Continuous Compounding Worksheet

Continuous Compounding Worksheet

Read each question carefully and provide the best answer. Show all your work for calculations.

1. The formula for continuous compounding is A = P * e^(rt), where 'e' represents  .

2. When interest is compounded continuously, it means that the interest is calculated and added to the principal an   number of times per year.

3. The variable 'r' in the continuous compounding formula represents the   interest rate, expressed as a decimal.

4. Which of the following scenarios is best represented by the continuous compounding formula?

5. If you invest $1000 at an annual interest rate of 5% compounded continuously, what will be the approximate value of your investment after 1 year?

6. You invest $5000 in an account that pays 3% annual interest, compounded continuously. How much money will you have after 7 years? Round your answer to two decimal places.

7. An initial investment of $2000 grows to $3000 in 5 years with continuous compounding. What is the annual interest rate? Express your answer as a percentage rounded to two decimal places.

8. Continuous compounding yields a higher return than daily compounding for the same principal, interest rate, and time period.

9. The constant 'e' in the continuous compounding formula is approximately 3.14159.

10. You want to have $15,000 in 10 years. If you can invest money at an annual interest rate of 4.5% compounded continuously, how much money should you invest today?

11. Compare and contrast continuous compounding with annual compounding. Explain a scenario where one might be preferred over the other.