Centre for Distance Learning and Innovation

Investigation 8: Continuous Interest and the Function y = ex

The number e can be calculated as .
= 2. 718 28. Thus, this is the value of the number e.
e is a constant value. It is not a variable.
To find the value of an investment, after one year, with n compounding periods, use the formula .
= e.
Similarly, as n increases, the value of the expression approaches .
Thus, the formula can be used to find the value of an investment, after one year, with continuous interest.
To find the value of an investment, with continuous interest, after t years, use the formula .
Be sure you know when to use each formula. One is associated with compound interest, and the other with continuous interest.