DEFINITION

Zero-coupon bond pricing refers to finding out the fair value of a zero-coupon bond, which is simply the present value of the redemption amount of that bond.

**CALCULATOR**

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**FORMULA AND DERIVATION **

A zero-coupon bond involves only one cash inflow to the investor. This single cash inflow is the redemption amount received. The price of the bond will therefore be the discounted value of this redemption payment. In order to determine the price that an investor is willing to pay, he/she would discount this cash flow at their required rate of return from the bond which is the yield \(i\).

So, the price \(P_n\) of an \(n-year\) zero-coupon bond would be:-

\[P_n=R\times {\left(1+i\right)}^{-n}\]

Where,

\(i\) is the yield

\(R\) is the redemption amount.

**EXAMPLES**

Example 1

Suppose an investor wishes to buy a \(10\) year zero-coupon bond that is redeemable at par. The price that the investor would be willing to pay for \(\textrm{₹}1000\) nominal of the bond, requiring a yield of \(10\%\) p.a. could be found out by the given formula.

\[P_n=R\times {\left(1+i\right)}^{-n}\]
\[P_{10}=1000\times {\left(1.1\right)}^{\left(-10\right)}\]
\[P_{10}=385.54\]

This means that the investor is willing to pay \(\textrm{₹}385.54\) for a zero coupon bond that will pay him back \(\textrm{₹}1000\) at the end of \(10\) years, giving him a yield of \(10\%\) p.a.