# Zero Coupon Bond Price Calculator, Formula and Example

In this Zero Coupon Bond Calculator:

1. Face Value ($): This represents the bond’s maturity value or the amount you’ll receive when the bond matures. For example, if you’ll receive$1,000 at the end of the bond’s term, you would enter 1000.0 in this field.
2. Discount Rate (%): The discount rate represents the interest rate used to bring future payments back to their present value. Think of it as the return rate you would expect from the bond. You should input this value as a percentage. For instance, if the discount rate is 4%, you’d input 4.0.
3. Time (years): Here, you specify the bond’s time to maturity, or in other words, how many years until the bond reaches its maturity date. If the bond matures in 5 years, you’d enter 5.

## Zero Coupon Bond Price Formula

A Zero Coupon Bond (ZCB) is a type of bond that does not pay periodic interest or coupons to its holder. Instead, it is issued at a discount to its face value and matures at its full face value. This means that the difference between the purchase price (or issue price) and the face value is the investor’s return.

The formula to calculate the price of a Zero Coupon Bond is given by:

\begin{align*}P=\frac{F}{(1+r)^t}\end{align*}

Where:

• P = Present value, or price of the zero coupon bond
• F = Face value of the bond (the amount it will be worth at maturity)
• r = Discount rate (expressed as a decimal)
• t = Time to maturity (in years)

Essentially, this formula discounts the bond’s future face value back to its present value using the specified discount rate, which gives the current price of the Zero Coupon Bond. The lower the purchase price compared to the face value, the higher the investor’s rate of return (and vice versa).

## Zero Coupon Bond Price Example

Imagine you’re interested in purchasing a zero coupon bond with a face value of 1,000 that will mature in 5 years. The current yield or discount rate in the market for such bonds is 4%. Using the formula, we can determine the price you should be willing to pay for the bond: \begin{align*}P&=\frac{\1,000}{(1+0.04)^5}\\[1em]&=\frac{\$1,000}{1.21665}\\[1em]&=\$821.93\end{align*}

Thus, you would be willing to pay $821.93 for the bond today to receive$1,000 in 5 years, given a 4% yield to maturity.