Continuously Compounded Interest
Explore continuously compounded interest with this worksheet, covering calculations and understanding the formula A = Pe^(rt).
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Continuously Compounded Interest
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Read each question carefully and calculate the future value of investments compounded continuously. Use the 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. Round your answers to two decimal places where appropriate.
1. The formula for continuously compounded interest is A = P .
2. In the formula, 'P' represents the amount.
3. The letter 'e' in the formula is known as number, approximately equal to 2.71828.
4. The variable 'r' stands for the annual rate, expressed as a decimal.
1. If you invest $1,000 at an annual interest rate of 5% compounded continuously, what will be the amount in your account after 10 years?
2. An initial investment of $5,000 is made into an account that earns 3.5% interest compounded continuously. How much will be in the account after 7 years?
1. Which of the following is the correct formula for continuously compounded interest?
A = P(1 + r/n)^(nt)
A = P(1 + rt)
A = Pe^(rt)
A = P + I
2. Approximately what value does 'e' represent?
3.14
2.72
1.62
100
1. Continuously compounded interest results in a higher return than interest compounded annually, quarterly, or monthly.
True
False
2. The 't' in the continuously compounded interest formula represents the total principal invested.
True
False
You are comparing two investment options. Option A offers 6% interest compounded annually. Option B offers 5.8% interest compounded continuously. If you invest $10,000 for 5 years, which option will yield a higher return?
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