what is continuous compounding 
continuous compounding is the mathematical limit that compound interest can reach if it s calculated and reinvested into an account s balance over a theoretically infinite number of periods while this is not possible in practice the concept of continuously compounded interest is important in finance it is an extreme case of compounding as most interest is compounded on a monthly quarterly or semiannual basis formula and calculation of continuous compoundinginstead of calculating interest on a finite number of periods such as yearly or monthly continuous compounding calculates interest assuming constant compounding over an infinite number of periods the formula for compound interest over finite periods of time takes into account four variables the formula for continuous compounding is derived from the formula for the future value of an interest bearing investment future value fv pv x 1 i n n x t calculating the limit of this formula as n approaches infinity per the definition of continuous compounding results in the formula for continuously compounded interest fv pv x e i x t where e is the mathematical constant approximated as 2 7183 