Continuous Compounding Worksheet
Explore continuous compounding with formulas and real-world problems for Grade 10 math students.
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Continuous Compounding Worksheet
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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 .
3. When interest is compounded continuously, the number of compounding periods approaches .
1. You invest $5,000 in an account that pays 3% annual interest compounded continuously. What will be the balance after 7 years?
2. An amount of $10,000 is invested at an annual interest rate of 4.5% compounded continuously. How much interest will be earned after 10 years?
1. Which of the following is equivalent to continuously compounded interest?
Simple interest
Interest compounded annually
Interest compounded infinitely often
Interest compounded quarterly
2. If you invest $1,000 at an annual interest rate of 5% compounded continuously, approximately how much will you have after 1 year?
$1,050.00
$1,051.27
$1,051.00
$1,051.25
1. Continuous compounding yields less interest than daily compounding over the same period.
True
False
2. The 'e' in the continuous compounding formula is a variable that changes based on the interest rate.
True
False
1. How long will it take for an investment to double if it is compounded continuously at an annual interest rate of 6%?