Continuous Compounding Worksheet
This worksheet helps Grade 9 students understand and apply the continuous compounding formula in financial calculations.
Includes
Standards
Continuous Compounding
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Read each question carefully and show all your work. Use the continuous compounding formula A = Pe^(rt) where A is the amount, P is the principal, e is Euler's number (approximately 2.71828), r is the annual interest rate (as a decimal), and t is the time in years.
1. The formula for continuous compounding is A = .
2. In the continuous compounding formula, 'e' represents , which is approximately .
3. The variable 'r' in the formula stands for the annual and must be expressed as a .
4. If you invest $500 at an annual interest rate of 4% compounded continuously, how much will you have after 3 years? Round your answer to two decimal places.
5. A sum of $1,200 is invested at a 5.5% annual interest rate compounded continuously. What will the investment be worth after 7 years? Round your answer to two decimal places.
6. Which of the following is the correct formula for continuous compounding?
A = P(1 + r/n)^(nt)
A = P(1 + rt)
A = Pe^(rt)
A = P + Prt
7. Continuous compounding yields less interest than daily compounding.
True
False
8. The value of 'e' is exactly 2.71828.
True
False
9. How long will it take for an investment of $1,000 to double if it is compounded continuously at an annual interest rate of 6%? Round your answer to two decimal places.
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