How amortization works (and how to read your amortization schedule)

What an amortization schedule shows

An amortization schedule is a month-by-month table for a loan that gets paid off in fixed payments over a set term. For every payment it shows three things: how much of that payment is interest, how much is principal, and what balance is left afterward. Run the table to the last payment and the balance lands on zero.

The same math sits under a mortgage, an auto loan, a personal loan, and most fixed-term student loans. The payment amount does not change from month to month, but the mix inside it does: interest and principal trade places gradually as the balance falls.

Why early payments carry more interest

Interest for a given month is simply the remaining balance times the monthly interest rate. Early in a loan, the balance is close to the full amount you borrowed, so the interest charge is at its largest in dollar terms, even though the total payment never changes. Whatever the fixed payment does not spend on interest goes to principal, so a bigger interest charge leaves a smaller slice for principal.

As principal gets paid down, next month's balance is smaller, so next month's interest charge is smaller too, and more of the same fixed payment flows to principal instead. This effect compounds gently across the whole term.

It shows up most dramatically on long loans. A $300,000 mortgage at 6% APR over 30 years has a fixed payment of $1,798.65, and in month 1 alone, $1,500.00 of that, over 83 percent, is interest, leaving only $298.65 to reduce the balance. A 5-year loan spreads the same front-loading effect over 60 payments instead of 360, so it is present but far less extreme, as the worked example below shows.

The formula behind the schedule

The fixed payment comes from the amortization formula above, the same one used to calculate a mortgage payment, because a mortgage is just a long-term amortized loan. Once you know the payment, building the schedule is mechanical.

Each month, interest equals the current balance times the monthly rate r. Principal is the payment minus that interest amount. Subtract principal from the balance to get the balance the next row starts from, and repeat for every payment in the term.

Worked example: $25,000 at 5% APR over 5 years

Borrow $25,000 at a 5% annual rate, paid off over 5 years. The monthly rate is r = 0.05 / 12 = 0.0041667, and the term is n = 60 payments. Plugging into the formula gives a fixed payment of M = $471.78.

Here is how the first three months break down:

• Month 1: payment $471.78, interest $104.17, principal $367.61, remaining balance $24,632.39
• Month 2: payment $471.78, interest $102.63, principal $369.15, remaining balance $24,263.24
• Month 3: payment $471.78, interest $101.10, principal $370.68, remaining balance $23,892.56

Where the balance ends up

Notice the interest column shrinks by about a dollar and a half each month while the principal column grows by roughly the same amount. That trade continues, slowly, for all 60 payments until the balance reaches zero on the final one.

Run the full schedule out and the loan collects $3,306.85 in total interest over its 5-year life, on top of the $25,000 borrowed, for $28,306.85 paid in all. That total interest figure is the real cost of the loan, and it is what extra principal payments go after.

How extra principal payments shorten the loan

Any amount paid beyond the required payment, if it is applied to principal, comes straight off the balance that next month's interest gets calculated on. Because every later month's interest is a percentage of a smaller number, that one extra payment keeps paying off in reduced interest for the rest of the loan.

Take the same $25,000 loan and add $100 a month in extra principal, for a total payment of $571.78. Instead of taking 60 months, the loan is paid off in 49, about 11 months, or nearly a year, sooner. Total interest drops from $3,306.85 to $2,655.84, a savings of $651.01, without changing the rate or the amount borrowed at all.

Before relying on this, confirm with your lender that extra payments are applied directly to principal on receipt. Some servicers instead hold extra money and apply it toward next month's regular payment, which does not touch the balance the same way and will not produce these savings.

Common mistakes

A schedule is only useful if you read it correctly. These are the errors that trip people up most often.

• Assuming a bigger payment always means more goes to principal early on: on longer loans, most of even a large early payment is still interest, and that is normal, not a sign of a bad loan.
• Not confirming how extra payments get applied: money labeled as extra needs to hit principal immediately, not sit as a credit toward a future regular payment, or it will not shorten the loan.
• Confusing an amortized loan with an interest-only loan: interest-only payments cover the interest charge and nothing else, so the balance never falls and there is no amortization happening at all.
• Restarting the clock by refinancing without checking the math: refinancing into a new full-length term, even at a lower rate, can mean paying more total interest than finishing out the original schedule, because you are back near the front-loaded, interest-heavy start.
• Ignoring prepayment penalties before sending extra principal: a small number of loans charge a fee for paying ahead of schedule, which can eat into or erase the interest savings.