To calculate loan amortization, take three numbers from your loan note — the principal, the stated annual interest rate converted to a monthly rate, and the total number of payments — plug them into the standard amortization formula to find your fixed monthly payment, and then repeat an interest-and-principal split against the shrinking balance for every period until it reaches zero. The same method works for a mortgage, a car loan, or any other fixed-payment installment debt.
What You Pull From the Loan Note First
Three inputs drive every calculation, and federal law requires lenders to disclose all three in a standardized format before you close.1eCFR. 12 CFR Part 1026 – Truth in Lending (Regulation Z)
- Principal (P): the total amount borrowed before any interest accrues. On a $250,000 mortgage, that’s $250,000.
- Stated interest rate: the annual rate the lender charges on the outstanding balance. This is not the APR.
- Number of payments (n): the total count of payments over the life of the loan. A 30-year mortgage paid monthly has 360. A five-year car loan has 60.
The APR mix-up trips people up constantly. The APR folds origination fees, mortgage insurance, and other costs into a single comparison figure. The amortization formula uses only the nominal rate on your loan note, because that’s the rate actually applied to your balance each period. If your note says 6% and your disclosure says the APR is 6.3%, use 6%.
To get the monthly rate (r), divide the annual stated rate by 12. Six percent becomes 0.06 ÷ 12 = 0.005 per month. That monthly rate is the engine of everything that follows.
The Monthly Payment Formula
The standard formula produces the fixed payment that retires the full balance, interest included, over exactly n periods:
M = P × [r(1 + r)n] / [(1 + r)n − 1]
- M is your fixed monthly payment.
- P is the principal.
- r is the monthly interest rate.
- n is the total number of payments.
The formula compounds the rate across every period and distributes the total cost evenly. The dollar amount stays the same every month even though the split inside that payment changes dramatically from the first month to the last.
A Worked Example End to End
Say you borrow $20,000 for a car at 6% annual interest, repaid over five years. Your inputs are P = $20,000, r = 0.005, and n = 60.
Start with (1 + r)n: (1.005)60 ≈ 1.3489. Then plug in:
M = 20,000 × [0.005 × 1.3489] / [1.3489 − 1]
M = 20,000 × 0.006744 / 0.3489
M = 20,000 × 0.01933
M = $386.66
That $386.66 is your fixed payment for all 60 months. You’ll pay roughly $23,200 total, so about $3,200 goes to interest. The next step is seeing how each $386.66 gets carved up.
Splitting Each Payment Between Interest and Principal
Every payment does two things: it covers the interest that accrued since the last payment, and it chips away at the balance. The split shifts every month.
For month one, multiply the outstanding balance by the monthly rate: $20,000 × 0.005 = $100.00 in interest. Subtract that from the fixed payment: $386.66 − $100.00 = $286.66 toward principal. The new balance is $20,000 − $286.66 = $19,713.34.
Month two starts from the updated balance: $19,713.34 × 0.005 = $98.57 in interest. Now $288.09 goes to principal, and the balance drops to $19,425.25. By month three, interest falls to $97.13 and principal climbs to $289.53.
That pattern is the whole point of amortization. Early on, interest eats a large share of each payment. As the balance shrinks, interest takes less and principal takes more. By the final year of a 30-year mortgage, nearly every dollar goes to principal. The front-loading is why people who sell or refinance after only a few years can feel like they barely dented the balance.
Building the Full Schedule
An amortization schedule is just the calculation above repeated for every payment, laid out as a table. Each row shows the payment number, interest paid, principal paid, and remaining balance. Using the car loan:
- Payment 1: $100.00 interest, $286.66 principal, balance $19,713.34
- Payment 2: $98.57 interest, $288.09 principal, balance $19,425.25
- Payment 3: $97.13 interest, $289.53 principal, balance $19,135.72
- Payment 60: balance reaches $0.00
Doing this by hand for a 360-payment mortgage is brutal. Spreadsheet software handles it easily. Set up formulas for one row and copy them down: the first row references your starting balance and payment, every row after that pulls the previous row’s ending balance as its starting point. Online calculators produce the same output instantly. But if you’re checking your lender’s numbers, running even the first five or six rows by hand is a solid sanity check.
