Continuously Compounded Interest
A Grade 12 math worksheet on continuously compounded interest, covering formulas and application problems.
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Continuously Compounded Interest
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Read each question carefully and provide your answers using the formula for continuously compounded interest: A = Pe^(rt). Show all your work for full credit.
1. Which of the following represents the formula for continuously compounded interest?
A = P(1 + r/n)^(nt)
A = P + Prt
A = Pe^(rt)
A = P(1 + r)^t
2. What does the 'e' in the continuously compounded interest formula represent?
The interest rate
The principal amount
Euler's number (approximately 2.71828)
The time in years
3. Continuously compounded interest means that interest is calculated and added to the principal an number of times per year.
4. The variable 'r' in the formula A = Pe^(rt) represents the annual interest rate as a .
5. You invest $5,000 at an annual interest rate of 3.5% compounded continuously. How much money will you have after 10 years? (Round to two decimal places)
6. An initial investment of $1,000 grows to $1,500 in 5 years with continuously compounded interest. What is the annual interest rate? (Round to three decimal places as a percentage)
7. For a given principal and interest rate, continuously compounded interest will always yield a higher future value than interest compounded annually.
True
False