Updated for the 2026-2027 CFA® Level I curriculum.
A spot rate is the return on a zero-coupon investment for one specific maturity. Bond pricing with spot rates discounts each cash flow at the rate that matches its timing.
Quick Answer
The spot curve plots zero-coupon spot rates across maturities. To price a coupon bond, discount each promised cash flow using its maturity-specific spot rate and add the present values. This avoids forcing every cash flow to use one yield.
Key Takeaways
Each spot rate applies to one maturity.
The spot curve is the term structure of spot rates.
Match each cash flow with its own spot rate.
Keep compounding frequency consistent.
Include principal with the final coupon.
What You Need to Know for CFA Level I
Define a spot rate and spot curve.
Select the correct rate for each cash flow.
Calculate a price from annual or periodic spot rates.
Explain why spot pricing can differ from a single-YTM approach.
Par rates and forward-rate calculations are taught on the next note. Broader curve comparisons are covered separately.
What Is a Spot Rate?
A spot rate is the discount rate on a single payment at a specified future date. It can be inferred from zero-coupon securities or bootstrapped from coupon instruments.
What Is the Spot Curve?
The spot curve shows maturity on one axis and spot rate on the other. Its shape summarizes how zero-coupon discount rates vary across time.
How to Price a Bond Using Spot Rates
With annual compounding:
With m compounding periods per year, adapt the rate and period count consistently:
where:
= current bond price
= cash flow in period t
= spot rate matched to period t
= payments per year
= number of payment periods
Worked Spot-Rate Bond Price Example
A two-year annual-pay USD 1,000 bond has a 5% coupon. The one-year spot rate is 4% and the two-year spot rate is 5%.
How to Interpret the Result
The price is slightly above par because the early coupon is discounted at 4%, while the later cash flow is discounted at 5%. A single rate would not preserve this maturity-specific information.
Working Example
The first coupon has present value USD 48.08. The second coupon plus principal has present value USD 952.38. Their sum is USD 1,000.46.
The process is simple: map time, match the rate, discount, and sum.
Common Exam Traps
Discounting every coupon at one YTM when a spot curve is supplied. Use the spot rate matched to each cash-flow date and add the resulting present values.
Applying the two-year spot rate to the first-year coupon. The one-year payment uses the one-year spot rate; the second-year coupon and principal use the two-year spot rate.
Forgetting par in the final cash flow. At maturity, a standard coupon bond pays its last coupon plus face value; omitting face value produces a severe understatement of price.
Mixing annual and semiannual rates. Match each spot rate's compounding convention to the payment period before discounting cash flows.
Treating a par yield curve as a spot curve. Par yields are coupon rates that price bonds at par, while spot rates discount individual maturity-specific cash flows. Convert or bootstrap as needed rather than substituting one for the other.
Practice Question
A two-year annual-pay bond has a USD 1,000 par value and a 5% coupon. The one-year spot rate is 4% and the two-year spot rate is 5%. The bond price is closest to:
USD 952.38
USD 1,000.46
USD 1,050.00
Correct Answer: Option B
Discounting each cash flow at its maturity-matched spot rate gives .
Option A: This amount effectively omits or misvalues part of the bond’s coupon cash flow.
Option C: Adding one coupon to par without discounting both cash flows does not produce the bond’s present value.
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FAQs About Spot Rates, the Spot Curve, and Bond Pricing
What is a spot rate?
It is the zero-coupon discount rate for a specific maturity.
How do you price a bond using spot rates?
Discount each cash flow with the spot rate matching its maturity and add the present values.
What is the difference between a spot rate and YTM?
A spot rate applies to one maturity; YTM is one rate applied to all promised bond cash flows.