What formula represents compound interest?

The formula that represents compound interest is A(t) = A0(1 + (i/n))^(nt). This formula illustrates how an initial investment or principal amount, A0, grows over time based on a certain interest rate, i, that is compounded n times per year. The variable t represents the number of years the money is invested or borrowed.

In this formula, the term (1 + (i/n)) signifies that the interest is being applied at intervals within the year, rather than just at the end of the year. Here, i is the annual interest rate expressed as a decimal, and n indicates how many times interest is compounded within a year. The exponent nt reflects the total number of compounding periods over the investment term. Therefore, this formula captures the effect of compounding, allowing for exponential growth of the investment.

The other options represent different relationships or types of interest calculation. For example, one may represent simple interest rather than compound interest, and another might express interest in a continuous compounding model. Understanding the nuances among these various formulas is crucial for distinguishing between simple and compound interest calculations.