# Zero Coupon Bond Calculator

## About Zero Coupon Bond Calculator (Formula)

The Zero Coupon Bond Calculator is a tool used to determine the value and yield of a zero coupon bond. A zero coupon bond is a type of bond that does not pay periodic interest but is sold at a discount from its face value. The formula for calculating the value and yield of a zero coupon bond involves the present value formula and is as follows:

Formula for zero coupon bond value:

Value = Face Value / (1 + Yield)^Number of Periods

Formula for zero coupon bond yield:

Yield = ((Face Value / Value)^(1 / Number of Periods)) – 1

In these formulas, “Face Value” represents the future value or maturity value of the bond, “Yield” represents the interest rate or yield to maturity, and “Number of Periods” represents the total number of compounding periods until the bond matures.

For example, suppose we have a zero coupon bond with a face value of \$1,000, a maturity period of 5 years, and a yield of 4%. The value and yield of the bond would be calculated as follows:

Value = 1000 / (1 + 0.04)^5 ≈ \$822.70

Yield = ((1000 / 822.70)^(1 / 5)) – 1 ≈ 0.0485 or 4.85%

This means that the value of the bond is approximately \$822.70, and the yield to maturity is approximately 4.85%.

The Zero Coupon Bond Calculator simplifies the process of determining the value and yield of zero coupon bonds, aiding in investment analysis and decision-making. By inputting the face value, yield, and number of periods, the calculator quickly provides the value and yield, allowing individuals and investors to assess the attractiveness and profitability of zero coupon bond investments.