TradingCalcBond Price Calculator
TIME VALUE OF MONEY · FIXED INCOME
What is this bond worth at a given yield, and how far does the price move when yields do? Price, Macaulay and modified duration, convexity and DV01.
Coupons paid
The price is on a coupon date, without accrued interest. The yield is the nominal yearly yield compounded as often as the coupons are paid, the bond-market convention. A zero coupon rate is a zero-coupon bond.
Bond price
$957.35
95.7349% of face value, at a discount to par
Macaulay duration
4.4717 years
Modified duration
4.3414 years
Convexity
22.3047
DV01
$0.42
Current yield
5.2228%
Coupon each period
$25.00
PV of coupons
$213.26
PV of face value
$744.09
10 coupons of 25.00, then 1,000.00 back. If the yield rises one basis point (0.01%), the price falls about $0.42; a 1% rise costs about 4.3414% of the price before convexity softens it.
How to use the bond price calculator
- Enter the face value, the years to maturity and the annual coupon rate.
- Enter the yield to maturity you want the bond priced at.
- Pick how often the coupons are paid (semiannual is common for US bonds).
- Read the price, the two durations, the convexity and the DV01.
Bond price, duration and convexity formulas
- Price = sum of CF_k / (1 + y)^k, y = yield / coupons per year
- Macaulay = (1 / m) x sum(k x CF_k / (1 + y)^k) / Price
- Modified = Macaulay / (1 + y)
- Convexity = (1 / m^2) x sum(k (k + 1) x CF_k / (1 + y)^k) / (Price x (1 + y)^2)
- DV01 = Modified x Price x 0.0001
Worked example: a 10-year zero-coupon bond at 5%
- Price = 1,000 / 1.05^10 = 613.91
- Macaulay duration = 10 years (one cash flow, at maturity)
- Modified duration = 10 / 1.05 = 9.5238
- DV01 = 9.5238 x 613.91 x 0.0001 = 0.5847
A rise of one basis point in the yield cuts the price by about 0.58. The estimate is the slope at the current yield; a large move differs by the convexity term.
Where to go next
Discount any other stream of payments with the Present Value Calculator, or find the rate behind a list of cash flows with the IRR Calculator.
Planning a leveraged trade? Check position size, liquidation distance and funding cost before you open it:
Run Pre-Trade Risk CheckUse via API or MCP
The same calculation is available as the MCP tool workflow.run_bond_price: a script or an AI agent gets the exact number with the formula published, instead of a model doing the arithmetic in its head.
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How is a bond priced?
A bond is worth its future cash flows discounted at the yield: every coupon plus the face value at maturity, each divided by (1 + yield per period) to the power of its period. A 10% annual bond with 3 years left and a 10% yield is worth exactly its face value, 1,000.
What is Macaulay duration?
The weighted average time until the bond pays its cash flows, in years, with each flow weighted by its present value. A zero-coupon bond has a duration equal to its maturity; the 3-year 10% bond above has 2.7355 years.
What is modified duration?
Macaulay duration divided by (1 + yield per period). It is the percent the price falls for a 1% rise in yield, to a first approximation. A 10-year zero-coupon bond at a 5% yield has a modified duration of 9.5238.
What is convexity?
How much the duration itself changes as the yield moves. Duration alone overstates the loss when yields rise and understates the gain when they fall; convexity is the second-order correction, in years squared. The 10-year zero at 5% has a convexity of 99.77.
What is DV01?
The dollar value of one basis point: how much the price falls when the yield rises by 0.01%. It equals modified duration x price x 0.0001. A 5-year 5% semiannual bond at a 6% yield costs 957.35 and has a DV01 of 0.4156 per 1,000 of face value.
Why does the price fall when the yield rises?
The coupons are fixed. A higher yield discounts the same cash flows harder, so they are worth less today. A bond with a coupon below the yield sells at a discount to face value; above the yield, at a premium.
Is this the price I will see on a screen?
Only on a coupon date. This calculator gives the clean price with a whole number of coupon periods left. Between coupon dates a market quote adds accrued interest, uses a day-count convention, and may reflect credit risk or a call feature that the formula does not.