Loan Amortization

4.5 Terminology and Glossary of the Symbols

Terminology

  • Loan amortization: The gradual reduction in the loan amount through periodic repayments, usually of equal amounts, over a predetermined length of time.
  • Amortization period: The time period set to repay the loan.
  • Amortization schedule: A detailed table that breaks down each loan repayment amount into its interest portion (INT) and principal portion (PRN)
  • Interest portion (INT): The interest portion of a payment amount (PMT)
  • Principal portion (PRN): The principal portion of a payment amount (PMT)
  • Principal balance (BAL): The loan balance at a given time
  • Term (t): In this unit refers to the term of a loan (i.e., an annuity), which is the time period (in years) from the beginning of the first payment interval to the end of the last payment interval.

Glossary of the Symbols

Annuities

  • I/Y Nominal interest rate per year (%)
  • C/Y: Frequency of interest compounding period per year
  • i: Interest rate per compounding period (%)
  • [asciimath]i_2[/asciimath]: Equivalent interest rate per payment period (%)
  • c: Number of compounding periods in each payment period
  • t: Term of the annuity (in years)
  • N: Total number of periodic payments in the annuity  term
  • P/Y: Number of payments per year
  • PMT: Amount of periodic payment ($)
  • PV: Present value of an annuity ($)
  • FV: Future (maturity) value of an annuity ($)
  • I: Interest Amount ($)

Amortization

  • PMT: the amount of periodic payment ($)
  • INT: the interest portion of a payment amount ($)
  • PRN: the principal portion of a payment amount ($)
  • BAL: The principal balance of a loan at a given time ($)

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Mathematics of Finance Copyright © 2024 by Amir Tavangar is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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