A technique which is used to convert an interest rate of a given period into an interest rate of a longer period. For example, an investor may need to imply an annual rate from a quarterly rate or semiannual rate. The compounding formula is:

Rate = (1+i/n)ⁿ – 1

where: i is the interest rate being compounded, n is the number of periods by which the original rate is being expanded.

Suppose an investor wants to convert a quarterly rate of 5% to an annual rate. The number of periods needed to make the shift is 4 (as a year = 4 quarters), as such the annual rate is:

Annual rate = (1+ 0.05/4)⁴ – 1 = 5.09%

In this sense, the difference between the annual rate and the quarterly rate is 0.09% or 9 basis points.