Calculate zero-coupon spot rates, implied forward rates or the present value of a single cash flow. Choose the rate compounding convention explicitly.

Use amounts in the same currency.

Semiannual is the initial convention. Rates are annualized.

Related Calculators

Spot Price (Present Value) Formula

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

S = (F) / ((1 + (r) / (m))m t) ; [4pt] S = F e - rt

Variables:

  • S is the spot price (present value today)
  • F is the single future cash flow at maturity
  • r is the annualized spot discount 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” 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). Choose Zero-coupon spot rate for the annualized yield of a single cash flow, Present value to discount that cash flow, or Implied forward rate for a curve-consistent future-period rate. An implied forward rate is not a guaranteed forecast; a bond yield is not necessarily risk-free.

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 single future cash flow at maturity (F).
  2. Next, determine the annualized spot discount rate (r) as a decimal in the formula, or as a percentage in the calculator.
  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 cash flow (F) = 100

spot discount rate (r) = 0.05 (enter 5% in the calculator)

time to maturity (t) = 2

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