The price (present value) of a zero-coupon bond is determined by discounting the bond’s terminal payout by the bond’s yield to maturity. For example, the current price of a zero-coupon bond with a face value of $1,000, a yield to maturity of 10%, and a five-year maturity is:
$620.92 = $1,000/1.15
Zero-coupon bonds are illustrative of why, ceteris paribus (that is, holding all other factors constant), bonds that have longer maturities have greater price risk in relation to otherwise comparable bonds with shorter maturities. This result can be generalized to coupon bonds as well.
Suppose a zero-coupon bond has a face value of $1,000, a yield to maturity of 10%, and a six-year maturity. The price is: