Definitions
Simple Interest: Simple interest is the calculation of interest on the principal, or original amount of a loan or investment. Unlike compound interest, simple interest is not calculated on the accumulated interest of previous periods.
Detailed Explanation
Simple interest can be easily understood and computed with the formula:
\[ \text{Simple Interest} = P \times r \times t \]
Where:
- \( P \) = Principal amount
- \( r \) = Interest rate per period
- \( t \) = Time periods that the money is invested or borrowed
For example, if you invest $1,000 at an interest rate of 10% per annum, the simple interest for 5 years would be:
\[ \text{Simple Interest} = 1000 \times 0.10 \times 5 = 500 \]
Therefore, the total amount after 5 years will be:
\[ \text{Total Amount} = P + \text{Simple Interest} = 1000 + 500 = 1500 \]
Examples
Example 1: Fixed Sum Deposit
If you deposit $1,000 in a savings account that offers a simple interest rate of 5% annually, the interest you earn in three years would be:
\[ \text{Simple Interest} = 1000 \times 0.05 \times 3 = 150 \]
The amount in the account after three years would be:
\[ 1000 + 150 = 1150 \]
Example 2: Loan Calculation
If you borrow $2000 with a simple interest rate of 8% per year for 4 years, the interest you owe at the end of the loan term would be:
\[ \text{Simple Interest} = 2000 \times 0.08 \times 4 = 640 \]
The total amount to be paid back after 4 years would be:
\[ 2000 + 640 = 2640 \]
Frequently Asked Questions (FAQs)
What is the difference between simple interest and compound interest?
Simple interest is calculated only on the principal amount, whereas compound interest is calculated on the principal amount as well as the interest that accumulates on it in each period.
How do I calculate simple interest?
Simple interest can be calculated using the formula:
\[ \text{Simple Interest} = P \times r \times t \]
Can simple interest be negative?
No, simple interest cannot be negative because it represents the cost of borrowing money or the gain from lending it.
What happens if the period changes in the simple interest calculation?
If the period of investment or loan changes, the interest to be gained or paid will change proportionally, as it is directly proportional to the time period (\( t \)).
Is simple interest better than compound interest for short term investments?
Simple interest could be beneficial for short-term investments or loans as it won’t result in interest on interest, but for long-term investments, compound interest typically yields more returns.
Related Terms
Compound Interest: The method of calculating interest whereby the interest earned over time is added to the principal, so that subsequent interest calculations accrue on the growing principal amount.
Principal: The initial sum of money borrowed or invested, upon which interest is calculated.
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.
Online Resources
- Khan Academy - Simple Interest
- Investopedia - Simple and Compound Interest
- The Balance - Understanding Simple Interest
References
- Brigham, Eugene & Houston, Joel. “Fundamentals of Financial Management” - Cengage Learning.
- Ross, Stephen; Westerfield, Randolph; Jordan, Bradford. “Essentials of Corporate Finance” - McGraw-Hill Education.
Suggested Books for Further Studies
- “The Complete Guide to Personal Finance: For Teenagers and College Students” by Tamsen Butler
- “Basic Finance: An Introduction to Financial Institutions, Investments, and Management” by Herbert B. Mayo
- “Finance for Nonfinancial Managers” by Gene Siciliano
