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Spot Rate Calculator

Enter the face value, current price, and years to maturity.

How it is calculated

A zero-coupon bond pays one amount, its face value, at maturity, so the annual compounded return is found by taking a root: spot = (face ÷ price)1/years − 1. The total return over the whole holding period is face ÷ price − 1. face is the redemption amount, price is what you pay today (same currency), and years is the time to maturity in years, fractions allowed (0.5 for six months). The spot rate is shown to four decimals and the total return to two. Price and years must be above zero. Annual compounding is assumed; a quoted bond yield on a semi-annual basis would be different. Taxes, fees and reinvestment are ignored.

Worked example

A zero-coupon bond has a face value of 1,000, costs 820 today and matures in 5 years. Step 1: face ÷ price = 1,000 ÷ 820 = 1.2195. Step 2: total return = 1.2195 − 1 = 21.95%. Step 3: take the fifth root, 1.21950.2 = 1.040488. Step 4: subtract 1, so the annual spot rate is 4.0488%. That is why the spot rate (4.05% a year) is far lower than 21.95 ÷ 5 = 4.39%: compounding does part of the work.

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Common mistakes

  • Dividing the total return by the years. 21.95% over 5 years is 4.05% a year compounded, not 4.39%, so the simple average overstates the rate.
  • Entering the price as a percentage of par (82) while the face value is 1,000. Both must be in the same unit: either 820 and 1,000, or 82 and 100.
  • Using the tool for a coupon-paying bond. Coupons change the cash flows, so this formula gives the wrong yield; it applies to zero-coupon or stripped bonds.
  • Entering months as years. Eighteen months is 1.5, not 18.
  • Comparing the result with a bond yield quoted on a semi-annual basis without converting. This tool compounds once a year.

Sources

About this calculator

A spot rate is the annualized yield implied by a single zero-coupon bond — a bond with no periodic interest payments that simply pays its face value at maturity, purchased today at a discount. Because there are no coupons to complicate the cash flow, the spot rate solves directly from (Face Value ÷ Current Price)^(1/n) − 1, where n is the number of years to maturity, giving the compound annual growth rate an investor earns by holding to maturity.

Spot rates for different maturities are the building blocks fixed-income analysts use to construct a yield curve — a process called bootstrapping, where spot rates derived from zero-coupon (or stripped) Treasury securities at each maturity are used to discount and price coupon-bearing bonds correctly. From a bond's face value, today's price and the years left to maturity it derives the annualized spot rate and the total return over the holding period.

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  • Editorial team

    The rate here compounds once a year. To compare it with a bond quoted on a semi-annual basis, convert it: take the square root of one plus the rate, subtract one and double it. The preset 5.5667% annual becomes about 5.49% on a semi-annual basis, so the two are close but not identical. Which quoting convention do your bond screens use, annual or semi-annual?

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