Why the Last Payment Usually Differs
Build a full schedule and the final payment rarely matches the others exactly. The reason is rounding. Your calculated payment almost certainly has fractions of a cent that get rounded to two decimal places, and that tiny difference compounds across dozens or hundreds of periods. If the payment was rounded up, the final payment drops to compensate; if rounded down, it ticks up. On a 25-year mortgage the final payment might differ by a few dollars. Lenders adjust automatically.
When the Formula Doesn’t Match Reality
The formula above assumes a standard, fully amortizing, monthly-interest loan. Several common situations break that assumption.
Daily Simple Interest
Mortgages typically use the monthly method shown above, but many auto loans and student loans use daily simple interest. The lender multiplies your balance by the daily rate (annual rate ÷ 365) and then by the number of days since your last payment. Pay a few days late and you owe slightly more interest for that period; pay a few days early and you save a small amount. The formula still gives the right baseline payment, but the actual interest-principal split shifts with payment timing.
Escrow and Insurance on Top
For most mortgages, the amount your lender actually collects each month runs higher than the formula’s output because of escrow for property taxes and homeowners insurance. If taxes are $3,000 a year and insurance is $1,200, that’s another $350 tacked onto the monthly bill. Escrow doesn’t appear in the amortization formula, and the amount can shift year to year as assessments and premiums change. Private mortgage insurance, if you put less than 20% down, adds another layer that sits outside the amortization math.
Negative Amortization
Some loans allow minimum payments that don’t even cover accrued interest. The unpaid interest gets rolled into principal, so you owe more after paying than before.2Consumer Financial Protection Bureau. What Is Negative Amortization Federal rules now prohibit this feature on qualified mortgages, but it can still appear on certain adjustable-rate or non-qualified products. The standard formula won’t describe these loans.
Balloon Payments
A balloon loan calculates payments as if the term were longer than it actually is, then demands a lump sum at the end. You might pay for 60 months on a schedule built for 30 years and owe the entire remaining balance on month 61. Federal disclosure rules define a balloon payment as any payment more than twice the regular periodic amount, and lenders must disclose the maximum balloon figure and its due date before closing.3eCFR. 12 CFR 1026.37 – Content of Disclosures for Certain Mortgage Transactions (Loan Estimate) If your schedule doesn’t reach zero on the last scheduled payment, you have a balloon.
Running the Numbers for Extra Payments
The formula assumes you pay exactly the scheduled amount. Any additional dollars applied to principal reduce the balance that accrues interest in every future period, and the savings compound through the remaining term.
On a $405,000 fixed-rate mortgage at 6.625% over 30 years, adding $200 a month to principal could save roughly $115,000 in interest and shave about 67 months off the term. Even the equivalent of one extra monthly payment per year, such as switching to biweekly payments, can cut a 30-year mortgage by more than four years.
One thing catches people off guard: extra money sent to your servicer doesn’t automatically go to principal. Some servicers apply the overpayment to the next scheduled payment, which pushes your due date forward but saves no interest. You have to explicitly instruct the servicer to apply the extra to principal.4Consumer Financial Protection Bureau. How Is My Student Loan Payment Applied to My Account Most will take the instruction in writing or through their online portal.
Check for a prepayment penalty before you start. For most residential mortgages originated after January 2014, federal rules sharply restrict them, capping any penalty at 2% of the prepaid balance in the first two years and 1% in the third, with none allowed after that.5eCFR. 12 CFR 1026.43 – Minimum Standards for Transactions Secured by a Dwelling Auto loans aren’t covered by the same rules, and whether you can prepay without penalty depends on your contract and state law.6Consumer Financial Protection Bureau. Can I Prepay My Loan at Any Time Without Penalty Read your Truth in Lending disclosure before writing a bigger check.