amortizing loan

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In
banking A bank is a financial institution that accepts deposits from the public and creates a demand deposit while simultaneously making loans. Lending activities can be directly performed by the bank or indirectly through capital markets. Because ...
and
finance Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of production, distribution, and consumption of money, assets, goods and services (the discipline of fin ...
, an amortizing loan is a loan where the
principal Principal may refer to: Title or rank * Principal (academia), the chief executive of a university ** Principal (education), the office holder/ or boss in any school * Principal (civil service) or principal officer, the senior management level ...
of the loan is paid down over the life of the loan (that is, amortized) according to an amortization schedule, typically through equal payments. Similarly, an amortizing bond is a bond that repays part of the principal (
face value The face value, sometimes called nominal value, is the value of a coin, bond, 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. Howe ...
) along with the coupon 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. In North America and elsewhere where it is common for public and priv ...
, 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 (), in civil law jurisdicions known also as a hypothec loan, 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 pu ...
s are typically amortizing loans. The calculations for an amortizing loan are those of an
annuity In investment, 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, mo ...
using the time value of money formulas and can be done using an amortization calculator. An amortizing loan should be contrasted with a bullet loan, 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 on a debt that may arise from a borrower failing to make required payments. In the first resort, the risk is that of the lender and includes lost principal and interest, disruption to cash flows, and increased co ...
of the loan or bond. In a bullet loan (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 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 theory of time an ...
of the debt, reducing the debt's sensitivity to
interest rate risk In finance and economics, interest is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum (that is, the amount borrowed), at a particular rate. It is distinct ...
, 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.

# Equated monthly installment

In EMI or
Equated Monthly Installment An equated monthly installment (EMI) is defined by Investopedia as "A fixed payment amount made by a borrower to a lender at a specified date each calendar month. Equated monthly installments are used to pay off both interest and principal each m ...
s, payments are divided into equal amounts for the duration of the loan, making it the simplest repayment model. A greater amount of the payment is applied to interest at the beginning of the amortization schedule, while more money is applied to principal at the end. This is captured by the formula :$P \,=\,A\cdot\frac$ or, equivalently, :$A \,=\,P\cdot\frac$ where: ''P'' is the principal amount borrowed, ''A'' is the periodic amortization payment, ''r'' is the periodic interest rate divided by 100 (nominal annual interest rate also divided by 12 in case of monthly installments), and ''n'' is the total number of payments (for a 30-year loan with monthly payments ''n'' = 30 × 12 = 360).

# Negative amortization

Negative amortization In finance, negative amortization (also known as NegAm, deferred interest or graduated payment mortgage) occurs whenever the loan payment for any period is less than the interest charged over that period so that the outstanding balance of the loa ...
(also called deferred interest) occurs if the payments made do not cover the interest due. The remaining interest owed is added to the outstanding loan balance, making it larger than the original loan amount. If the repayment model for a loan is "fully amortized", then the last payment (which, if the schedule was calculated correctly, should be equal to all others) pays off all remaining principal and interest on the loan. If the repayment model on a loan is not fully amortized, then the last payment due may be a large balloon payment of all remaining principal and interest. If the borrower lacks the funds or assets to immediately make that payment, or adequate credit to refinance the balance into a new loan, the borrower may end up in
default Default may refer to: Law * Default (law), the failure to do something required by law ** Default (finance), failure to satisfy the terms of a loan obligation or failure to pay back a loan ** Default judgment, a binding judgment in favor of e ...
.

# Weighted-average life

The number weighted average of the times of the principal repayments of an amortizing loan is referred to as the
weighted-average life In finance, the weighted-average life (WAL) of an amortizing loan or amortizing bond, also called average life, is the weighted average of the times of the ''principal repayments'': it's the average time until a dollar of principal is repaid. In a ...
(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 $i$.