The Standard Amortization Formula, As Implemented
Our mortgage calculator uses the standard annuity formula for a fixed payment loan.
monthly = P x (r x (1+r)^n) / ((1+r)^n - 1)
P is the loan amount. r is the annual interest rate divided by 100, then divided by 12, which gives the monthly rate. n is the term in years multiplied by 12, which gives the total payment count. The code applies this formula directly with one exponentiation, one multiplication, and one division.
Amounts carry no currency symbol, so the tool works in any currency you enter. The inputs get no sanity check beyond missing values, so an unusual term computes without complaint and the numbers you enter remain your responsibility.
Two totals follow from the payment. Total paid equals monthly times n. Total interest equals total paid minus the loan amount. Nothing in the tool estimates taxes, insurance, or fees, so the payment covers principal and interest only.
A Worked Example With Round Numbers
This example is an illustration with round inputs, not a rate quote or a market claim. Loan of 120,000, annual rate of 6 percent, term of 10 years.
- r equals 0.005, from 6 divided by 100 divided by 12.
- n equals 120, from 10 times 12.
- Monthly payment equals 1,332.25.
- Total paid equals 159,869.52, from 1,332.25 times 120.
- Total interest equals 39,869.52.
Every figure above came from running the tool logic, not from a marketing table. Under this formula the payment stays at 1,332.25 for all 120 months.
How the Amortization Table Is Built
The schedule is simulated month by month, in a loop the code runs twelve times per year row. Each month, interest equals the current balance times r. Principal equals the payment minus that interest. The balance then drops by the principal amount. Each row is rounded to two decimals, and the balance never displays below zero.
For the example, year 1 shows 9,032.67 of principal and 6,954.29 of interest, leaving a balance of 110,967.33. Year 10 shows 15,479.28 of principal and 507.68 of interest, leaving a balance of 0.
The very first month is the sharpest illustration. Interest for month one is 120,000 times 0.005, which is 600, leaving 732.25 of the 1,332.25 payment as principal.
The interest share of year 1 is about 43.5 percent. That share falls every year as the balance falls, which is the entire mechanism of amortization.
A Longer Term Shifts the Split Sharply
A second verified example shows why term length dominates interest cost. Loan of 300,000, annual rate of 6 percent, term of 30 years.
The monthly payment is 1,798.65 and total interest is 347,514.57. In year 1, principal paid is 3,684.04 against 17,899.78 of interest, so about 83 percent of the first year of payments is interest. Compare that with the 43.5 percent share in the 10 year example at the same rate.
The crossover arrives late. Principal paid passes interest paid only in year 19, at 10,819.15 of principal against 10,764.67 of interest, with 173,497.21 still owed. The year 10 row shows 6,313.33 of principal, 15,270.49 of interest, and a remaining balance of 251,057.17.
The rate is identical in both examples. Only the term changed, and the first year interest share nearly doubled.
What the Tool Rejects and Omits
A zero interest rate returns nothing, because the input guard treats zero as missing input. The formula itself would divide by zero at a zero rate, so the rejection prevents an error display.
The amortization table shows the first ten years, then prints a count of the remaining years. For the 30 year example you see years 1 through 10 plus a note about the other 20, which is why the year 19 crossover above comes from our verification run rather than the visible table. The schedule assumes exactly the fixed payment to term. Extra payments, rate changes, and fees are not modeled, so a real payoff will differ from the table the moment you pay extra.
Steps to Read Any Result Correctly
1. Enter the loan amount in your currency.
2. Enter the annual rate as a percentage, for example 6, not 0.06.
3. Enter the term in years, not months.
4. Read the monthly payment, total payment, and total interest.
5. Scan the table for the year when principal paid passes interest paid.
Checklist Before You Sign Anything
- [ ] Rate entered as a percentage, not a decimal.
- [ ] Term entered in years.
- [ ] Tax, insurance, and fees added separately by you.
- [ ] Zero rate understood as unsupported input.
- [ ] Full lender schedule compared for years beyond the first ten.
If you compared the tool against your actual lender schedule, send us the inputs and the row where the figures diverge. Amortization should match to the cent for a fixed payment loan, and any divergence is a bug we want. Run your own numbers on the [mortgage calculator](/en/mortgage-calculator).
