The compound interest formula calculates the interest on both the initial principal and the accumulated interest from previous periods. The general formula for the compound amount AAA when the interest is compounded nnn times per year is:

A=P(1+rn)ntA=P\left(1+\frac{r}{n}\right)^{nt}A=P(1+nr​)nt

where:

• PPP is the principal amount,
• rrr is the annual interest rate (in decimal form),
• nnn is the number of compounding periods per year,
• ttt is the total number of years.

The compound interest CICICI is then found by subtracting the principal from the compound amount:

CI=P(1+rn)nt−PCI=P\left(1+\frac{r}{n}\right)^{nt}-PCI=P(1+nr​)nt−P

If the interest is compounded annually (n=1n=1n=1), the formula simplifies to:

A=P(1+r)tA=P(1+r)^tA=P(1+r)t

CI=P(1+r)t−PCI=P(1+r)^t-PCI=P(1+r)t−P

This formula reflects how interest is calculated on both the original principal and the accumulated interest, which leads to exponential growth over time.