Amortization is the process of gradually paying off a loan through regular payments that cover both interest and principal, so the loan is fully paid at the end of the term.

• Each payment includes interest + principal
• Early payments are mostly interest
• Later payments are mostly principal
• Loan balance decreases over time
• A fully amortized loan has a zero balance at maturity

• Loan amount (principal)
• Interest rate
• Loan term (years)
• Payment amount (if provided)
• Number of payments made (to find remaining balance)

• No payments made
  • Loan balance = original loan amount

• Some payments made
  • Loan balance = original loan amount − principal paid
  • (Interest paid does not reduce balance)

• Fully amortized loan
  • Balance = $0 at end of term

• Monthly payment is fixed
• Interest portion = loan balance × periodic interest rate
• Principal portion = payment − interest portion
• New balance = old balance − principal portion

• Payments do not equal principal reduction
• Only the principal portion builds equity
• If the problem says no payments were made, ignore interest and amortization details