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Bond Price Calculator

Find what a bond is worth today by discounting its coupons and face value.

How it is calculated

The price is the present value of all cash flows at the yield to maturity. With f payments a year, n = years × f, the coupon per period is C = face × coupon% ÷ f and the rate per period is i = YTM% ÷ f. Then price = C × (1 − (1 + i)−n) ÷ i + face ÷ (1 + i)n. If the yield is 0 the coupons are simply added. If the rate per period comes to −100% or lower (a yield of −200% or less on a semiannual bond), there is no result. An empty coupon counts as 0 (a zero-coupon bond), and an empty or non-positive frequency counts as 2, semiannual. Besides the price, the tool shows the coupon per period, the current yield (annual coupon ÷ price) and whether the bond is at a discount, premium or par. It assumes a whole number of periods remain, so no accrued interest is included.

Worked example

A bond with face value 1,000, a 5% coupon paid twice a year, 10 years to maturity and a yield to maturity of 6%. Payments: 10 × 2 = 20. Coupon per period: 1,000 × 5% ÷ 2 = $25.00. Rate per period: 6% ÷ 2 = 3%. Present value of the coupons: 25 × (1 − 1.03−20) ÷ 0.03 = 371.9. Present value of the face: 1,000 ÷ 1.0320 = 553.7. Price: $925.61, shown as a discount because the yield is above the coupon rate. Current yield: 50 ÷ 925.61 = 5.40%.

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Common mistakes

  • Confusing the yield shown in the result with the yield to maturity. It is the current yield, annual coupon divided by price, and ignores the gain or loss at maturity.
  • Entering the coupon rate or the yield as a decimal. Both fields take percentages, so 5 means 5%.
  • Leaving the payment frequency at its default for an annual bond. An empty frequency counts as 2, so a bond paying once a year needs 1 entered.
  • Expecting the price to include accrued interest. The tool prices the bond as if a coupon was just paid, so a price quoted between coupon dates will differ.
  • Mixing an annual yield with a monthly or quarterly coupon count. The yield is divided by the frequency you enter, so state both on the same annual basis.

Sources

About this calculator

This calculator finds the fair price of a bond by discounting its future cash flows: the price equals the present value of each coupon payment plus the present value of the face value repaid at maturity, all discounted at the yield to maturity (YTM). When YTM is above the coupon rate the bond trades below par (a discount); when it's below the coupon rate the bond trades above par (a premium).

Bond traders, portfolio managers, and finance students use this to price fixed-income securities, check whether a bond is over- or under-valued relative to current market yields, and understand how bond prices move inversely to interest rates.

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Comments (1)

  • Editorial team

    To feel how rate-sensitive a bond is, run it twice with yields one point apart. A 5 percent coupon, 10-year bond priced at 6 percent costs 925.61 per 1,000 face, but at 7 percent it falls to 857.88. Shorten the same bond to 2 years at 7 percent and the price is 963.27, so the longer the maturity, the harder a yield change bites. Which maturities are you comparing, and at what yields?

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