An amortized bond is a type of bond in which the principal amount, or face value, is paid back to the bondholder gradually over time. This is in contrast to a bullet bond, where the entire principal is repaid at once upon maturity. The process of paying off the principal in installments over the bond’s life is known as amortization.

Here’s how amortized bonds work and an example:

### How Amortized Bonds Work:

1. **Principal Repayment:**
– With an amortized bond, the issuer repays a portion of the principal in each period. This can be achieved through periodic payments that include both interest and a partial repayment of the principal.

2. **Interest Payments:**
– In addition to the principal repayment, the bond issuer makes regular interest payments to bondholders. The interest is calculated on the remaining principal balance.

3. **Amortization Schedule:**
– The repayment schedule for an amortized bond is often presented in an amortization schedule. This schedule details the amount of each payment that goes toward interest, the amount that goes toward reducing the principal, and the remaining balance after each payment.

4. **Gradual Reduction of Principal:**
– Over the life of the bond, the principal amount is gradually reduced as each installment is paid. By the time the bond reaches maturity, the full face value has been repaid.

### Example of an Amortized Bond:

Let’s consider a $1,000 face value bond with a 5% annual interest rate and a 5-year term. The bond is amortized over its life with annual payments.

1. **Calculate Annual Payment (P):**
– Use the amortization formula to calculate the annual payment. The formula is:

\[ P = \frac{P_0 \times r \times (1 + r)^n}{(1 + r)^n – 1} \]

– \( P \) is the annual payment,
– \( P_0 \) is the face value of the bond,
– \( r \) is the periodic interest rate, and
– \( n \) is the total number of periods.

\[ P = \frac{1,000 \times 0.05 \times (1 + 0.05)^5}{(1 + 0.05)^5 – 1} \]

This calculation results in the annual payment that includes both interest and principal.

2. **Create Amortization Schedule:**
– Use the calculated annual payment to create an amortization schedule. For each year, calculate the interest payment, principal repayment, and the remaining balance.

\text{Year} & \text{Interest} & \text{Principal} & \text{Remaining Balance} \\
1 & 50.00 & 166.67 & 833.33 \\
2 & 41.67 & 175.00 & 658.33 \\
3 & 32.92 & 183.75 & 474.58 \\
4 & 23.73 & 192.94 & 281.64 \\
5 & 13.69 & 203.98 & 77.66 \\

The amortization schedule shows the interest, principal, and remaining balance for each year.

In this example, by the end of the 5-year term, the bond issuer would have made annual payments that, when added up, result in the full repayment of the $1,000 face value. Bondholders receive both interest income and a return of their principal over the bond’s life.