How to Calculate Loan Repayments

Taking out a loan—whether for a vehicle, education, personal emergency, or real estate mortgage—is one of the most consequential financial commitments most people make. Understanding the mathematics behind loan repayment helps you compare competing lender offers and avoid paying thousands of dollars in unnecessary interest.

How Amortization Works

Most consumer loans are amortized with fixed monthly installments. Each monthly payment is split into two components:

1. Interest: The fee the lender charges for the use of their capital during that monthly billing cycle.
2. Principal: The portion that directly reduces the outstanding loan balance.

In the early years of a loan, the principal balance is at its highest, meaning the bulk of your monthly payment goes toward interest. Over time, as principal is paid down, less interest accrues each month, and an increasingly large share of your payment reduces principal.

The Standard Amortization Formula

The standard fixed-rate monthly installment formula is:

M = P × [ r(1 + r)^n ] ÷ [ (1 + r)^n - 1 ]

Where:

• M: Monthly payment amount
• P: Principal loan amount borrowed
• r: Monthly interest rate (Annual Interest Rate ÷ 12 ÷ 100)
• n: Total number of monthly installments (Years × 12)

A Worked Borrowing Example

Consider a $12,000 personal loan at a fixed annual rate of 7.0% repaid over 3 years (36 months).

• Principal P = $12,000
• Monthly rate r = 0.07 ÷ 12 = 0.005833
• Total periods n = 36
• Evaluating the formula yields a monthly payment of $370.53.
• Total paid over 3 years: $370.53 × 36 = $13,339.08.
• Total interest paid: $13,339.08 - $12,000 = $1,339.08.

Estimates vs. Actual Loan Offers

Keep in mind that this formula computes baseline principal and interest. Actual lender agreements may include loan origination fees, closing fees, private mortgage insurance (PMI), property escrow taxes, and prepayment stipulations. Always review the official Loan Estimate provided by your financial institution.

Test different loan terms, interest rates, and loan amounts with our Loan Repayment Calculator.