from Spot Curve

You can derive the forward rate from a spot rate using this equation

If the spot curve is upward sloping the forward curve is above the spot curve
If the spot curve is downward sloping the forward curve is below the spot curve

Calculate from Spot Rates

Supposing that a bank assesses and quotes the following rates to a company, based on the annual spot yield curve for that company's risk class:

One-year: 3.50%
Two-year: 4.60%
Three-year: 5.40%
Four-year: 6.10%
Five-year: 6.30%

This indicates that the company would have to: pay interest at 3.50% if it wants to borrow a sum of money for one year; pay interest at 4.60% per year if it wants to borrow a sum of money for two years; pay interest at 5.40% per year if it wants borrow a sum of money for three years; and so on.

Alternatively, for a two-year loan, the company could opt to borrow a sum of money for only one year, at an interest rate of 3.50%, and then again for another year, commencing in one year's time, instead of borrowing the money for a total of two years.

Although the company would be uncertain about the interest rate in one year's time, it could request a forward rate from the bank that is fixed today - for example, through a 12v24 forward rate agreement (FRA). The question then arises: how may the value of the 12v24 FRA be determined?

A forward rate commencing in one year for a borrowed sum lasting a year can be calculated as follows:

In summary:

Supposing the company wants to borrow a sum of money for three years on the basis of the above rates:
i. it could pay annual interest at a rate of 5.40% in each of the three years, or
ii. it could pay interest at a rate 3.50% in the first year, 5.71% in the second year and 7.02% in the third year, or
iii. it could pay annual interest at a rate of 4.60% in each of the first two years and 7.02% in the third year.