Bond Price Calculator: Price, Yield & Duration

Why bond prices move opposite to interest rates

A bond's fixed coupon rate is set when it's issued, but market interest rates move over time. When market rates rise above a bond's coupon rate, the bond becomes less attractive relative to newer bonds paying more, so its price falls below face value (trading 'at a discount') to compensate buyers. When market rates fall below the coupon rate, the bond becomes more attractive and trades above face value ('at a premium').

This inverse relationship is one of the most fundamental concepts in bond investing — it's why bond prices and interest rates are often described as moving in opposite directions.

By Suhaib Hassan · Formula verified 27 Sep 2026 · How CalculatePilot verifies formulas →

What this price represents

This calculator computes fair value using present value math — discounting all future coupon payments and the final face value repayment back to today's dollars using the current market rate. This is the standard approach used throughout fixed-income valuation.

Price = C × [1 − (1 + y)^−n] ÷ y + F ÷ (1 + y)^n — C = coupon per period · y = market yield per period · n = number of periods · F = face value

Real-world bond prices can differ slightly from this theoretical fair value due to factors like credit risk (perceived risk of default), liquidity, and specific market supply and demand — this calculator provides the baseline valuation these real-world factors adjust from.

Not for savings bonds

This calculator prices bonds that trade on the market, using a market yield. U.S. savings bonds (Series EE and I) are not priced that way: they cannot be bought or sold between investors, and their value comes from the issue date, series and interest rules. To value one, use the official TreasuryDirect savings bond calculator, or read how EE and I bond values work.

Worked example: pricing a 10-year 5% bond at a 6% yield

Take a $1,000 bond with a 5% coupon, 10 years to maturity and semi-annual payments, when the market yield is 6%. That gives 20 periods, a $25 coupon each period and a 3% yield per period.

Step	Calculation	Result
PV of the 20 coupons	$25 × [1 − 1.03−20] ÷ 0.03	$371.94
PV of the $1,000 face value	$1,000 ÷ 1.0320	$553.68
Bond price	$371.94 + $553.68	$925.61 (92.56% of par)
Current yield	$50 ÷ $925.61	5.40%
Macaulay / modified duration	weighted average time to cash flows	7.89 / 7.67 years

The price is below $1,000 because the 6% market yield is higher than the 5% coupon, so the bond trades at a discount.

Price at different yields (5% coupon, 10 years, semi-annual)

Market yield	Price per $1,000	Trades at	Current yield
3%	$1,171.69	Premium	4.27%
4%	$1,081.76	Premium	4.62%
5%	$1,000.00	Par	5.00%
6%	$925.61	Discount	5.40%
7%	$857.88	Discount	5.83%

Each full percentage point of yield moves this bond’s price by roughly 7–8%. The move is not symmetrical: a 1-point fall from 6% to 5% adds $74.39, while a 1-point rise to 7% takes away $67.73. That asymmetry is convexity.

How the price pulls toward par as maturity approaches

For the same 5% bond priced at a constant 6% yield, the discount shrinks as time passes:

Time to maturity	Price per $1,000
10 years	$925.61
5 years	$957.35
2 years	$981.41
1 year	$990.43
6 months	$995.15

At maturity the holder receives exactly the face value, so any premium or discount fades to zero.

Pricing a zero-coupon bond

A zero-coupon bond pays nothing until maturity, so its price is just the discounted face value: Price = F ÷ (1 + y/m)ⁿ. A $1,000 zero maturing in 10 years at a 4% yield with semi-annual compounding costs $1,000 ÷ 1.02²⁰ = $672.97. Annual compounding gives $675.56. Set the coupon rate to 0% in the calculator to see this.

Does coupon frequency change the price?

Slightly. For a 6% coupon, 10-year bond priced at a 5% yield, more frequent payments mean cash arrives sooner:

Coupon frequency	Price per $1,000
Annual	$1,077.22
Semi-annual	$1,077.95
Quarterly	$1,078.32

Duration by maturity

Duration grows with maturity and falls with higher coupons. For bonds with a 4.5% coupon priced at par with a 4.5% yield and semi-annual payments:

Bond	Macaulay duration	Modified duration
2-year	1.93	1.89
5-year	4.53	4.43
10-year	8.16	7.98
30-year	16.74	16.37
10-year zero-coupon (4.5% yield)	10.00	9.78

Using modified duration, the estimated price change is about −modified duration × yield change. For the 5% bond at 6%, a 1-point rise is estimated at −7.67%, and the actual move is −7.32% (to $857.88) because convexity softens the fall.

Clean price, accrued interest and dirty price

This calculator shows the clean price on a coupon date. Between coupon dates, a buyer also pays the seller accrued interest, and the total is the dirty (invoice) price. Accrued interest = coupon × days since the last coupon ÷ days in the coupon period. For a $25 semi-annual coupon, 60 days into a 182-day period: $25 × 60 ÷ 182 = $8.24. Quoted prices are normally clean prices.

Tax-equivalent yield for municipal bonds

Municipal interest is federally tax-exempt, so compare it with taxable bonds using: tax-equivalent yield = tax-free yield ÷ (1 − tax rate). A 3.5% municipal yield equals 4.61% taxable for someone in the 24% bracket and 5.38% in the 35% bracket.

Frequently asked questions

Why would a bond trade below its face value?expand_more

When current market interest rates are higher than the bond's fixed coupon rate, the bond becomes less attractive compared to newer bonds, so its price falls below face value to compensate buyers with a better effective return.

What happens to a bond's price at maturity?expand_more

A bond's price converges to its face value as it approaches maturity, since at maturity the holder receives exactly the face value back — any premium or discount gradually shrinks to zero over the bond's remaining life.

How do I calculate the price of a bond?expand_more

Discount every future cash flow at the market yield per period and add them up: price = coupon × [1 − (1 + y)^−n] ÷ y + face value ÷ (1 + y)^n. For a $1,000, 5% bond with 10 years left and a 6% yield (semi-annual), that is $925.61.

What is the difference between clean price and dirty price?expand_more

The clean price excludes accrued interest and is the price usually quoted. The dirty price is the clean price plus the interest accrued since the last coupon date, and it is what the buyer actually pays.

How do I price a zero-coupon bond?expand_more

Discount the face value only: price = face value ÷ (1 + y/m)^n. A $1,000 zero maturing in 10 years at a 4% yield with semi-annual compounding is about $672.97.

What does modified duration tell me?expand_more

It estimates the percentage price change for a one-percentage-point change in yield. A modified duration of 7.67 means the price falls roughly 7.67% if yields rise 1 point, ignoring convexity.

What is a tax-equivalent yield?expand_more

It is the taxable yield that would leave you with the same after-tax return as a tax-exempt bond: tax-free yield ÷ (1 − tax rate). A 3.5% municipal yield equals about 4.61% taxable at a 24% bracket.