What formula is commonly used to determine the future value of an annuity?

The formula used to determine the future value of an annuity accounts for a series of cash flows that are made at regular intervals over a specified period. The correct formula expresses this future value as the sum of all periodic payments compounded at a defined interest rate.

The formula FV = PMT * [((1 + r)^nt - 1) / r] directly addresses how to calculate the future value of these payments. Here, PMT represents the amount of each individual payment, r is the interest rate per period, and nt reflects the total number of payments made across all periods. The term ((1 + r)^nt - 1) captures the cumulative effect of compounding interest on each individual payment, while dividing by r adjusts the formula to account for the fact that each payment is made at different times through the annuity period.

This formula helps to easily sum the future values of each payment when the effects of compounding interest are considered over time, making it ideal for valuing financial products like retirement savings or loan repayments, where regular payments are made over time. Understanding this is crucial for any financial modeling involving annuities, as it allows for precise estimation of future cash flows.