Calculate bond prices from yield, coupon rate, face value, and maturity with duration and convexity analysis.
Enter a bond's face value, coupon rate, yield to maturity, years to maturity, and payment frequency, and the calculator discounts each coupon payment plus the final redemption back to today at the periodic yield, then reports Macaulay duration, modified duration, and convexity alongside the price. The result that surprises people most: price and yield move in opposite directions, so raising the yield input lowers the computed price, and any bond whose coupon rate sits below the entered yield will always price under face value, never at or above it.
A concrete input and expected output from the current implementation.
Input
Face value $1,000; annual coupon rate 5%, paid semiannually ($25 every 6 months); yield to maturity 6% annual, compounded semiannually; 2 years to maturity (4 periods).
Expected output
Price approximately $981.41 (a discount to face value).
Each $25 coupon and the final $1,000 redemption are discounted at 3% per semiannual period across 4 periods; the discounted cash flows sum to about $981.41. Because the 6% yield exceeds the 5% coupon rate, the bond prices below its $1,000 face value.
The bond is split into its periodic coupon payments (face value times coupon rate, divided by payments per year) plus a single final face-value redemption. Each cash flow is discounted back to today using the periodic yield (annual yield to maturity divided by the compounding frequency) raised to the power of the number of periods remaining, and the discounted amounts are summed to get the price.
Macaulay duration is the present-value-weighted average time to each cash flow; modified duration divides that by (1 + periodic yield) to approximate the percent price change for a 1 percentage-point yield move. Convexity measures the curvature that a linear duration estimate misses, refining the price-change approximation for larger yield swings.
Because the yield to maturity entered is higher than the coupon rate. When yield exceeds the coupon rate the bond prices below face value (a discount); when yield is lower than the coupon it prices above face value (a premium); the two match only when coupon rate equals yield.
Not clearly - the underlying formula prices as of a coupon date with a whole number of periods left, which is a clean price. If you're checking this against a broker's dirty-price quote for a mid-period settlement, verify separately whether accrued interest needs to be added on top.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
Calculate gross, operating, and net profit margins from cost and revenue with breakeven analysis.
Convert between annual salary and hourly rate with adjustments for work hours, overtime, and benefits.
Calculate sales tax amounts, tax-inclusive and tax-exclusive prices for any tax rate or jurisdiction.
Calculate return on investment from initial cost and final value with annualized ROI and comparison tables.
Convert between markup and margin percentages, calculate selling price, and compare pricing strategies.
Convert numeric amounts to written words for invoices, checks, and legal documents in multiple currencies.