How Loan Amortization Works, Month by Month
An amortizing loan is one you pay off in equal instalments, where each payment covers all the interest due for that period plus a bit of the principal. Mortgages, car loans, and most personal loans work this way. The payment stays the same every month; what changes is the split between interest and principal.
Where the monthly payment comes from
The standard fixed-rate formula is:
M = P × r × (1 + r)n ÷ ((1 + r)n − 1)
- P — the amount borrowed (the principal)
- r — the interest rate per period, i.e. the annual rate divided by 12 for monthly payments
- n — the total number of payments (years × 12)
Worked example. Borrow $20,000 at 6.5% annual interest over 5 years. Then r = 0.065 ÷ 12 = 0.0054167, and n = 60. Plugging in gives M = $391.32 per month. Over 60 payments you hand back $23,479, so the interest cost is about $3,479. The loan calculator computes this and shows the running balance as a chart.
If the rate is 0%, the formula above breaks (you would divide by zero). In that case the payment is simply P ÷ n — the principal spread evenly, no interest.
Why early payments are mostly interest
Interest each month is charged on the balance still outstanding. At the start the balance is large, so most of your fixed payment goes to interest and only a little to principal. As the balance shrinks, the interest portion shrinks with it and more of each payment chips away at principal. The effect accelerates toward the end.
For the $20,000 example above:
| Payment | Interest | Principal | Balance after |
|---|---|---|---|
| 1 | $108.33 | $282.99 | $19,717.01 |
| 30 (halfway) | $57.72 | $333.60 | $10,321 |
| 60 (last) | $2.11 | $389.21 | $0 |
Notice the payment is $391.32 every time; only the columns inside it move. A full month-by-month breakdown like this is what the amortization schedule generates.
What extra payments do
Any amount you pay above the scheduled M goes straight to principal. Because it removes balance that would otherwise have accrued interest for the entire remaining term, a small extra payment early on has an outsized effect. Paying an extra $50/month on the loan above clears it roughly 8 months early and saves several hundred dollars in interest. The debt payoff calculator models this across several debts at once, including the avalanche and snowball ordering strategies.
What the basic formula leaves out
- Fees and points — origination fees, closing costs, and mortgage insurance are not in M. The APR is meant to fold some of these in, which is why APR is usually a little above the nominal rate.
- Taxes and insurance — a mortgage "payment" often bundles property tax and homeowners insurance into an escrow account. That is a real cash outflow but not part of loan amortization.
- Variable rates — an adjustable-rate loan re-computes M each time the rate resets, using the then-current balance and remaining term.
- Compounding conventions — some loans (notably in Canada and the UK) compound semi-annually rather than monthly, which slightly changes the effective rate.
The relationship to compound interest
Amortization and compound growth are the same mechanism seen from opposite sides. In a savings account, interest is added to a balance that then earns more interest. In a loan, interest is added to a balance that you then pay down. The compound interest calculator shows the savings side — useful for comparing "pay down the loan" against "invest the money instead" when you have spare cash.