Explain in your own words what the term compound interest means. What does continuous compounding mean?
Explain in your own words what the term compound interest means. What does continuous compounding mean?
Solution Summary: The author explains that compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest.
Explain in your own words what the term compound interest means. What does continuous compounding mean?
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To determine
Explain in your own words what the term compound interest means. What does continuous compounding mean?
Answer to Problem 73AYU
Solution:
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. Compound interest is standard in finance and economics.
Compound interest may be contrasted with simple interest, where interest is not added to the principal, so there is no compounding. The simple annual interest rate is the interest amount per period, multiplied by the number of periods per year. The simple annual interest rate is also known as the nominal interest rate.
Explanation of Solution
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. Compound interest is standard in finance and economics.
Compound interest may be contrasted with simple interest, where interest is not added to the principal, so there is no compounding. The simple annual interest rate is the interest amount per period, multiplied by the number of periods per year. The simple annual interest rate is also known as the nominal interest rate.
Continuous compounding is the mathematical limit that compound interest can reach if it’s calculated and reinvested into an account’s balance over a theoretically infinite number of periods. While this is not possible in practice, the concept of continuously compounded interest is important in finance. It is an extreme case of compounding, as most interest is compounded on a monthly, quarterly or semiannual basis. Continuous compounding calculates interest assuming constant compounding over an infinite number of periods. Even with very large investment amounts, the difference in the total interest earned through continuous compounding is not very high when compared to traditional compounding periods.
University Calculus: Early Transcendentals (4th Edition)
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