The compounding of interest earned or paid on an interest-bearing instrument (e.g., bond, deposit, etc), or generally any type of investment, four times per year. This refers to the process of determining the future or present value of a cash flow or a stream of cash flows when interest is earned or paid every three months. For example, an amount of $1,000 invested for one year at an annual rate of 5%, would grow annually, with semi-annual compounding, to:

At year-end, investment = initial investment x (1+ ¼ interest rate)⁴ = 1,000 x (1.0125)⁴ = 1,050.9

In other words, the semi-annually compounded interest that is earned will grow the investment to $1,050.9 at the end of the year.