# Forward rate

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The **forward rate** is the future yield on a bond. It is calculated using the yield curve. For example, the yield on a three-month Treasury bill six months from now is a *forward rate*.^{[1]}

## Forward rate calculation[edit]

To extract the forward rate, we need the zero-coupon yield curve.

We are trying to find the future interest rate for time period , and expressed in **years**, given the rate for time period and rate for time period . To do this, we use the property that the proceeds from investing at rate for time period and then **reinvesting** those proceeds at rate for time period is equal to the proceeds from investing at rate for time period .

depends on the rate calculation mode (**simple**, **yearly compounded** or **continuously compounded**), which yields three different results.

Mathematically it reads as follows:

### Simple rate[edit]

Solving for yields:

Thus

The discount factor formula for period (0, t) expressed in years, and rate for this period being , the forward rate can be expressed in terms of discount factors:

### Yearly compounded rate[edit]

Solving for yields :

The discount factor formula for period (0,*t*) expressed in years, and rate for this period being , the forward rate can be expressed in terms of discount factors:

### Continuously compounded rate[edit]

**EQUATION→**

Solving for yields:

**STEP 1→**

**STEP 2→**

**STEP 3→**

**STEP 4→**

**STEP 5→**

The discount factor formula for period (0,*t*) expressed in years, and rate for this period being , the forward rate can be expressed in terms of discount factors:

is the forward rate between time and time ,

is the zero-coupon yield for the time period , (*k* = 1,2).

## Related instruments[edit]

## See also[edit]

## References[edit]

**^**Fabozzi, Vamsi.K (2012),*The Handbook of Fixed Income Securities*(Seventh ed.), New York: kvrv, p. 148, ISBN 0-07-144099-2.