What is the factor name of the formula [i(1+i)^n]/[(1+i)^n - 1]?

The factor represented by the formula [ \frac{i(1+i)^n}{(1+i)^n - 1} ] is known as the capital recovery factor. This factor is used in engineering economics to determine the annual equivalent amount of a series of cash flows that arise from an initial investment over a specified period.

Specifically, it shows how much needs to be set aside annually to recover the original investment, considering a certain interest rate (i) over a number of periods (n). The concept is integral in determining how much capital must be recovered to service debts or investments effectively.

This formula derives from the time value of money, where cash flows are adjusted for interest. It illustrates the relationship between the interest rate and the number of periods in which payments are made, allowing for the calculation of equal cash flows over time.

The other choices represent different financial concepts. For instance, a uniform gradient future worth factor calculates the future worth of cash flows that increase or decrease at a uniform rate. Single payment present worth refers to the current value of a single future payment discounted at a specific interest rate, while single payment compound amount deals with the total accumulated value of a single investment at a future date based on compound interest. However, the