Final answer:
To calculate the ending balance and interest earned for the scenarios, one must apply the compound interest formula and simple interest formula, respectively. Compound interest accumulates on both the initial principal and the interest from previous periods, leading to larger earnings over time compared to simple interest.
Step-by-step explanation:
The question requires calculations of compound interest and simple interest to determine the ending balances and interest earned in the given scenarios. To solve the compound interest for part (a), we use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (initial amount), r is the annual interest rate (in decimal form), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. As for part (b), the total interest earned with simple interest is given by the formula I = P * r * t, where I stands for interest, P is the principal amount, r is the annual interest rate (in decimal), and t is the time in years.
For example, compounding $100 at a 5% annual interest rate for three years would result in a total future amount of $115.76, demonstrating the power of compound interest. In contrast, simple interest calculation for the same amount and period would yield $115. Therefore, compound interest results in more earnings than simple interest over time.