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Zero Coupon Bond Calculator

A bond that pays nothing until it matures, priced as a single discounted payment. With no coupons to reinvest, the quoted yield is the return you actually get.

Also called: deep discount bond calculator, zero coupon price.

$
%
Price today
$747.26

$747.26 today for 1,000 in 5 years at 6%. The $252.74 of gain is the entire return, since there are no coupons at all.

Total gain
$252.74
Total return
33.82%
Discount factor
0.75
Value at the halfway point
$864.44
How this is calculated

An estimate, not an offer or a guarantee. Projected returns assume the rate you entered holds for the whole term, which no market does.

Method and background

This is what the calculation gives for the numbers you entered. It is an estimate, not advice, and it knows nothing about your situation beyond those numbers. Rules for United States change on a published schedule; the effective date is shown on every rule-based tool.

How this is calculated

One payment, discounted once. Because there are no interim coupons there is nothing to reinvest, so the reinvestment assumption that muddies ordinary yield to maturity simply does not arise. That also makes a zero the most rate-sensitive bond of its maturity: all of its value sits at the far end.

price = face value / (1 + yield) ^ years
F
Amount at maturity (currency)
y
Annual yield (decimal)
n
Years (years)

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

five years at six percent

Amount at maturity
$1,000.00
Years to maturity
5
Required yield
6%

Price today$747.26

1000 / 1.06^5, computed independently

Open this example

a zero yield means no discount at all

Amount at maturity
$1,000.00
Years to maturity
5
Required yield
0%

Price today$1,000.00

degenerate case

Open this example

doubling the term more than doubles the discount

Amount at maturity
$1,000.00
Years to maturity
10
Required yield
6%

Price today$558.39

boundary: compounding makes the relationship convex, not linear

Open this example

Method and limits

What it assumes

  • Annual compounding of the quoted yield.

What it deliberately does not model

  • In many markets the annual accretion is taxable each year even though no cash arrives, which this does not model.

Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator

Frequently asked questions

Why is a zero more volatile than a coupon bond?
Because none of the money comes back early. Its duration equals its maturity, which is the longest a bond of that term can be.