Amortizing loan

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.

In EMI or Equated Monthly Installments, payments are divided into equal amounts for the duration of the loan, making it the simplest repayment model.[1] 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

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

or, equivalently,

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

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 (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.

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 ${\displaystyle i}$.

• Amortization calculator
• Amortization schedule
• Amortization (accounting)
• Sinking fund
• Weighted-Average Life