The Loan Payment Formula
Monthly loan payments are calculated using the standard amortization formula:
M = P × [r(1+r)ⁿ] ÷ [(1+r)ⁿ − 1]
Where M is the monthly payment, P is the loan principal, r is the monthly interest rate (annual rate ÷ 12), and n is the total number of monthly payments (years × 12).
Why This Formula Works
This formula ensures that each fixed monthly payment covers that month's interest charge plus a portion of the principal, structured so the loan balance reaches exactly zero at the end of the term — a process called amortization. In the early years of a loan, a larger share of each payment goes toward interest; over time, more goes toward principal.
Standard vs. Income-Driven Repayment
This calculator models a standard fixed repayment plan, where you pay the same amount each month until the loan is paid off. Federal student loans in the US also offer income-driven repayment (IDR) plans, where your payment is based on your income rather than a fixed amortization schedule — these can result in very different monthly payments and total interest paid, so check your specific loan servicer's options.
Factors That Affect Your Payment
- Interest rate: Even a small rate difference compounds significantly over a long loan term
- Loan term: A longer term lowers your monthly payment but increases total interest paid over the life of the loan
- Loan amount: Directly proportional to your payment — a larger loan means a larger payment at the same rate and term