Which equation represents compound interest?

The equation representing compound interest is correctly identified as FV = PV (1 + r/m)^(mt). This formula captures how compound interest is calculated over multiple periods.

In this equation:

• FV stands for the future value of the investment or loan, which is the amount of money accrued after interest has been applied.

• PV represents the present value, or the initial amount of money that is being invested or loaned.
• r indicates the annual nominal interest rate (in decimal form).
• m denotes the number of times interest is compounded within a year.
• t is the number of years the money is invested or borrowed.

The key aspect of compound interest is that interest is calculated on both the initial principal and the accumulated interest from previous periods. By dividing r by m, the formula accounts for the effective interest rate applied during each compounding period. Raising the expression (1 + r/m) to the power of (mt) captures the effect of compounding over the total number of periods.

This is essential for understanding how investment growth can accelerate over time due to compounding, distinguishing it from simple interest, where the interest is calculated only on the initial principal.