Why is compound interest generally more advantageous than simple interest when investing money over time?

• A. Because compound interest is not affected by the frequency of compounding periods.
• B. Because simple interest rates are always lower than compound interest rates.
• C. Because compound interest earns interest on both the initial principal and the accumulated interest from previous periods.
• D. Because compound interest is calculated only on the initial principal, leading to higher returns.

Answer: (C)

Verified step by step guidance

1. Understand the concept of simple interest: Simple interest is calculated only on the initial principal amount over the investment period. The formula for simple interest is: $I=P\times r\times t$, where $I$ is the interest, $P$ is the principal, $r$ is the annual interest rate, and $t$ is the time in years.
2. Understand the concept of compound interest: Compound interest is calculated on the initial principal and also on the accumulated interest from previous periods. The formula for compound interest is: $A=P(1+r){\left(}^n$, where $A$ is the total amount, $P$ is the principal, $r$ is the annual interest rate, and $n$ is the number of compounding periods.
3. Compare the two methods: In simple interest, the interest earned does not grow over time because it is based solely on the initial principal. In compound interest, the interest earned grows exponentially because it is calculated on both the principal and the accumulated interest from previous periods.
4. Recognize the advantage of compound interest: Compound interest allows the investment to grow faster over time due to the 'interest on interest' effect. This makes it more advantageous for long-term investments compared to simple interest.
5. Understand the correct answer: The correct answer is 'Because compound interest earns interest on both the initial principal and the accumulated interest from previous periods.' This highlights the key difference and advantage of compound interest over simple interest.