Question

If the face value of a bond is \(\$ 10,000\) and the coupon rate is 5 percent, what is the annual payment to the bondholder?

Short answer

The annual payment to the bondholder is \$500.

Step-by-step solution

Understand the values given

In this case, the face value of the bond is \$10,000 and the coupon rate is 5%.

Convert the coupon rate to a decimal

To use the coupon rate in calculations it needs to be in decimal form, which can be done by dividing it by 100. So, the decimal form of the coupon rate is \(0.05 = \frac{5}{100}\).

Calculate the annual payment

The annual payment is calculated by multiplying the face value of the bond by the coupon rate in decimal form. So, the annual payment is \(0.05 \times \$10,000 = \$500\).

Key concepts

Financial Bonds Education

When diving into the world of investing, understanding financial bonds is crucial for any budding investor. Bonds are essentially loans that investors make to corporations or governments, in return for periodic interest payments and the return of the principal amount at maturity. These interest payments are based on the bond's coupon rate, which is determined at issuance and does not change over the life of the bond. Bonds can be purchased directly when they are issued or later on in the secondary market.

Bonds are often considered lower risk compared to stocks, which makes them an appealing option for conservative investors. They can provide a regular stream of income through the interest payments, which are known as 'coupons' because in the past, physical bond certificates had coupons that you would actually clip and redeem for the interest owed. Bonds come in different types, including but not limited to government bonds, municipal bonds, and corporate bonds, each with their own risk profile and tax implications.

Coupon Rate Calculation

The coupon rate of a bond is a critical factor that affects its yield and investment value. It represents the annual interest rate paid by the issuer to the bondholder and is expressed as a percentage of the bond's face value. To calculate the coupon rate, understanding the terminology is essential.

A bond's face value, or 'par value,' is the amount the issuer agrees to pay back at maturity. The coupon rate, on the other hand, tells us what percentage of this face value will be paid out in interest each year. To accurately calculate the coupon rate when given in percentage, you need to convert it to decimal form. This is a straight-forward process where you divide the coupon rate by 100. For instance, a coupon rate of 5% becomes 0.05 in decimal form. This step is the springboard for further calculations involving bonds, like determining the actual dollar amount you will receive in interest payments.

Annual Bond Payment

Understanding how to determine the annual bond payment is essential for investors as it affects their cash flow and investment planning. Once you have the coupon rate in decimal form, you'll multiply it by the bond's face value to calculate the annual interest payment, also known as the bond's 'coupon payment'.

The formula for this is quite simple: Annual Bond Payment = Face Value of Bond × Coupon Rate (in decimal form). For example, with a \(10,000 bond and a coupon rate of 5%, the annual bond payment can be calculated as follows: \)10,000 (Face Value) × 0.05 (Coupon Rate) = \(500. Thus, the bondholder will receive \)500 each year until the bond reaches maturity. This fixed payment is a predictable source of income, which is why bonds are often favored by investors who need steady cash flows, such as retirees.