# Amortizing loan

In banking and finance, an amortizing loan is a loan where the principal 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) along with the coupon payments. Compare with a sinking 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 loans are typically amortizing loans. The calculations for an amortizing loan are those of an annuity 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 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 of the debt, reducing the debt's sensitivity to interest rate risk, as compared to debt with the same maturity and coupon rate. 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 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,

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

where:

• ${\displaystyle P}$ is the principal,
• ${\displaystyle P_{i}}$ is the principal repayment in coupon ${\displaystyle i}$, hence
• ${\displaystyle {\frac {P_{i}}{P}}}$ is the fraction of the principal repaid in coupon ${\displaystyle i}$, and
• ${\displaystyle t_{i}}$ is the time from the start to coupon ${\displaystyle i}$.