Compound Interest

Compound Interest Interest Calculation Finance Investing Loans Deposits
Compound interest refers to the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. It is a crucial concept in finance and investing, offering greater returns compared to simple interest.
On this page

Compound interest is a fundamental concept in the financial world. Unlike simple interest, which is calculated only on the principal amount, compound interest is calculated on the principal plus any interest that has been added to it over time. This leads to “interest on interest,” significantly increasing the amount of interest earned or paid over time.

Examples

  1. Savings Account

    • Suppose you deposit $1,000 into a savings account with an annual interest rate of 5%, compounded annually. After the first year, you will earn $50 in interest, for a total of $1,050. In the second year, you will earn 5% on $1,050, which is $52.50, bringing your total to $1,102.50.

  2. Investment

    • If you invest $10,000 at an annual interest rate of 8%, compounded monthly, after 5 years (60 months), your investment will grow to approximately $14,693.28. This is calculated using the compound interest formula with monthly compounding.

Frequently Asked Questions

Q1: What is the formula for calculating compound interest?

  • A: The basic formula for compound interest is: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where:
    • \( A \) = the future value of the investment/loan, including interest
    • \( P \) = the principal investment amount (initial deposit or loan)
    • \( r \) = the annual interest rate (decimal)
    • \( n \) = the number of times that interest is compounded per year
    • \( t \) = the number of years the money is invested or borrowed for

Q2: How does compound interest benefit long-term investments?

  • A: Compound interest benefits long-term investments by increasing the amount of interest earned exponentially over time, as interest is calculated on the accumulated interest from previous periods.

Q3: Can compound interest be a disadvantage?

  • A: Yes, compound interest can be a disadvantage for borrowers, as it can significantly increase the total amount to be repaid, especially for long-term loans.

Q4: What is the difference between compound and simple interest?

  • A: Simple interest is calculated only on the principal amount, whereas compound interest is calculated on the principal amount and the accumulated interest from prior periods.

Q5: How often can interest be compounded?

  • A: Interest can be compounded on various frequencies, such as annually, semi-annually, quarterly, monthly, daily, or even continuously.
  • Interest: The cost of borrowing money, usually expressed as an annual percentage of the principal.
  • Principal: The initial amount of money borrowed or invested, before interest.
  • Annual Percentage Rate (APR): The annual rate charged for borrowing or earned through an investment, which does not account for compound interest within the year.
  • Effective Annual Rate (EAR): The interest rate on an investment or loan that is compounded annually.

Online References

Suggested Books for Further Studies

  • “The Compound Effect” by Darren Hardy
  • “Compound Interest & Time Value of Money: The Foundation of Investing” by Robert C. Appleby
  • “Financial Planning & Analysis and Performance Management” by Jack Alexander

Accounting Basics: “Compound Interest” Fundamentals Quiz

### What is compound interest? - [ ] Interest calculated only on the initial principal. - [x] Interest calculated on the initial principal and the accumulated interest. - [ ] Interest calculated on the principal minus accrued interest. - [ ] Interest added to a savings bond once at the end of the term. > **Explanation:** Compound interest is calculated on both the initial principal and the accumulated interest from previous periods, differing from simple interest which is only calculated on the initial principal. ### Can compound interest lead to exponential growth of an investment? - [x] Yes, because of the interest-on-interest effect. - [ ] No, because interest is only calculated annually. - [ ] It depends if the interest rate is high. - [ ] Only if the investment amount is large. > **Explanation:** Yes, compound interest can lead to exponential growth because the interest is calculated on the accumulated interest from previous periods, not just the initial principal. ### What does the 'n' represent in the compound interest formula? - [ ] Number of years - [x] Number of times interest is compounded per year - [ ] Interest rate - [ ] Principal amount > **Explanation:** In the compound interest formula, 'n' represents the number of times interest is compounded per year. ### How does the compounding frequency affect the amount of compound interest earned? - [x] More frequent compounding leads to more interest. - [ ] Less frequent compounding leads to more interest. - [ ] Compounding frequency does not matter. - [ ] Only annual compounding generates more interest. > **Explanation:** More frequent compounding (e.g., monthly instead of annually) leads to more interest earned over the same period, as interest is calculated on the accumulated interest more frequently. ### How does compound interest differ from simple interest over a long period? - [ ] Compound interest is less beneficial. - [x] Compound interest accumulates more due to interest-on-interest. - [ ] Simple interest accumulates the same amount. - [ ] Both remain unaffected by the time period. > **Explanation:** Over a long period, compound interest accumulates more than simple interest because of the interest-on-interest effect, resulting in higher amounts due to frequent compounding. ### What is required for compound interest to occur? - [x] Initial principal, interest rate, time period, and compounding frequency. - [ ] Principal alone. - [ ] Interest rate alone. - [ ] Just the time period of the investment. > **Explanation:** For compound interest to occur, an initial principal, interest rate, time period, and compounding frequency are required to calculate the future value. ### Which investment scenario benefits more from compound interest? - [ ] High-interest rate investment with no compounding. - [x] Moderate interest rate investment with high compounding frequency. - [ ] Low-interest rate investment with daily compounding. - [ ] Any investment with an initial high principal. > **Explanation:** A moderate interest rate investment with high compounding frequency benefits more because the accrued interest also earns interest over time. ### Why might compound interest be disadvantageous for borrowers? - [x] It increases the total interest payable. - [ ] It simplifies the interest calculation. - [ ] It does not affect the total repayment. - [ ] It reduces the overall principal amount. > **Explanation:** Compound interest can be disadvantageous for borrowers as it increases the total interest payable due to interest being calculated on the accumulated interest, resulting in higher total amounts owed. ### If a savings account promises 5% annual interest compounded monthly, what does it signify? - [x] Interest is calculated each month on the accumulating amount. - [ ] Interest is calculated annually then divided by 12. - [ ] Simple interest is distributed monthly. - [ ] Interest compounding starts after one year. > **Explanation:** It signifies that the interest is calculated each month on the accumulating amount, leading to more interest earned compared to simple annual compounding. ### What is the Effective Annual Rate (EAR) if the APR is 12% and compounded monthly? - [x] Approximately 12.68% - [ ] 12% - [ ] 13% - [ ] 11.39% > **Explanation:** The EAR takes into account the effect of monthly compounding on the annual rate. Using the formula, \\(EAR = (1 + \frac{APR}{n})^n - 1\\), the EAR = (1 + 0.01)^12 - 1 ≈ 12.68%.

Thank you for exploring the intricacies of compound interest and testing your knowledge with our quiz. Keep delving deeper into the world of finance and investing!

$$$$
Tuesday, August 6, 2024
Compound Journal Entry
Compound Instrument
Interest January 1, 1
Simple Interest January 1, 1
Amount of One Per Period January 1, 1
Arrearage January 1, 1
Bank January 1, 1
Bank Money January 1, 1
Base Rate January 1, 1
Bullet Loan January 1, 1
Contract Interest Rate January 1, 1
Contract Rate January 1, 1

Accounting Terms Lexicon

Discover comprehensive accounting definitions and practical insights. Empowering students and professionals with clear and concise explanations for a better understanding of financial terms.