷ ((1+r)ⁿ − 1) is the single number that charges fair rent each month and lands the balance on exactly zero after n months — $1,896.20 for our example. Over 360 payments that totals $682,633, of which $382,633 is interest.
- The Amortisation RevealSee why early payments are almost entirely interest, and why that shape is subtraction rather than policy.Payment one splits $1,625.00 interest / $271.20 principal — 85.7% rent. The crossover, where principal first exceeds interest, is payment 233: nineteen years and five months into a thirty-year loan. The shape is forced: a level payment charged rent on a balance that starts at its maximum must start with its principal portion at its minimum.
- Term: The Same Loan, Two LengthsWork the 15-vs-30 arithmetic and state the trade honestly in both directions.Same $300,000 at 6.5%: 30 years costs $1,896.20/month and $382,633 of interest; 15 years costs $2,613.32/month and $170,398. Less than half the interest for 38% more per month — because the balance falls faster and rent is charged for fewer months. What the shorter term costs is monthly flexibility, and which side matters depends on facts about a specific person that no course can know.
- Who Is Holding the Rate Risk?Locate interest-rate risk in fixed and adjustable loans, and learn to price the cap instead of forecasting the rate.A long fixed rate leaves the lender holding rate risk — and the borrower holding an option to refinance if rates fall. An ARM hands that risk back: your rate is index + margin, resetting on schedule, which is why ARMs typically start lower. Caps (initial / periodic / lifetime) bound the damage, and the lifetime cap is the only honest answer to "how bad can this get" — a fact you can compute against rather than a forecast.
- The Rest of the PaymentDecompose PITI and understand escrow, PMI, points and APR by asking whose risk each one answers.Most payments are PITI: principal and interest (your loan) plus taxes and insurance, collected through an escrow account that exists to protect the collateral. PMI, required on conventional loans with less than 20% down, "protects the lender—not you." A point is 1% of the loan paid up front to buy a lower rate — which is why APR, the cost of credit including rate, points and certain fees, is the number that makes two offers comparable.
- After You SignUnderstand equity, LTV, what a refinance really is, and why your loan gets sold — then restate the course's through-line.Equity is value minus balance: one half is a printed schedule, the other is a market nobody can forecast. A refinance is not a modification but a new loan with a new schedule that restarts at payment one. Loans are routinely sold and pooled because a 30-year asset is awkward for a short-funded bank, while a servicer collects — but the note, and every risk allocation in it, survives the transfer.
Questions this course answers
Why can a mortgage charge single-digit interest when a credit card charges twenty-something percent for far less money?
The lien is the price difference. Collateral converts trust into arithmetic: if the promise fails, the lender has recourse to an asset that still exists and is legally spoken for. The credit card lender has only a phone call and a lawyer — so it charges for that.
On a $300,000 loan at 6.5% annual, the first month's interest is $1,625. What does that figure actually depend on?
Interest is rent on the balance you still hold: $300,000 × (6.5% ÷ 12) = $1,625. Term and payment size don't enter the calculation at all — they determine what happens to the money left over after the rent is charged.
On a 30-year loan at 6.5%, roughly when does the first payment arrive that puts more toward principal than interest?
Payment 233 — nineteen years and five months in. For roughly the first two-thirds of a 30-year mortgage, most of every cheque is rent on money. It isn't a trick: a level payment plus rent charged on a balance that starts at its maximum forces this shape.
Why does an extra $200 a month have such a lopsided effect — about $103,000 less interest on our example loan?
Interest is charged on the balance, month after month. A dollar removed from the balance early is a dollar that never gets charged rent again for the remaining ~29 years — so its effect compounds. (Whether $200 belongs there is a question about a whole financial life, not about mortgages.)
Halving the term from 30 years to 15 raises the payment from $1,896 to $2,613 — only 38% more, not double. Why?
Same rate, same principal — but the balance falls much faster, so the rent charged each month is smaller, and it's charged for 180 months instead of 360. Total interest drops from $382,633 to $170,398. What it costs is $717 of monthly obligation that is due whether or not the month goes well.
On an adjustable-rate mortgage, which number is a fact you can plan against rather than a forecast?
Nobody can tell you where rates go. The lifetime cap tells you where your rate can go — contractually, at worst. That means you can compute your payment at the capped rate today, before signing. Pricing the cap is honest; predicting the index isn't.
Grounded in trusted sources
- Consumer Financial Protection Bureau, "What is private mortgage insurance?" — https://www.consumerfinance.gov/ask-cfpb/what-is-private-mortgage-insurance-en-122/
- Consumer Financial Protection Bureau, "What is an escrow or impound account?" — https://www.consumerfinance.gov/ask-cfpb/what-is-an-escrow-or-impound-account-en-140/
- Consumer Financial Protection Bureau, "What is the difference between a mortgage interest rate and an APR?" — https://www.consumerfinance.gov/ask-cfpb/what-is-the-difference-between-a-mortgage-interest-rate-and-an-apr-en-135/
- Consumer Financial Protection Bureau, "How should I use lender credits and points (also called discount points)?" — https://www.consumerfinance.gov/ask-cfpb/what-are-discount-points-and-lender-credits-and-how-do-they-work-en-136/
- Consumer Financial Protection Bureau, "What is a prepayment penalty?" — https://www.consumerfinance.gov/ask-cfpb/what-is-a-prepayment-penalty-en-1957/
- Consumer Financial Protection Bureau, "What are rate caps with an adjustable-rate mortgage (ARM), and how do they work?" — https://www.consumerfinance.gov/ask-cfpb/with-an-adjustable-rate-mortgage-arm-what-are-rate-caps-and-how-do-they-work-en-1951/
- Consumer Financial Protection Bureau, "For an adjustable-rate mortgage (ARM), what are the index and margin, and how do they work?" — https://www.consumerfinance.gov/ask-cfpb/what-is-an-index-rate-en-1949/
- Consumer Financial Protection Bureau, "Your home loan toolkit" (the definition of a point, p. 8) — https://files.consumerfinance.gov/f/201503_cfpb_your-home-loan-toolkit-web.pdf
Every Wunder lesson is built from real, reputable sources — never invented.
Related Math courses
Wunder is a personalized learn-anything platform — tell it any topic and it builds a beautiful, fact-checked course in minutes, with narration, a knowledge check, and a college-style University track.
Browse more Math courses · All topics · Home
© 2026 Wunder Learning LLC · Terms & Privacy