Bonds Calculators

Zero Coupon Bond Yield Calculator

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To use the Zero Coupon Bond Yield Calculator:

  1. Face Value ($): Here, you should input the bond’s face value, which is the amount the bond will be worth at maturity. As an example, a typical value might be $1000.0.
  2. Present Value ($): You need to enter the present value of the bond in this field. This represents how much you are paying for the bond today. For instance, you might input $925.0 if you are buying the bond for that amount.
  3. Time to Maturity (Years): In this field, you need to specify the number of years until the bond matures. If the bond matures in 2 years, you would enter ‘2’.

Zero Coupon Bond Yield Formula

When dealing with a zero coupon bond, you’re essentially looking at a bond that doesn’t make any interest payments during its entire tenure. Instead, it is sold at a discount to its face value and, upon maturity, pays out the full face value. This difference between the purchase price and the face value represents the bond’s yield or interest.

The yield on a zero coupon bond can be determined using the following formula:

\begin{align*} y = \left(\frac{F}{P}\right)^{\frac{1}{t}} – 1 \end{align*}

Where:

  • y is the yield or annualized rate of return.
  • F is the face value or maturity value of the bond.
  • P is the present or purchase price of the bond.
  • t is the time to maturity, in years.

Simply put, this formula helps you understand the effective annual yield you would receive if you held the bond until maturity. For example, if you purchased a bond at a significant discount to its face value and it matures in 5 years, the formula would allow you to determine the annual rate of return you’d achieve over those 5 years.

Zero Coupon Bond Yield Calculation Example

Imagine you’re considering purchasing a zero-coupon bond with a face value of $1,000. The current price of this bond is $925 and it will mature in 2 years.

Using the formula:

\begin{align*} y = \left(\frac{F}{P}\right)^{\frac{1}{t}} – 1 \end{align*}

Plug in the values:

\begin{align*} y &= \left(\frac{1000}{925}\right)^{\frac{1}{2}} – 1 \\[1em] &\approx (1.0811)^{\frac{1}{2}} – 1 \\[1em] &\approx 1.0398 – 1 \\[1em] &\approx 0.0398 \end{align*}

To get the yield as a percentage, multiply by 100:

\begin{align*} y &= 3.98\% \end{align*}

So, if you buy this bond at $925, you can expect a yield of approximately 3.98% per year until it matures in 2 years.

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