In this paper, the principal growth equation for continuous compounding interest is derived from an ordinary differential equation, offering a new perspective for the derivation of the equation.

Based on the returns of portfolio investment caculated by continuous compound interest,we study the decision making model for portfolio investment under E V risk and come up with a method for caculating optimal investment proportional coefficient.

We develop the conception of simple interest,compound interest and continuous compound interest,and prove that the continuous compound interest is maximum and the simple interest is minimum,real rate of interest is more than nominal interest rate,further,the range and quality of the continuous compound interest are developed.

The research on continuously compounded interest and time value of money;

According to deduction of the geometric sequence of continuously compounded interest\'s formula,compared with the difference of interrupted compound interest and continuously compounded interest,continual cash flow to the time value of money influence in the sequence of geometric conditions is explored.