Final answer:
The total amount of money is the same for both simple and compound interest systems at the end of the first cycle. Beyond the first cycle, compound interest starts accumulating on the interest from the previous period, resulting in higher amounts than simple interest. Option a.
Step-by-step explanation:
The total amount of money (Principal plus Interest) in simple and compound interest systems becomes the same at the end of the first cycle because compound interest is equivalent to simple interest in the first period.
This is because the compound interest has not yet had the opportunity to compound; it is only calculated on the principal amount, which is the same method used for simple interest.
Let's look at a basic example. Assume you invest $100 at a 5% annual interest rate.
Simple interest for the first year is calculated by multiplying the principal amount of $100 by the interest rate of 0.05, which equals $5. Therefore, the total future amount with simple interest after one year would be $100 principal plus $5 interest, totaling $105.
Compound interest, for the first interest cycle (year), is also $5 because it is calculated only on the principal amount of $100, thus also resulting in a total amount of $105.
However, beyond the first cycle, compound interest begins to accumulate interest on the previous periods' interest, which will lead to a higher amount compared to simple interest over the same period. Therefore, the answer to the student's question is: a. Only in the End of the First cycle. Option a.