Continuously Compounded Interest Worksheet
This worksheet provides exercises on calculating continuously compounded interest for Grade 10 students.
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Continuously Compounded Interest
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Read each question carefully and show all your work. Use the formula for continuously compounded interest: 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 continuously compounded interest is A = .
2. In the formula A = Pe^(rt), 'e' represents , which is approximately .
3. The 'r' in the formula must be expressed as a .
1. If you invest $5,000 at an annual interest rate of 3.5% compounded continuously, how much will you have after 7 years? Round your answer to two decimal places.
2. An initial investment of $10,000 grows to $14,000 in 5 years with continuous compounding. What is the annual interest rate? Express your answer as a percentage rounded to two decimal places.
1. Which of the following represents the approximate value of Euler's number 'e'?
3.14159
2.71828
1.61803
0.57721
2. If the interest rate is 6% per year, what value should be used for 'r' in the continuously compounded interest formula?
6
0.6
0.06
60
1. Continuous compounding yields a smaller amount than daily compounding over the same period.
True
False
2. The variable 't' in the continuously compounded interest formula represents the time in months.
True
False
1. You want to have $25,000 in 10 years. If you can invest money at an annual interest rate of 4% compounded continuously, how much money should you invest today to reach your goal? Round your answer to two decimal places.
2. Compare the final amount of an investment of $8,000 for 6 years at an annual interest rate of 5% compounded continuously versus compounded annually. Explain the difference.