Calculate Forward Rates – Cost Calculator | Online Quote & Profit Estimator

Forward Rate Calculator

Calculate future spot rates based on current spot rates and time to maturity. This is crucial for pricing futures contracts and understanding market expectations for future interest rates.

Current Spot Rate (Year 1):

Current Spot Rate (Year 2):

Result

Enter the current spot rates to see the calculated forward rate.

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Understanding Forward Rates

In finance, a forward rate represents the interest rate that is expected to prevail at some point in the future. It's essentially a prediction of what a future spot rate will be, based on current market conditions. Forward rates are derived from current spot rates (also known as zero-coupon yields) for different maturities.

The Relationship Between Spot and Forward Rates

The core principle is that investing for a longer period at a single rate should yield the same return as investing for shorter periods sequentially. For example, investing for two years should have the same outcome as investing for one year and then reinvesting for another year at the forward rate.

Let:

$ S_1 $ be the current spot rate for a 1-year maturity.
$ S_2 $ be the current spot rate for a 2-year maturity.
$ f_{1,2} $ be the forward rate for the period from year 1 to year 2.

The value of an investment of $1 at maturity 2 using the 2-year spot rate $ S_2 $ would be $ (1 + S_2)^2 $.

Alternatively, the value of that same $1 investment after 2 years, by investing for 1 year at $ S_1 $ and then reinvesting the proceeds for the second year at the forward rate $ f_{1,2} $, would be $ (1 + S_1) \times (1 + f_{1,2}) $.

Equating these two scenarios gives us:

$ (1 + S_2)^2 = (1 + S_1) \times (1 + f_{1,2}) $

To find the forward rate $ f_{1,2} $, we can rearrange the formula:

$ 1 + f_{1,2} = \frac{(1 + S_2)^2}{(1 + S_1)} $

And finally:

$ f_{1,2} = \frac{(1 + S_2)^2}{(1 + S_1)} – 1 $

Example Calculation

Suppose the current spot rate for a 1-year investment is 2.0% ($ S_1 = 0.02 $) and the current spot rate for a 2-year investment is 2.5% ($ S_2 = 0.025 $).

Using the formula:

$ 1 + S_1 = 1 + 0.02 = 1.02 $
$ (1 + S_2)^2 = (1 + 0.025)^2 = (1.025)^2 = 1.050625 $
$ 1 + f_{1,2} = \frac{1.050625}{1.02} \approx 1.0300245 $
$ f_{1,2} = 1.0300245 – 1 \approx 0.0300245 $

So, the forward rate from year 1 to year 2 is approximately 3.0025%. This implies that the market expects the 1-year interest rate to be 3.0025% one year from now.

Applications of Forward Rates

Forward rates are vital tools for:

Pricing Futures and Forwards: They are used to determine the fair price of financial contracts that settle at a future date.
Interest Rate Expectations: They provide insights into market participants' expectations about future interest rate movements.
Risk Management: Businesses and investors use them to hedge against potential interest rate volatility.
Investment Decisions: They help in making informed decisions about allocating capital across different maturities.