Compound interest

Definition

Compound interest is the interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods. This concept highlights the effect of earning interest on interest over time, leading to exponential growth of an investment or debt. It’s a key principle in finance as it emphasizes how time and the frequency of compounding can significantly influence financial outcomes.

5 Must Know Facts For Your Next Test

1. Unlike simple interest, which only calculates interest on the principal, compound interest takes into account the accumulated interest from previous periods.
2. The more frequently interest is compounded, the more total interest will be earned or paid over time.
3. Compound interest can significantly increase the total amount earned on investments or owed on loans, especially over longer periods.
4. To calculate compound interest, the formula used is 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 time in years.
5. Understanding compound interest is crucial for effective financial planning and investment strategies.

Review Questions

• How does compound interest differ from simple interest in terms of calculation and impact over time?
  • Compound interest differs from simple interest in that it not only calculates interest on the principal but also includes any accumulated interest from previous periods. This means that with compound interest, each period's interest earns its own interest in subsequent periods. Over time, this leads to a much greater total amount of money earned or paid compared to simple interest, especially when compounded frequently.
• Discuss how the compounding frequency affects the total amount of compound interest earned on an investment.
  • The compounding frequency significantly affects the total amount of compound interest earned on an investment. The more often interest is compounded—such as monthly instead of annually—the more opportunities there are for the investment to grow. This results in a higher overall return because each time interest is added to the principal, future calculations will use this new total amount. Therefore, even small differences in compounding frequency can lead to substantially different outcomes over time.
• Evaluate the implications of compound interest in financial decision-making for individuals planning for retirement.
  • The implications of compound interest in financial decision-making are profound, especially for individuals planning for retirement. Understanding how compound interest works allows individuals to appreciate the importance of starting investments early and choosing accounts with favorable compounding frequencies. For example, even small contributions made consistently over time can grow significantly due to compound interest. Thus, being strategic about when and how much to invest can greatly enhance financial security in retirement.

Related terms

Principal: The original sum of money invested or loaned, on which interest is calculated.

Interest Rate: The percentage at which interest is charged or paid on the principal amount over a specific period.

Compounding Frequency: The frequency with which interest is applied to the principal balance, such as annually, semi-annually, quarterly, or monthly.