What is Zero Coupon Bond?
A zero-coupon bond pays no periodic interest: it is issued (or purchased) at a deep discount to face value and returns the full face value at maturity. The return comes entirely from this accretion to par. US Treasury STRIPS are the most well-known zero-coupon instruments. Zero-coupon bonds have the longest possible duration for a given maturity (duration = maturity exactly) and are therefore the most price-sensitive to interest rate changes. They are popular for liability-matching in pension funds and for tax-advantaged growth in education savings accounts. The implied yield from price to par is the effective annualised return.
Formula
Price = Face Value / (1 + r)^n
Implied Yield = (Face Value / Price)^(1/n) − 1
r = required yield (as a decimal)
n = years to maturity
Face Value = par value at redemption
Calculator
How to Use
- 1To price from yield: Enter face value, required yield, and years to maturity. Price = F / (1+r)^n.
- 2To find implied yield: Enter the purchase price and face value. Yield = (F/P)^(1/n) − 1.
- 3Compare to coupon bonds: The zero-coupon price is always a discount to par; the larger the discount or longer the maturity, the higher the implied yield.
- 4Duration note: Duration = maturity for zero-coupon bonds, making them the most rate-sensitive bond type. A 10-year zero has 10-year duration; a 10-year 5%-coupon bond has ~8-year duration.
Worked Example
Example: 10-year zero-coupon Treasury STRIP
Face Value
$1,000
Required Yield
4.5%
Years
10
Price = $1,000 / (1.045)^10 = $643.93. Pay $643.93 today, receive $1,000 in 10 years, a $356 gain representing 4.5% annualised return. No coupon reinvestment risk. Fully price-sensitive: if rates rise to 5.5%, price falls to $585.43, a 9.1% loss from a 1% rate move (confirming duration ≈ 10).