Zero Coupon Bond Value Calculator

The formula

Present value = face value ÷ (1 + yield)ⁿ

There are no coupons, so there is only one cash flow to discount: the face value at maturity. At 5% over 10 years, (1.05)¹⁰ = 1.6289, and 1,000 ÷ 1.6289 = 613.91.

Worked examples

$1,000 at 5% for 10 years → $613.91
$1,000 at 5% for 5 years → $783.53
$1,000 at 5% for 20 years → $376.89
$1,000 at 8% for 10 years → $463.19
$1,000 at 3% for 10 years → $744.09
$5,000 at 5% for 10 years → $3,069.57

Why the discount is so deep

Compounding runs the whole way to maturity with nothing paid in between. A 5% bond paying coupons returns cash along the way, which reduces its sensitivity to the discount rate; a zero has all its value concentrated at the end, so every year of discounting bites the full amount. That is why zeros are far more price-sensitive than coupon bonds of the same maturity.

The relationship is not linear. Doubling the term from 10 to 20 years at 5% does not halve the price — it takes $613.91 down to $376.89, a 39% fall. Moving the yield from 5% to 8% over ten years takes the price from $613.91 to $463.19. Small changes in either input move the value a great deal.

The tax wrinkle, and the use case

In the United States, the annual accretion on a zero-coupon bond is taxable as interest income even though no cash is received — the imputed interest rule. Held in a taxable account, that means paying tax on money you have not been given. Zeros are therefore usually held in tax-advantaged accounts, or bought in a jurisdiction where the treatment differs.

Their main appeal is certainty: if you hold to maturity, you know the exact amount and date, which makes them useful for matching a future liability such as a tuition bill or a known repayment. Municipal zeros can also deliver tax-free income at a known date, and stripped Treasuries serve the same purpose for institutions. The price risk only matters if you sell before maturity.

Frequently Asked Questions