Which formula calculates compound interest when compounding occurs more than once per year?

The formula that calculates compound interest when compounding occurs more than once per year is indeed represented by the second option: P x (1 + [i/m])^mn.

In this formula, P represents the principal amount (the initial sum of money), i is the annual interest rate expressed as a decimal, m is the number of times interest is compounded in one year, and n is the total number of years the money is invested or borrowed.

The expression [i/m] adjusts the annual interest rate to reflect the interest rate applicable for each compounding period. By dividing the annual interest rate by m, you get the interest rate per compounding period. Raising this adjusted term to the power of mn accounts for how many compounding periods occur over the entire investment duration.

This formula is essential for accurately calculating compound interest in situations where interest is not simply added annually, providing a more nuanced and beneficial understanding of how your investment grows over time when reinvested more frequently.