How is Loan Interest Calculated? The Math Behind Amortization
Demystify how your mortgage or auto loan payment is split between principal and interest, and learn how to run the math behind amortization.
When you take out a mortgage, car loan, or student loan, you agree to make a fixed monthly payment for a set number of years. Many borrowers assume that their outstanding balance drops by this full payment amount each month. However, this is not how loans work. In the beginning, the majority of your payment goes toward paying off the interest charges, with only a small fraction reducing the actual loan balance (the principal). This shifting division of payments is called amortization. This guide explains the exact math banks use to calculate your loan payments, matching our Amortization Calculator.
The Core Rule: Interest is calculated based on the remaining principal balance at the start of each month. As you pay down the principal, the interest charge for the next month drops, allowing more of your payment to target the loan balance.
The Monthly Payment Formula
Lenders calculate your fixed monthly payment using the standard amortization formula:
Here is what each variable represents:
- M: The total monthly payment.
- P: The principal loan amount (the initial amount borrowed).
- r: The monthly interest rate (annual interest rate divided by 12 months).
- n: The total number of monthly payments (loan term in years multiplied by 12).
Visualizing the Amortization Split
As shown in the graph above, the fixed monthly payment stays the same, but the internal split shifts. In the first year, interest takes up the largest share of your money. By the middle of the loan term, the lines cross, and in the final years, almost your entire payment goes directly to clearing out the remaining principal.
How Lenders Divide Your Payment
Every month, the bank calculates your interest charge first. Here are the two equations used to allocate your monthly payment:
1. Calculate Monthly Interest
Multiply the current remaining loan balance by the monthly interest rate:
2. Calculate Principal Paid
Subtract the interest charge from your fixed monthly payment. The remaining amount goes to reduce your loan balance:
Worked Example: A $200,000 Loan at 6% Interest
Assume you borrow $200,000 for a 30-year home mortgage at a 6% interest rate. The monthly payment is fixed at $1,199.10 per month:
- The monthly interest rate is 0.06 / 12 = 0.005 (0.5% per month).
Month 1 Allocation:
- Interest: $200,000 x 0.005 = $1,000.00 (83% of your payment).
- Principal: $1,199.10 - $1,000.00 = $199.10.
- New Loan Balance: $200,000 - $199.10 = $199,800.90.
Month 2 Allocation:
- Interest: $199,800.90 x 0.005 = $999.00.
- Principal: $1,199.10 - $999.00 = $200.10.
- New Loan Balance: $199,800.90 - $200.10 = $199,600.80.
Each month, your principal payment increases by a few cents as the interest charge falls. By Year 15, your payment is split evenly, and by Year 29, almost the entire $1,199.10 goes directly to principal.
The Power of Extra Payments
Because interest is calculated on your remaining balance, making any extra principal payment pays off in two ways: it immediately reduces your balance, and it permanently lowers the interest charges for every single remaining month of the loan. Adding an extra payment each year or paying an extra $100 per month can shave 4 to 5 years off a 30-year mortgage and save you tens of thousands of dollars in lifetime interest.
Map Your Payoff Schedule
Our online Amortization Calculator generates a complete month-by-month table showing your principal and interest split, total interest paid, and remaining balance. You can add one-time, monthly, or yearly extra payments to see exactly how much money and time you will save.