Continuously Compounded Interest Worksheet
Explore continuously compounded interest with this Grade 11 math worksheet, featuring calculations and conceptual understanding.
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Continuously Compounded Interest
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit. Round all monetary answers to two decimal places.
1. The formula for continuously compounded interest is A = P * e^(rt), where 'e' represents , 'P' is the , 'r' is the annual interest rate, and 't' is the time in .
2. Continuously compounded interest is the theoretical limit of compounded interest as the compounding frequency approaches .
3. Which of the following best describes the constant 'e' in the continuously compounded interest formula?
The interest rate
The principal amount
Euler's number, approximately 2.718
The number of compounding periods
4. If you invest $1,000 at an annual interest rate of 5% compounded continuously, what will be the approximate value of your investment after 1 year?
$1,050.00
$1,051.27
$1,052.50
$1,055.00
5. You deposit $5,000 into an account that pays 3.5% annual interest compounded continuously. What will be the balance in the account after 7 years?
6. How long will it take for an investment of $2,000 to double if it is compounded continuously at an annual interest rate of 6%? (Hint: Use natural logarithms)
7. Continuously compounded interest always yields a higher return than interest compounded annually, semi-annually, or quarterly, given the same principal, rate, and time.
True
False
8. The value of 'e' is a rational number.
True
False
9. Compare and contrast continuously compounded interest with interest compounded daily. In what scenarios might one be preferred over the other?