Compound and Continuous Interest Worksheet
Explore compound and continuous interest calculations with this Grade 10 math worksheet, covering formulas and real-world applications.
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Compound and Continuous Interest
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Read each question carefully and show all your work. Use the appropriate formulas for compound and continuous interest.
1. The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times interest is per year, and t is the time in years.
2. The formula for continuous compound interest is A = Pe^(rt), where e is Euler's number, approximately equal to .
3. When interest is compounded more frequently, the effective annual rate .
4. What is the future value of an investment of $5,000 at an annual interest rate of 4% compounded quarterly for 3 years?
$5,634.12
$5,624.32
$5,630.81
$5,618.32
5. Which compounding frequency will yield the highest return for a given annual interest rate?
Annually
Semi-annually
Monthly
Continuously
6. An investment of $10,000 earns an annual interest rate of 5%. Calculate the future value after 2 years if the interest is compounded annually.
7. Calculate the future value of the same $10,000 investment after 2 years if the interest is compounded continuously.
8. Continuous compounding is always better than discrete compounding for the investor.
True
False
9. The 'e' in the continuous compounding formula represents the interest rate.
True
False
10. You have two investment options: Option A offers an annual interest rate of 6% compounded monthly. Option B offers an annual interest rate of 5.9% compounded continuously. If you invest $1,000 for 5 years, which option will yield a higher return and by how much? Show all your calculations.