What is a mortgage?
Key takeaways
04 · ideas- A mortgage lets you buy a home by borrowing against the property itself
- On a $300k loan at 7%, you pay $418k total — $118k in interest
- Monthly payment covers principal, interest, taxes, and insurance (PITI)
- Amortization means early payments are mostly interest, not equity
Basic level
The essentials · 1 min
A mortgage is a loan to buy property where the property itself is the collateral. If you stop paying, the lender can take the home — this is called foreclosure.
Here's how it works in plain terms:- You find a home priced at $300,000
- You pay $60,000 down (20%)
- The bank lends you $240,000
- You repay that loan over 30 years with interest
What you actually pay: On a $240,000 loan at 7% for 30 years, your monthly payment is about $1,597. Over 30 years, you pay $575,000 total — more than twice what you borrowed. The extra $335,000 is interest.
The four parts of every mortgage payment (PITI):- Principal — pays down your loan balance
- Interest — the lender's fee for borrowing
- Taxes — property taxes collected monthly and paid annually
- Insurance — homeowner's insurance (and PMI if down payment < 20%)
Intermediate level
How it applies · 2 min
Fixed vs. adjustable rate mortgages
| Type | How it works | Best for | Risk |
|---|---|---|---|
| 30-year fixed | Same rate for 30 years | Long-term owners | None (rate locked) |
| 15-year fixed | Same rate, paid off faster | Those who can afford higher payments | None (rate locked) |
| 5/1 ARM | Fixed 5 years, then adjusts annually | Selling within 5 years | Rate can rise sharply |
| 7/1 ARM | Fixed 7 years, then adjusts annually | Medium-term owners | Rate can rise sharply |
The amortization effect
The surprising truth: in the early years, most of your payment goes to interest, not your home.
$300,000 at 7% — where does Year 1 money go?
| Month | Payment | Interest portion | Principal portion | Balance remaining |
|---|---|---|---|---|
| 1 | $1,996 | $1,750 | $246 | $299,754 |
| 12 | $1,996 | $1,746 | $250 | $296,953 |
| 60 | $1,996 | $1,665 | $331 | $284,616 |
| 120 | $1,996 | $1,532 | $464 | $261,286 |
| 180 | $1,996 | $1,341 | $655 | $228,505 |
| 360 | $1,996 | $12 | $1,984 | $0 |
By month 180 (year 15), you've paid $359,280 but only reduced your balance by $71,495.
Comparing 15 vs 30 year mortgages
| 15-year | 30-year | Difference | |
|---|---|---|---|
| Monthly payment | $2,697 | $1,996 | +$701/mo |
| Total interest paid | $185,460 | $418,560 | Save $233,100 |
| Years to pay off | 15 | 30 | 15 years sooner |
| Equity after 5 years | $64,300 | $18,400 | +$45,900 |
The 15-year costs $701 more per month but saves $233,000 total.
Advanced level
The math, step by step · 2 min
The mortgage pricing formula
The standard fixed-payment amortization formula:
- M = monthly payment
- P = principal (loan amount)
- r = monthly interest rate (annual rate ÷ 12)
- n = total number of payments (years × 12)
- r = 0.07/12 = 0.005833
- n = 360
- M = 300,000 × 0.005833 × (1.005833)³⁶⁰ / ((1.005833)³⁶⁰ - 1) = $1,995.91
Outstanding balance at any point
Where k is the payment number. This tells you exactly how much you owe after any payment — critical for refinancing decisions.
The true cost of a lower rate
A 1% rate difference on a $300,000 30-year mortgage:- At 7%: total interest = $418,527
- At 6%: total interest = $347,515
- Savings from 1% lower rate = $71,012
Every 0.25% rate difference costs approximately $15,000 over a 30-year loan. This is why shopping multiple lenders — and improving your credit score before applying — can be worth tens of thousands of dollars.