Continuous compounding of interest is a method used to calculate the compound interest earned on a sum of money in a cascading manner, that is, with the interest being added on a continuous basis instead of periodically, typically quarterly or annually. By taking into account the effect of compounding, it allows investors to earn a compounding rate of return that is higher than the customary periodic interest paid by a financial institution.

Though puzzling at first, the concept of continuously compounded interest is important in finance as it provides a powerful tool to value financial securities such as bonds and annuities. The formula to compute continuously compounded interest takes into account four variables: the principal sum of the investment, the rate of return, the length of time of the investment, and both the interest rate and compounding frequency of the investment. Respectively, these four components of the equation can be shown as P, R, t and r, where P and t are the principal and length of investment, R is the overall Return on Investment (ROI), and r is the Nominal Effective Interest Rate (EIR).

As a general rule, money will grow faster the longer it is left on a continuously compounded basis, rather than the more traditional perodically compounded basis. For a given rate of return, a longer compounding period of continuous compounding will produce a higher return than that of a shorter, periodic compounding period. For instance, for an investment with a 10% nominal rate of return, the actual return with continuous compounding adjusted to an annual period would be 10.5%; as compared to 10.3% when using a quarterly compounding schedule, or 10.1% when using a monthly compounding schedule.

The concept of continuously compounded interest is a powerful tool to understand all types of investments, and to evaluate whether an investment is worth its face value or not. It is also useful to calculate the annuity factor, which is the amount of money an investor will need today in order to receive a given stream of payments in the future. By adjusting for the compounding rate, investors are able to adjust the annuity factor to better fit their investment goals.

At the same time, the concept of continuously compounded interest is a benchmark against which to compare other longer term investments, providing investors with an indication of the potential returns they can expect from an investment if all else remains constant. In this way, while continuously compounded interest is not possible in practice, it provides investors with the necessary information to have an informed investment decision.