What is the formula for future value with monthly compounding?

The formula for future value with monthly compounding is correctly identified as utilizing the formula FV = C((1+r/m)^(tm) - 1) / (r/m). Here’s why this formula is appropriate for calculating future value with monthly compounding.

In this formula, C represents the initial capital investment or cash flow; r is the annual nominal interest rate; m indicates the number of compounding periods per year (in this case, 12 for monthly compounding); and t represents the total number of years.

The term (1 + r/m) reflects the periodic interest rate per month, since we take the annual rate and divide it by the number of compounding periods. Raising this to the power of tm accounts for the total number of compounding periods involved (i.e., the number of months over the total number of years).

Thus, the entire equation calculates the future value of an investment or series of cash flows that are compounded monthly over t years. This understanding is essential for effective financial planning and investment analysis, as it helps in assessing how much an investment will grow over time under different compounding intervals.

The other options provided do not accurately represent the calculations required for future value with monthly compounding, making them unsuitable for this