How do you calculate the future value of a single sum?

The future value of a single sum is calculated using the formula that involves compounding the present value over a specific period at a given interest rate. This formula is particularly effective for understanding how money grows over time due to interest.

In this case, the correct formula states that the future value (FV) is equal to the present value (PV) multiplied by the quantity of one plus the interest rate (r) raised to the power of the number of periods (n). This accounts for the concept of compounding, where interest is earned not only on the initial principal but also on any interest that has previously been added to it.

Thus, this method accurately models how money accumulates over time, providing a realistic projection of how much an investment will be worth at a future date when interest is compounded. It is widely used in finance to determine how much a lump sum today will grow into in the future, which is essential for making informed investment decisions.

The other options do not represent valid methods for calculating future value in the context of compound interest; they may involve incorrect applications of arithmetic or misunderstandings of interest calculations.