How amortization actually works
Every fixed-rate mortgage has the same dollar payment for 30 years — but the split between interest and principal changes every single month. Here's the math behind that split, why it matters, and what extra payments really do.
The puzzle: why is the payment constant?
If you borrow $300,000 at 6% over 30 years, your payment is $1,798.65/month. That number doesn't budge — not in year 1, not in year 29. But your balance changes constantly, and so does the interest charged on it. So how can the payment stay flat?
Because the formula that produces the payment is reverse-engineered to make it flat. It picks the one number that, when applied month after month against a shrinking balance, drains the loan to zero in exactly 360 payments. Different starting balance, rate, or term → different magic number, but the same constancy.
The formula
The fixed monthly payment M for a loan of principal P, monthly rate r, over n months is:
The monthly rate r is the annual rate divided by 12 (so 6% / 12 = 0.005). The number of months n is the term in years times 12 (30 years = 360 payments). Plug $300,000, 0.005, and 360 in and you get $1,798.65.
The expression looks intimidating but it has a clean derivation. The present value of an annuity that pays $M every month for n months at monthly rate r is exactly the formula's denominator times M. Setting that equal to P (the amount you borrowed) and solving for M gives the formula. The lender's "today" present value of all your future payments has to match what they hand you at closing.
How each payment is split
The mechanics of one month are simpler than the formula. For every payment:
- Compute interest owed: balance × monthly rate.
- Whatever's left of the payment after interest goes to principal.
- The new balance is the old balance minus the principal portion.
Month 1 of our example: balance is $300,000, so interest = $300,000 × 0.005 = $1,500. Payment is $1,798.65, so principal = $298.65. New balance: $299,701.35.
Month 2: balance is $299,701.35, interest = $1,498.51, principal = $300.14. Tiny shift — but it compounds. By month 60 (5 years in), principal is $401 and interest is $1,397. By month 240 (20 years in), it's $1,107 principal and $691 interest. By the last month, it's $1,789 principal and $9 interest.
The unintuitive part: 67% of the interest you'll ever pay on this loan is paid in the first half of the term. That's not a quirk; it's mathematically guaranteed. Interest is charged on the outstanding balance, and the balance is highest in the early years.
What extra payments actually do
Suppose you pay an extra $200 toward principal in month 1. Your balance drops to $299,501.35 instead of $299,701.35 — a $200 difference. But every subsequent month, you're now being charged interest on a balance $200+ smaller. That $200 saves you a few cents of interest in month 2, slightly more in month 3, and on and on for 359 more months.
The compounded savings over 30 years on that one extra $200: about $1,000 of interest avoided. That's a 5× return on the prepayment over the loan's life. And it shortens the term by about one month — your last payment moves earlier.
This is why "throw any windfall at the principal" is good advice for anyone who plans to keep the loan to term. The earlier the extra payment lands, the more interest it kills. An extra $200 in month 360 saves you exactly $0; the same $200 in month 1 saves $1,000.
Try it on your numbers
The amortization calculator shows month-by-month interest vs. principal split, plus the effect of any extra monthly payment.
The "biweekly trick"
You may have heard: "Switch to biweekly payments and pay off your mortgage 7 years early!" This isn't a trick of compounding. It's just that 26 biweekly half-payments = 13 monthly payments per year, not 12. You're making one extra month's payment per year. The math is the same as just adding ~8% to each monthly payment.
It works because of the same dynamic: extra principal early kills compounded interest later. But "biweekly" obscures what's happening. If you want the same result, divide your annual payment by 12, multiply by 13, divide that by 12, and pay that amount monthly. Identical outcome, simpler tracking.
Why amortization matters beyond mortgages
The same formula applies to auto loans, student loans, personal loans, business loans, and most installment debt. If the loan is fixed-rate with equal payments, it's amortizing. Different terms (5 years vs 30) and different rates (4% vs 24%) produce dramatically different interest/principal splits, but the structure is identical.
Two practical heuristics that fall out of the formula:
- Shorter terms front-load principal. A 15-year mortgage has you paying ~40% principal in month 1 instead of 17%. You build equity faster, but the payment is much higher.
- Higher rates dramatically extend the "mostly interest" phase. A 24% credit card minimum payment may be 95%+ interest for years. This is why credit-card minimums are a debt trap — they're designed to keep the balance high enough to be lucrative for the issuer.
One more useful number: the half-life
At what month is your balance half of what you started with? Not month 180 (halfway through). It's much later — for a 30-year mortgage at 6%, it's month 220. The first 60% of months pay off only the first 40% of principal.
The takeaway: when people say "the first half of mortgage payments is mostly interest," they're being roughly accurate but underselling it. The first two-thirds of payments are majority-interest. Knowing this lets you make informed choices: refinancing into a new 30-year mortgage resets you to month 1, even if you're 10 years in. Sometimes worth it for the rate; sometimes not.
The TL;DR
Amortization is the math that makes a fixed payment work against a shrinking balance. Interest is charged on the balance, so early payments are mostly interest; late payments are mostly principal. Extra principal payments are most powerful when made early. The biweekly trick is just "pay 13 months instead of 12." And refinancing resets the clock — beware.