Which type of interest is compounded at the end of each finite length period?

The correct answer is Discrete Compounding, which refers to interest that is added (compounded) at the end of defined, specific intervals of time, such as annually, semi-annually, quarterly, or monthly. This periodic compounding allows for the interest earned during each period to be calculated based on the principal and any interest that has already been accrued up until that point.

In the context of discrete compounding, the process can be visualized as follows: at the end of each period, the interest is calculated, added to the principal, and then the new total becomes the basis for calculating interest in the next period. This approach aligns with many traditional savings accounts and loans where the interest is calculated and paid out at consistent intervals rather than continuously.

Other forms of compounding, such as continuous compounding, imply that interest is computed and added to the principal at every possible instant, resulting in a different calculation method and growth rate for the investment or loan. The concept of discrete payment or continuous payment typically pertains more to cash flow management or loan repayment structures rather than the specific question regarding compounding periods. Thus, the discrete compounding model is the appropriate choice for interest that is compounded at fixed finite intervals.