Final answer:
Continuous Compound Interest concerns the calculation of interest on the principal and past accumulated interest. Compound interest differs from simple interest by taking into account the interest that is accumulated over time, not just on the initial investment. A $100 investment compounded annually at 5% for three years will grow to $115.76, demonstrating the effects of compounding.
Step-by-step explanation:
The concept in question here appears to be Continuous Compound Interest, which is the calculation of interest on both the initial principal and the accumulated interest from previous periods. To determine the compound interest earned over a particular time period, you subtract the present value (initial amount invested) from the future value (amount after interest has been applied). If we consider a scenario where the initial investment is $100 at a 5% interest rate compounded annually, after three years, the amount would be:
Future Value = Principal x (1 + interest rate) ^time.
Future Value = $100 x (1 + 0.05) ^3.
Future Value = $100 x 1.157625
Future Value = $115.76
Thus, the total compound interest is $115.76 - $100 = $15.76. This shows that compound interest is $0.76 more than the simple interest over the same period, which indicates the power of compounding even over a short time and with a modest sum.