Exponentials: Compounded Continuously

Exponentials

Compounded Continuously

One other type of compound interest is when interest is compounded continuously. This formula involves the constant e and has the form A = Pe^rt , where all variables mean the same as in the previous application.

Application 7 You invest $500 in a stock that compounds continuously at a rate of 2.5%. Write an equation to model this situation.

Step 1. Determine P. The initial amount invested is $500.

P = 500

Step 2. Determine r. The interest rate is 2.5%.

r = 0.025

Step 3. Write the equation.

A = Pe^rt

A = 500e^0.025t