What formula is used to calculate compound interest?

The formula used to calculate compound interest is derived from the concept of growth over time due to interest being calculated on the initial principal and also on the accumulated interest from previous periods.

In the correct formula, the principal amount is multiplied by the quantity of one plus the interest rate (expressed as a decimal) raised to the power of the time period (in years or whatever time unit is appropriate). This reflects the exponential growth of the investment or loan over time as interests are added to the principal.

For example, if an amount is invested at a fixed interest rate, the interest earned in the first year is added to the principal, meaning that in the second year, interest is calculated not just on the original amount but also on the interest previously earned. This compound effect results in a larger amount earned or owed over time compared to simple interest calculations, which do not account for interest on accumulated interest.

The other provided formulas do not accurately represent how compound interest is calculated. Some suggest linear calculations or are structured in a way that doesn't account for the compounding effect, which is essential to understanding how investments grow under compound interest.