Continuous Compounding Worksheet
This worksheet focuses on understanding and applying the continuous compounding formula for financial calculations, suitable for Grade 11 students.
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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 , an irrational number approximately equal to 2.71828.
3. When interest is compounded continuously, it means that the interest is calculated and added to the principal an number of times per year.
1. What does 'r' represent in the continuous compounding formula?
Rate of return
Annual interest rate
Real interest
Risk factor
2. If you invest $1000 at an annual interest rate of 5% compounded continuously, how would you set up the formula to find the amount after 1 year?
A = 1000(1 + 0.05)^1
A = 1000 * e^(0.05 * 1)
A = 1000 * (0.05 * 1)
A = 1000 / e^(0.05 * 1)
1. You invest $5,000 in an account that pays 3.5% annual interest compounded continuously. What will be the value of your investment after 7 years?
2. An initial investment of $12,000 is made into an account with an annual interest rate of 6% compounded continuously. How much interest would be earned after 10 years?
1. Continuous compounding yields less interest than daily compounding over the same period.
True
False
2. The value of 'e' is exactly 2.71828.
True
False