In scenario A, the formula to calculate the future value after 20 years is indeed Ct = PV (1 + r)20. This formula considers 20 compounding periods because the interest is applied annually. Each year, the interest is added to the initial principal (PV), and then the interest is calculated based on the new total for the next year.

This process repeats for 20 years.

If there were 10 compounding periods instead of 20, it would mean that the interest is applied every two years. In that case, the correct formula would be Ct = PV (1 + r)10, as you mentioned. However, in scenario A, the interest is applied annually, resulting in 20 compounding periods over the course of 20 years.

Therefore, to accurately calculate the future value after 20 years in scenario A, we use the formula Ct = PV (1 + r)20, considering 20 compounding periods.

Does mean that compounding period is each 2 year?