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 the interest earned in one period is added to the principal for the next period, leading to exponential growth of the investment over time. It plays a crucial role in understanding how money grows, emphasizing the importance of both time and interest rates in wealth accumulation.

5 Must Know Facts For Your Next Test

1. Unlike simple interest, which only calculates interest on the principal, compound interest can significantly increase returns due to earning 'interest on interest.'
2. The frequency of compounding—such as annually, semi-annually, quarterly, or daily—affects how much total interest is earned over time.
3. The formula for calculating compound interest is given by $$A = P(1 + r/n)^{nt}$$, 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 unit t, and t is the time in years.
4. Starting to invest early takes advantage of compound interest over time, allowing even small contributions to grow substantially due to the power of compounding.
5. Compound interest can work against borrowers as well, leading to growing debts if they fail to pay off loans in a timely manner.

Review Questions

• How does compound interest differ from simple interest in terms of calculation and impact on investment growth?
  • Compound interest differs from simple interest primarily in that it calculates interest not just on the principal but also on accumulated interest from prior periods. This leads to a significantly greater impact on investment growth over time since each compounding period adds more interest to the principal. Consequently, investments using compound interest can grow exponentially compared to those using simple interest, which only offers linear growth based on the initial principal.
• Discuss how the frequency of compounding affects the overall returns on an investment. Provide an example illustrating this concept.
  • The frequency of compounding directly influences the total returns on an investment because more frequent compounding periods lead to more instances where interest is calculated and added back into the principal. For example, if you invest $1,000 at an annual rate of 5%, compounded annually, you would have $1,050 after one year. However, if compounded quarterly instead, your investment would yield approximately $1,051.16 at the end of the year. This shows how even slight differences in compounding frequency can result in noticeably higher returns.
• Evaluate the long-term effects of starting to invest early versus delaying investments when considering compound interest. What implications does this have for financial planning?
  • Starting to invest early takes full advantage of compound interest's exponential growth potential, allowing investments to accrue significant returns over time. For instance, investing $100 monthly starting at age 20 could yield much more than waiting until age 30 to start investing the same amount. This emphasizes that time in the market can be more beneficial than timing the market itself. For financial planning, this underscores the importance of early contributions and consistently investing over longer periods, as it can lead to substantial wealth accumulation through compounding effects.

Related terms

Principal: The principal is the original sum of money invested or loaned, before any interest is added.

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

Future Value:

Future value refers to the amount of money that an investment will grow to over a period at a specified interest rate.