Final answer:
Simple interest is calculated on the principal amount while compound interest is calculated on the principal plus accumulated interest. The formulas for simple and compound interest are different, with compound interest typically resulting in a higher amount due to the interest compounding over time.
Step-by-step explanation:
The concepts of simple and compound interest are essential topics in mathematics, specifically in financial mathematics. Simple interest is calculated only on the principal amount, which is the initial sum of money that is deposited or loaned. The formula for simple interest is given by I = P × r × t, where I represents the interest, P is the principal amount, r is the annual interest rate, and t is the time in years.
On the other hand, compound interest is calculated on the principal amount plus the accumulated interest over past periods. This means that interest is earned not only on the initial principal but also on the interest that has been added to the principal. To calculate compound interest, we use the formula: Future Value = Principal × (1 + interest rate)^time. The compound interest is then found by subtracting the original principal from this future value. This method of interest calculation can lead to a significantly larger amount over time compared to simple interest.
An example of this difference can be seen when we consider a total future amount with simple interest: $100 + ($100 × 0.05 × 3) = $115. However, with compound interest, because the interest accumulates, the future value would be higher. This effect of compound interest is particularly striking over long periods, which is why it is often referred to as the eighth wonder of the world in terms of its powerful effect on growing savings or investments over time.