If the payback period is 6 months, what is the annualized value of an ROI of 50%?

The annualized value of a return on investment (ROI) can be calculated using the payback period, which indicates how long it takes for an investment to generate enough income to recover its initial cost. In this case, if the payback period is 6 months for an investment with an ROI of 50%, it indicates that the investment returns 50% of the original investment over the course of those 6 months.

To annualize this ROI, we need to consider how many 6-month periods fit into a year. There are two 6-month periods in a year. Therefore, if the investment returns 50% in 6 months, it would theoretically double that ROI in a full year, leading to an annualized ROI of 100%.

However, when considering compounded returns, if you invest at a 50% ROI for 6 months, you can calculate the annualized ROI more accurately by applying the formula for effective annual return:

[ \text{Annualized ROI} = (1 + \text{ROI})^{n} - 1 ]

Here, ( n = 2 ) for two 6-month periods. Thus, it becomes:

[ \text{Annualized ROI} = (1 +