Compound and Continuous Interest Worksheet
Explore compound and continuous interest calculations with this Grade 9 math worksheet, covering formulas, comparisons, and real-world applications.
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Compound and Continuous Interest
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Read each question carefully and provide your answers in the space provided. Show all your work for calculations.
1. The formula for compound interest is A = P(1 + r/n)^(nt), where 'n' represents the number of times interest is per year.
2. For continuous compounding, the formula used is A = Pe^(rt), where 'e' is constant, approximately equal to 2.71828.
3. When interest is compounded more frequently, the effective annual rate of return will .
4. The principal amount in an investment is the amount of money invested or borrowed.
5. Which of the following compounding frequencies would yield the highest amount for a given principal, interest rate, and time period?
Annually
Semi-annually
Monthly
Continuously
6. The variable 't' in the compound interest formula represents:
Total amount
Principal amount
Time in years
Annual interest rate
7. Calculate the future value of an investment of $5,000 at an annual interest rate of 4% compounded quarterly for 5 years.
8. What is the future value of $10,000 invested for 3 years at an annual interest rate of 6% compounded continuously?
9. Compare the future value of $2,000 invested for 10 years at an annual interest rate of 5% when compounded annually versus compounded monthly.
10. Continuous compounding always yields a higher future value than any form of discrete compounding for the same principal, rate, and time.
True
False
11. The more times interest is compounded within a year, the smaller the total interest earned will be.
True
False
12. You want to have $15,000 in 8 years. If you can invest at an annual interest rate of 3.5% compounded semi-annually, how much should you invest today?
13. A savings account offers an annual interest rate of 2.75%. If the interest is compounded continuously, how long will it take for an initial investment to double?
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