What Is a Loan Amortization Schedule?
A loan amortization schedule is a detailed table that shows how a fully-amortizing loan is paid off over time with equal periodic payments. Each payment is the same amount, but the split between interest and principal changes with every payment: early on, most of the money goes toward interest, and over time more goes toward reducing the balance. This calculator works for mortgages, car loans, student loans, and personal loans with a fixed rate.
How to Use It
Enter the loan amount (principal), the nominal annual interest rate, the total number of payments over the life of the loan, and how often you pay. The payment frequency simply tells the calculator how many periods there are per year, which is used to convert the annual rate into a periodic rate. The tool then computes your fixed payment, the total of all payments, the total interest, and a complete payment-by-payment table.
The Formula Explained
The periodic interest rate is the annual rate divided by the periods per year: \(i = (\text{annualRate} / 100) / \text{periodsPerYear}\). The fixed payment is
$$A = \frac{P \cdot i}{1 - (1 + i)^{-n}}$$If the rate is zero, the payment is simply the principal divided by the number of payments. For each period, interest equals the current balance times \(i\), principal equals the payment minus that interest, and the balance drops by the principal portion. This can be written as
$$\text{interest}_k = B_{k-1}\cdot i,\quad \text{principal}_k = A - \text{interest}_k$$The final payment is adjusted slightly so the balance lands exactly on zero, absorbing any rounding drift.
Worked Example
For a $275,000 loan at 4.875% paid monthly over 360 payments, the periodic rate is \(0.0040625\). The fixed payment is
$$A = \frac{275{,}000 \cdot 0.0040625}{1 - (1 + 0.0040625)^{-360}} \approx 1{,}455.31$$Total of payments is roughly $523,911, and total interest is about $248,911. The first payment includes \(1{,}117.19\) of interest and \(338.12\) of principal, leaving a balance near $274,661.88 — and the interest share shrinks each month thereafter.
FAQ
Does changing the payment frequency change the number of payments? No. You enter the total number of payments directly. Frequency only sets the rate divisor.
Why is my last payment slightly different? Rounding each payment to cents can leave a tiny residual, so the final payment is adjusted so the balance reaches exactly zero.
What if the interest rate is 0%? The payment is just the loan amount divided by the number of payments, and total interest is zero.
