Compound interest

Definition

Compound interest is the interest calculated on the initial principal, which also includes all accumulated interest from previous periods. It can be expressed by the formula $A = P(1 + \frac{r}{n})^{nt}$ where A is the amount of money accumulated after n years, including interest.

5 Must Know Facts For Your Next Test

1. The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$.
2. In the compound interest formula, P represents the initial principal balance.
3. $r$ in the formula stands for the annual interest rate (decimal).
4. $n$ denotes the number of times that interest is compounded per unit time.
5. Compound interest grows faster than simple interest because it accumulates on previously earned interest.

Review Questions

• What does each variable represent in the compound interest formula $A = P(1 + \frac{r}{n})^{nt}$?
• How does increasing the number of compounding periods per year affect the total amount of compound interest earned?
• Why does compound interest grow faster than simple interest?

Related terms

Principal: The original sum of money invested or loaned, before any interest.

Annual Interest Rate: The percentage increase per year applied to an investment or loan.

Exponential Growth: \textgrowth pattern characterized by an accelerating increase as a function of time, similar to how compound interest accumulates.