Final answer:
Simple interest is calculated only on the principal amount, whereas compound interest is calculated on the principal plus any interest earned. Over three years, compound interest earns slightly more than simple interest ($6.12 vs. $15), and this difference can be more pronounced over longer periods or with larger sums.
Step-by-step explanation:
When comparing simple interest and compound interest, we need to understand how each is calculated. For simple interest, the interest is calculated on the initial amount only, which does not change over time. Using an example with a $100 deposit at a simple interest rate of 5% held for three years, the calculation would be:$100 × 0.05 × 3 = $15
For compound interest, interest is calculated on the initial amount plus any accrued interest. Compounding annually with a 2% interest rate on a $100 deposit after three years equates to: $100 × 1.02³ = $106.12. With compound interest, the total interest earned after three years is $6.12, while with simple interest, it is $5. As time increases, the discrepancy grows — at three years, compound interest earns $0.76 more than simple interest. This difference becomes more significant with larger amounts and over longer periods.