Calculate Future Value of an Investment with Continuously Compounded Interest – Formula and Explanation

A(t)=Pe^rt

continuous compound interest formula

The given expression is the formula for calculating the future value of a principal investment (P) with continuously compounded interest rate (r) over a certain time period (t). Below are some detailed explanations about the terms in the expression:

– A(t): It represents the future value or total amount of the investment after t years.

– P: This is the principal or initial investment amount.

– e: This is a mathematical constant equal to approximately 2.71828.

– r: This is the rate of interest applied to the investment, expressed as a decimal. In the context of continuously compounded interest, it is the annual interest rate that is applied infinitely many times throughout the year. For example, if the annual interest rate is 5%, then the continuously compounded rate would be ln(1+0.05) = 0.0488, where ln is the natural logarithm function.

– t: This is the time period in years over which the investment earns interest.

To use this formula, simply substitute the values of P, r, and t into it and then evaluate e^rt using a calculator. The resulting value will be the future value of the investment after t years, assuming no additional contributions or withdrawals are made. It is important to note that this formula assumes that the interest rate remains constant throughout the entire investment period, which may not be the case in reality.

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