Amortizing loan

Inbankingandfinance,anamortizing loanis a loan where theprincipalof the loan is paid down over the life of the loan (that is, amortized) according to anamortization schedule,typically through equal payments.

Similarly, anamortizing bondis abondthat repays part of the principal (face value) along with thecouponpayments. Compare with asinking fund,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 loansare typically amortizing loans. The calculations for an amortizing loan are those of anannuityusing thetime value of moneyformulas and can be done using anamortization calculator.

An amortizing loan should be contrasted with abullet 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.

Anaccumulated amortization loanrepresents 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 thecredit riskof the loan or bond. In abullet loan(orbullet 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 thedurationof the debt, reducing the debt's sensitivity tointerest rate risk,as compared to debt with the samematurityandcoupon rate.This is because there are smaller payments in the future, so the weighted-average maturity of the cash flows is lower.

Equated monthly installment

Main article:Equated monthly installment

In EMI orEquated Monthly Installments,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

$P\,=\,A\cdot {\frac {1-\left({\frac {1}{1+r}}\right)^{n}}{r}}$

or, equivalently,

$A\,=\,P\cdot {\frac {r(1+r)^{n}}{(1+r)^{n}-1}}$

where:Pis the principal amount borrowed,Ais the periodic amortization payment,ris the periodic interest rate divided by 100 (nominal annual interest rate also divided by 12 in case of monthly installments), andnis the total number of payments (for a 30-year loan with monthly paymentsn= 30 × 12 = 360).

Negative amortization

Main article:Negative amortization

Negative amortization(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 largeballoon paymentof 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 indefault.

Weighted-average life

Main article:Weighted-average life

The numberweighted averageof the times of the principal repayments of an amortizing loan is referred to as theweighted-average life(WAL), also called "average life". It's the average time until a dollar of principal is repaid.

In a formula,

${\text{WAL}}=\sum _{i=1}^{n}{\frac {P_{i}}{P}}t_{i},$

where:

• $P$is the principal,
• $P_{i}$is the principal repayment in coupon$i$,hence
• ${\frac {P_{i}}{P}}$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
• Amortization schedule
• Amortization (accounting)
• Sinking fund
• Weighted-Average Life