How is variable compound interest calculated?

Variable compound interest is calculated using the formula that takes into account the effect of compounding over time. The correct formula, represented here, is P(1 + R/n)^(nt), where P is the principal amount, R is the annual interest rate (expressed as a decimal), n is the number of compounding periods per year, and t is the number of years.

This calculation effectively determines the total amount of money accumulated after a certain number of years, allowing for interest to be earned on both the initial principal and on the interest already added to that principal. The term (1 + R/n) represents the amount of interest earned in each compounding period, and raising this term to the power of nt accounts for all the compounding that occurs over the entire duration of the investment.

The other provided formulas do not adequately reflect the nature of variable compound interest. For instance, the first option ignores the number of compounding periods within a year, which is crucial for calculating compound interest accurately. The third option represents simple interest instead of compound interest and does not incorporate the effect of compounding over time, while the fourth option represents a straightforward multiplication rather than any form of interest calculation. Thus, the selected answer reflects the correct methodology for