Compound interest

Definition

Compound interest is the interest calculated on the initial principal and also on the accumulated interest from previous periods. This means that interest is earned not only on the original amount invested but also on the interest that has already been added, which can significantly increase the total amount over time. Understanding compound interest is essential for evaluating investments and savings plans, as it emphasizes the benefits of earning interest on both the principal and previously accrued interest.

5 Must Know Facts For Your Next Test

1. Compound interest grows exponentially over time, meaning that the longer you leave your money invested, the more you can earn.
2. It can be calculated using the formula: A = P(1 + r/n)^{nt}, where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years the money is invested for.
3. The frequency of compounding (e.g., annually, semi-annually, quarterly, or monthly) can have a significant impact on the total amount of interest earned.
4. Even a small difference in interest rates can lead to large differences in accumulated wealth over long periods due to the effect of compounding.
5. Compound interest is often referred to as 'interest on interest' because it allows earnings to be reinvested to generate additional earnings.

Review Questions

• How does compound interest differ from simple interest, and why is it important to understand this difference in financial planning?
  • Compound interest differs from simple interest in that simple interest only calculates interest on the principal amount throughout the entire investment period, whereas compound interest calculates interest on both the principal and previously earned interest. This distinction is crucial for financial planning because compound interest can lead to significantly higher returns over time. Knowing how to leverage compound interest can help individuals make informed decisions about savings and investments, maximizing their financial growth.
• Discuss how the frequency of compounding impacts overall investment growth when using compound interest.
  • The frequency of compounding can greatly affect how much an investment grows over time with compound interest. For example, if an investment compounds annually versus monthly, the latter will yield a higher return because it allows for more frequent application of interest on previously earned amounts. As a result, understanding how different compounding frequencies work helps investors choose financial products that maximize their returns and achieve their savings goals more effectively.
• Evaluate a scenario where an investor chooses between two savings accounts: one with a lower interest rate compounded monthly and another with a higher rate compounded annually. How should they make their decision based on compound interest principles?
  • In evaluating which savings account to choose, the investor should calculate the total future value of both options using the compound interest formula. Even if one account offers a higher nominal rate but compounds less frequently, it might still yield a lower return compared to an account with a slightly lower rate that compounds more frequently. By performing these calculations and understanding how different compounding frequencies influence their earnings, the investor can make an informed decision that aligns with their financial goals and maximizes their potential growth over time.

Related terms

Principal: The original sum of money borrowed or invested, excluding any interest or profits.

Annual Percentage Rate (APR): The annual rate charged for borrowing or earned through an investment, expressed as a percentage.

Time Value of Money: The concept that money available today is worth more than the same amount in the future due to its potential earning capacity.