What is compound interest?

Compound interest refers to the method of calculating interest whereby the interest earned over time is added to the principal amount, and future interest calculations are based on this new total. This means that not only does the initial principal earn interest, but any interest that has previously been added to the principal also earns interest. This leads to a situation where the amount of interest grows exponentially over time, compared to simple interest, which is calculated only on the original principal.

In this context, the first choice accurately describes compound interest; it highlights the crucial aspect of accumulation. When interest is calculated on both the initial principal and the accumulated interest, it results in a rapid increase in the total balance over time, especially noteworthy in long-term investments or loans.

The other options do not capture the essence of compound interest. Interest calculated solely on the initial principal ignores the benefits of compounding. A separate fee charged by the bank does not relate to how interest is calculated and represents a different financial concept. Lastly, simple interest, which is calculated only on the principal, fails to incorporate the growth that comes from reinvested or accumulated interest. This illustrates the distinct nature of compound interest and underscores why option A is the correct choice.