How this calculator works
This calculator works for any fixed-rate, fully amortizing loan: mortgages, car loans, personal loans and student loans. Every payment is the same size, but its composition shifts — early payments are mostly interest, late payments mostly principal.
Open the amortization schedule to see that shift year by year. It is the clearest way to understand why extra payments early in a mortgage save so much more than the same payments near the end.
The amortization formula
Monthly payment M = P × i ÷ (1 − (1 + i)^−n)i = annual rate ÷ 12 (as a decimal) · n = years × 12At 0% interest the formula reduces to simply P ÷ n. Total interest is M × n − P.
Worked example: $200,000 at 6% for 30 years
- Monthly rate i = 0.06 ÷ 12 = 0.005; number of payments n = 360.
- M = 200,000 × 0.005 ÷ (1 − 1.005^−360) = $1,199.10.
- Total paid: 1,199.10 × 360 = $431,676.
- Total interest: 431,676 − 200,000 = $231,676 — more than the amount borrowed.
Frequently asked questions
Why is my first payment almost all interest?
Interest each month is the outstanding balance times the monthly rate. At the start the balance is the full loan, so interest eats most of the fixed payment. As the balance falls, more of each payment goes to principal.
How much does one extra payment a year save?
On a 30-year mortgage it typically shortens the loan by 4–5 years and saves tens of thousands in interest, because every extra dollar goes straight to principal. Run your own numbers by shortening the term until the payment matches what you would actually pay.
Does this include taxes and insurance?
No — this is principal and interest only. Property tax, homeowners insurance and any mortgage insurance come on top and vary by location and lender.
What is the difference between APR and the interest rate?
The interest rate is what the amortization math uses. APR also folds in certain fees and closing costs to make offers comparable — it is a shopping tool, not a payment input.
What is my payment if the loan has 0% interest?
At 0% interest, the amortization formula reduces to simply the loan amount divided by the number of payments (P ÷ n), since there is no interest component to add. For the $200,000, 360-payment example on this page, a 0% loan would cost 200,000 ÷ 360 ≈ $555.56 a month, with zero total interest — every dollar of every payment goes straight to principal.