Enter the future price (or forward/futures price at maturity), the risk-free rate, and the time to maturity into the calculator to determine the spot price (present value). This calculator can also solve for any of the variables (including the implied annualized “spot”/risk‑free rate) when the others are known.

Spot Rate Calculator

Find the yield on a zero-coupon bond, or an implied forward rate.

Zero-Coupon Yield
Forward Rate
Enter a price greater than 0.
Enter a face value greater than 0.
Enter years greater than 0.

Related Calculators

Spot Price (Present Value) Formula

The following formulas are used to relate a spot price (today) to a future/forward price (at maturity) using a constant annualized rate.

S = \frac{F}{\left(1+\frac{r}{m}\right)^{m t}}
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S = F e^{-rt}

Variables:

  • S is the spot price (present value today)
  • F is the future/forward price at maturity
  • r is the annualized risk-free rate (decimal)
  • t is the time to maturity (in years)
  • m is the number of compounding periods per year (discrete compounding only)

To calculate the spot price, discount the future price back to today using the chosen compounding method. If you instead know the spot price and the future price, you can rearrange the same relationship to solve for the implied annualized rate (often called a “spot” or “risk‑free” rate for that maturity).

What is a Spot Rate?

The meaning of “spot” depends on the market context. A spot price is the current market price for immediate delivery and payment. In foreign exchange, the term spot rate commonly means the spot exchange rate (also a price). In fixed‑income markets, a spot rate (often called a zero rate) is the annualized yield for a specific maturity implied by a single cash flow (for example, a zero‑coupon bond). This page’s calculator primarily relates a spot price to a future/forward price using a rate; the “Zero‑Coupon / Bond” tab is appropriate when you want the yield/spot rate for a single cash flow.

How to Calculate Spot Price (Present Value)?

The following steps outline how to calculate the spot price (present value) from a future price.

  1. First, determine the future/forward price at maturity (F).
  2. Next, determine the annualized risk‑free rate (r) as a decimal.
  3. Next, determine the time to maturity (t) in years.
  4. Next, choose a compounding convention and use the appropriate formula from above (for example, with annual compounding: S = F / (1 + r)^t).
  5. Finally, calculate the spot price (S).
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

future price of the asset (F) = 100

risk-free rate (r) = 0.05

time to maturity (t) = 2

Using annual compounding, the spot price is: S = 100 / (1.05)2 = 90.7029.