# Zero Coupon Bond Formula: A Comprehensive Guide

**Table Contents**show

## What is a Zero Coupon Bond?

A zero coupon bond (also known as a discount bond or deep discount bond) is a debt security that does not pay interest (a coupon) but is traded at a deep discount, rendering profit at maturity when the bond is redeemed for its full face value. A zero coupon bond is typically sold at a substantial discount from its face amount, with the difference between the purchase price and the face value representing the investor’s return. For example, if you purchase a $1000 zero coupon bond with a 2023 maturity date at a cost of $800, you will receive $1000 when the bond matures.

## How Does a Zero Coupon Bond Work?

A zero coupon bond works in a similar way to other types of debt securities, such as Treasury bonds. A bond issuer offers to pay a certain face value of the bond at a certain maturity date. The issuer can be a government, corporation, or other entity and must be deemed creditworthy by the bond-buying public. When the bond is first issued, it is sold at a deep discount from its face value. This difference in price is the investor’s return on the bond.

## Zero Coupon Bond Formula

The zero coupon bond formula is used to calculate the amount of money an investor will receive when the bond matures. The formula is as follows:

Zero Coupon Bond Value = Face Value / (1 + (r/m))^n

Where:

Face Value = The face value of the bond at maturity

r = The current market rate of interest

m = The frequency of compounding (usually 12)

n = The number of years until maturity

### Example of Zero Coupon Bond Formula

Let’s say you purchase a $1000 zero coupon bond with a maturity date of 2023. The current market rate of interest is 5%. The frequency of compounding is 12 (monthly). The number of years until maturity is 5. Using the formula above, we can calculate the value of the bond at maturity:

Zero Coupon Bond Value = 1000 / (1 + (0.05/12))^5

Zero Coupon Bond Value = 1000 / (1 + 0.004167)^5

Zero Coupon Bond Value = 1000 / 1.0212

Zero Coupon Bond Value = $978.69

## Advantages of Zero Coupon Bonds

Zero coupon bonds have several advantages for investors. First, they are a reliable source of income, as the investor will always receive the face value of the bond at maturity. Second, they are relatively low risk, as the bond issuer must be deemed creditworthy by the bond-buying public. Third, zero coupon bonds can be held until maturity, meaning that the investor will not experience fluctuations in the bond’s value due to changes in the market or interest rates.

## Disadvantages of Zero Coupon Bonds

Zero coupon bonds also have some disadvantages. First, they are subject to price fluctuations due to changes in the market or interest rates. Second, they are not as liquid as other types of investments, meaning they cannot be sold quickly or easily. Finally, they are taxed each year on the “phantom income” that is earned through the discount rate, even though the investor does not actually receive this income until the bond matures.

## Conclusion

Zero coupon bonds are a reliable source of income for investors, as they will always receive the face value of the bond at maturity. They are relatively low risk, as the bond issuer must be deemed creditworthy by the bond-buying public. However, they are subject to price fluctuations and are not as liquid as other types of investments. The zero coupon bond formula can be used to calculate the value of the bond at maturity.