If $2,000 is invested for t years at 4% compounded continuously, the total amount is given by A(t) = 2000e.04t

Find A(10) 

The total amount after 10 years, $ A(10) $, is approximately \$2983.65.

Would you like more details or have any questions?

Here are 5 related questions you might want to explore:
1. What is the value of $ A(t) $ after 15 years?
2. How does the formula change for different interest rates?
3. What would the amount be if the initial investment was \$3,000 instead?
4. How do we calculate the amount for discrete compounding instead of continuous compounding?
5. What is the time $ t $ required for the investment to double?

**Tip**: Continuous compounding uses the formula $ A = P e^{rt} $, where $ P $ is the principal, $ r $ is the rate, and $ t $ is the time.

If $2,000 is invested for t years at 4% compounded continuously, the total amount is given by A(t) = 2000e^0.04t. Find A(10).

Discover how to calculate the total amount of a $2,000 investment after 10 years with 4% interest compounded continuously. Learn key concepts in exponential growth and the continuous compounding formula, suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation