Bond price, yield and duration calculator
Price a bond from its yield or find the yield from its price, with duration, convexity and how much the price moves when yields change.
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How this is calculated
The bond is valued on a coupon date, so there is no accrued interest and the price is the clean price. With n coupon periods, a coupon c each period, face value F and yield y per period (the annual yield divided by the coupons a year):
price = c ÷ (1 + y) + c ÷ (1 + y)² + … + (c + F) ÷ (1 + y)ⁿ
Finding the yield from a price reverses that sum; the calculator searches for the yield that reproduces the price to within a tiny fraction of a cent.
Macaulay duration is the average time to the bond's cash flows, each weighted by its present value. Modified duration (Macaulay ÷ (1 + y)) is the approximate percentage fall in price for a one-percentage-point rise in yield. Because the price–yield curve is curved, duration alone overstates falls and understates rises for large moves; adding convexity (½ × convexity × Δy²) corrects most of that. DV01 is the price change for a 0.01 percentage point move in yield.
Real bonds settle between coupon dates, may be callable or inflation-linked, and trade on yields quoted with market-specific conventions, so a broker's or the issuer's figures can differ slightly.