# Zero-Coupon Bond

An accrual bond, also known as a zero-coupon bond, is a type of financial security that doesn't pay interest but trades at a considerable discount, producing income when it matures and is realized for its full face value.

## Understanding Zero-Coupon Bonds

A zero-coupon bond trades at a discount to its face value because it doesn't issue regular coupons. Take into account the temporal value of money to comprehend why.

Money is worth more now than it will be at some point in the future, according to the idea of the time value of money. For example, an investor would rather get $100 today than $100 in a year. The investor will have more than $100 after a year if they invest the $100 they get today and earn interest on it by putting it in a savings account.

Applying the previous concept to zero-coupon bonds, a buyer of the bond today must receive compensation in the form of a greater future value. Since the issuer is obligated to offer the investor a return for purchasing the bond, a zero-coupon bond is traded at a reduced price.

## Pricing & Calculation Zero-Coupon Bond

Bond's price can be computed as follows:

`Price = M รท (1 + r) n`

where:

M = Maturity value or face value of the bond

r = required rate of interest

n = number of years until maturity

## What Makes A Zero-Coupon Bond Unique?

The principal distinction between a zero-coupon and normal bond is the payment of interest, or coupons. Regular bonds, also known as coupon bonds, pay interest throughout their lifetime in addition to repaying the principal at maturity. A zero-coupon bond trades at a considerable discount instead of paying interest, making the investor money when they redeem the bond for its full face value at maturity.

## Example Of A Zero-Coupon Bond

### Example 1: Annual Compounding

John is looking to buy a $1,000 zero-coupon bond with a five-year maturation period. The bond carries an annual interest rate of 5% compounded. What cost will John put on the bond right now?

The bond's value is calculated as $1,000 divided by (1+0.05)5, resulting in a price of $783.53.

John will spend $783.53 today to purchase the bond.

### Example 2: Semi-annual Compounding

John wants to buy a zero-coupon bond with a $1,000 face value and a five-year maturation period. The bond's interest rate is 5% compounded semi-annually. What price will John accept today for the bond?

The bond's cost is calculated as $781.20 using the formula: $1,000 / (1+0.05/2)5*2.

John will spend $781.20 today in order to purchase the bond.

## Conclusion

- Zero-coupon bonds are a type of debt security that don't pay interest.
- Zero-coupon bonds are traded at huge discounts and mature at their face value (par).
- The return on a zero-coupon bond is computed as the difference between the purchase price and the par value.