What is the relationship between the number of periods (N) and future value?

The relationship between the number of periods (N) and future value is such that a larger N results in a larger future value. This outcome is fundamentally grounded in the concepts of compound interest and the time value of money.

When you invest money, the future value is influenced by how long that money remains invested or earns interest. The longer the investment period, the more interest it can generate through compounding. Compound interest means that not only does your initial investment (the principal) earn interest, but the interest itself earns interest over time. Therefore, as you increase the number of periods (N), you allow more time for this compounding effect to take place, leading to an exponential increase in the future value.

In contrast, if the number of periods is smaller, there’s less time for compounding to work, resulting in a lower future value. This principle illustrates why investing for longer periods often leads to greater wealth accumulation.

The other options are not valid: a larger N cannot lead to a smaller future value, as that contradicts the principle of compounding; the future value does indeed depend on N, as it directly affects the calculation; and while it is important to ensure the consistency of time periods in financial calculations, N does not need to