Why is compound interest generally preferable to simple interest when investing?

• A. Simple interest is calculated more frequently than compound interest, resulting in higher returns.
• B. Compound interest always has a lower interest rate than simple interest.
• C. Compound interest allows interest to be earned on both the initial principal and previously accumulated interest, leading to greater returns over time.
• D. Compound interest only benefits short-term investments, while simple interest benefits long-term investments.

Answer: (C)

Verified step by step guidance

1. Understand the definition of simple interest: it is calculated only on the original principal amount throughout the investment period. The formula for simple interest is \(SI = P \times r \times t\), where \(P\) is the principal, \(r\) is the interest rate, and \(t\) is the time.
2. Understand the definition of compound interest: it is calculated on the initial principal and also on the accumulated interest from previous periods. The formula for compound interest is \(A = P \times \left(1 + \frac{r}{n}\right)^{nt}\), where \(A\) is the amount after time \(t\), \(n\) is the number of compounding periods per year, and other variables as before.
3. Recognize that compound interest leads to 'interest on interest,' meaning the investment grows faster because each period's interest is added to the principal for the next period's interest calculation.
4. Compare the growth of investments under simple and compound interest over time, noting that compound interest generally results in higher returns, especially as the number of compounding periods and the length of the investment increase.
5. Conclude that compound interest is generally preferable because it maximizes returns by reinvesting earned interest, unlike simple interest which only pays interest on the original principal.