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In
banking A bank is a financial institution Financial institutions, otherwise known as banking institutions, are corporation A corporation is an organization—usually a group of people or a company—authorized by the State (polity), stat ...

banking
and
finance Finance is a term for the management, creation, and study of money In a 1786 James Gillray caricature, the plentiful money bags handed to King George III are contrasted with the beggar whose legs and arms were amputated, in the left corn ...

finance
, an amortizing loan is a loan where the
principal Principal may refer to: Title or rank * Principal (academia) The principal is the chief executive and the chief academic officer of a university A university ( la, universitas, 'a whole') is an educational institution, institution of higher ...
of the loan is paid down over the life of the loan (that is,
amortized In computer science, amortized analysis is a method for Analysis of algorithms, analyzing a given algorithm's Computational complexity theory, complexity, or how much of a resource, especially time or memory, it takes to Execution (computing), execu ...
) according to an
amortization schedule An amortization schedule is a table detailing each periodic payment on an amortizing loan (typically a mortgage loan, mortgage), as generated by an amortization calculator. Amortization refers to the process of paying off a debt (often from a loan ...
, typically through equal payments. Similarly, an amortizing bond is a
bond Bond or bonds may refer to: Common meanings * Bond (finance) In finance Finance is the study of financial institutions, financial markets and how they operate within the financial system. It is concerned with the creation and management of ...
that repays part of the principal (
face value The face value, sometimes called nominal value, is the value of a coin, Postage stamp, stamp or paper money as printed on the coin, stamp or bill itself by the issuing authority. The face value of coins, stamps, or bill is usually its legal value ...
) along with the
coupon In marketing, a coupon is a ticket or document that can be redeemed for a financial discounts and allowances, discount or rebate (marketing), rebate when purchasing a product (business), product. Customarily, coupons are issued by manufacturers ...
payments. Compare with a
sinking fund A sinking fund is a fund established by an economic entity by setting aside revenue over a period of time to fund a future capital expense, or repayment of a long-term debt Debt is an obligation that requires one party, the debtor, to pay ...
, which amortizes the total debt outstanding by repurchasing some bonds. Each payment to the lender will consist of a portion of interest and a portion of principal.
Mortgage loan A mortgage loan or simply mortgage () is a loan used either by purchasers of real property to raise funds to buy real estate, or by existing property owners to raise funds for any purpose while putting a lien on the property being mortgaged. T ...
s are typically amortizing loans. The calculations for an amortizing loan are those of an
annuity An annuity is a series of payments made at equal intervals.Kellison, Stephen G. (1970). ''The Theory of Interest''. Homewood, Illinois: Richard D. Irwin, Inc. p. 45 Examples of annuities are regular deposits to a savings account A savings account ...
using the
time value of money The time value of money is the widely accepted conjecture that there is greater benefit to receiving a sum of money Image:National-Debt-Gillray.jpeg, In a 1786 James Gillray caricature, the plentiful money bags handed to King George III are co ...
formulas and can be done using an
amortization calculator An amortization calculator is used to determine the periodic payment amount due on a loan In finance, a loan is the lending of money by one or more individuals, organizations, or other entities to other individuals, organizations etc. The rec ...
. An amortizing loan should be contrasted with a
bullet loanIn banking and finance, a bullet loan is a loan where a payment of the entire principal Principal may refer to: Title or rank * Principal (academia) The principal is the chief executive and the chief academic officer of a university A univers ...
, where a large portion of the loan will be paid at the final maturity date instead of being paid down gradually over the loan's life. An accumulated amortization loan represents the amount of amortization expense that has been claimed since the acquisition of the asset.


Effects

Amortization of debt has two major effects: ;Credit risk: First and most importantly, it substantially reduces the
credit risk A credit risk is risk of default Default may refer to: Law * Default (law), the failure to do something required by law ** Default (finance) In finance Finance is the study of financial institutions, financial markets and how they ope ...
of the loan or bond. In a
bullet loanIn banking and finance, a bullet loan is a loan where a payment of the entire principal Principal may refer to: Title or rank * Principal (academia) The principal is the chief executive and the chief academic officer of a university A univers ...
(or bullet bond), the bulk of the credit risk is in the repayment of the principal at maturity, at which point the debt must either be paid off in full or rolled over. By paying off the principal over time, this risk is mitigated. ;Interest rate risk: A secondary effect is that amortization reduces the
duration Duration may refer to: * The amount of Time#Terminology, time elapsed between two events * Duration (music) – an amount of time or a particular time interval, often cited as one of the fundamental aspects of music * Duration (philosophy) – a th ...
of the debt, reducing the debt's sensitivity to
interest rate risk Interest rate risk is the risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty Uncertainty refers to Epistemology, epistemic situations involving imperfect or unknown information. It applies to ...
, as compared to debt with the same maturity and
coupon rate In marketing, a coupon is a ticket or document that can be redeemed for a financial discount or rebate when purchasing a product. Customarily, coupons are issued by manufacturers of consumer packaged goods or by retailers, to be used in r ...
. This is because there are smaller payments in the future, so the weighted-average maturity of the cash flows is lower.


Weighted-average life

The number
weighted average The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The ...
of the times of the principal repayments of an amortizing loan is referred to as the weighted-average life (WAL), also called "average life". It's the average time until a dollar of principal is repaid. In a formula, :\text = \sum_^n \frac t_i, where: * P is the principal, * P_i is the principal repayment in coupon i, hence * \frac is the fraction of the principal repaid in coupon i, and * t_i is the time from the start to coupon i.


See also

*
Amortization calculator An amortization calculator is used to determine the periodic payment amount due on a loan In finance Finance is the study of financial institutions, financial markets and how they operate within the financial system. It is concerned wi ...
*
Amortization schedule An amortization schedule is a table detailing each periodic payment on an amortizing loan (typically a mortgage loan, mortgage), as generated by an amortization calculator. Amortization refers to the process of paying off a debt (often from a loan ...
*
Amortization (business) In business, amortization refers to spreading payments over multiple periods. The term is used for two separate processes: amortization of loans and amortization of assets. In the latter case it refers to allocating the cost of an intangible asset ...
*
Sinking fund A sinking fund is a fund established by an economic entity by setting aside revenue over a period of time to fund a future capital expense, or repayment of a long-term debt Debt is an obligation that requires one party, the debtor, to pay ...
* Weighted-Average Life


References

{{reflist Debt Bonds (finance) Loans