Why do you earn more money using compound interest than you would using simple interest?

• A. Because simple interest is paid out more frequently than compound interest.
• B. Because compound interest is calculated only on the initial principal.
• C. Because simple interest rates are always lower than compound interest rates.
• D. Because compound interest earns interest on both the initial principal and the accumulated interest from previous periods.

Answer: (D)

Verified step by step guidance

1. Understand the difference between simple interest and compound interest. Simple interest is calculated only on the initial principal, while compound interest is calculated on the initial principal plus any accumulated interest from previous periods.
2. For simple interest, use the formula: I = P × r × t, where I is the interest, P is the principal, r is the annual interest rate, and t is the time in years.
3. For compound interest, use the formula: A = P × (1 + r/n)^(n×t), where A is the total amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.
4. Compare the two methods: In simple interest, the interest earned remains constant over time because it is based only on the initial principal. In compound interest, the interest grows exponentially because it is calculated on the principal plus accumulated interest.
5. Conclude that compound interest earns more money over time because it allows interest to be earned on both the initial principal and the interest that has already been added to the account.