Simple Interest vs. Compound Interest

Sample Solution

Simple Interest

Simple interest is calculated only on the principal amount of a loan or investment. It does not take into account the interest earned on previous interest. This means that the interest earned remains constant over time.

Example 1: Simple Interest Loan

Suppose you borrow $1,000 from a friend at a simple interest rate of 5% per year. After one year, the interest earned would be:

• Interest = Principal * Rate * Time
• Interest = $1,000 * 5% * 1 year = $50

Full

Compound Interest

Compound interest is calculated on both the principal amount and the accumulated interest. This means that the interest earned in one period is added to the principal for the next period, resulting in exponential growth.

Example 2: Compound Interest Investment

Suppose you invest $1,000 in a savings account that earns a compound interest rate of 5% per year. After one year, the interest earned would be $50, just like in the simple interest example. However, in the second year, the interest would be calculated on the total amount ($1,050), resulting in $52.50 of interest.

Therefore, after two years, your investment would be worth $1,102.50 ($1,000 principal + $50 interest from year 1 + $52.50 interest from year 2).

Key Differences

• Calculation: Simple interest is calculated only on the principal amount, while compound interest is calculated on both the principal and accumulated interest.

Growth: Compound interest leads to exponential growth, while simple interest results in linear growth.

• Time: Over longer time periods, the difference between simple and compound interest becomes more significant.

In conclusion, understanding the difference between simple and compound interest is crucial for financial planning and decision-making. While simple interest is straightforward to calculate, compound interest can have a significant impact on the growth of investments or the cost of loans over time.

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