Compound interest

Definition

Compound interest is the interest calculated on the initial principal and also on the accumulated interest of previous periods. It is commonly used in finance and investments to calculate growth over time.

5 Must Know Facts For Your Next Test

1. The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after n years, including interest.
2. $P$ represents the principal amount (the initial sum of money), $r$ is the annual interest rate (decimal), $n$ is the number of times that interest is compounded per year, and $t$ is the time in years.
3. Compound interest results in exponential growth because it includes interest on both the initial principal and the accumulated interest from previous periods.
4. When compounding continuously, the formula becomes $A = Pe^{rt}$, using Euler's number ($e \approx 2.71828$).
5. The more frequently interest is compounded within a given period, the higher the total amount of compound interest will be.

Review Questions

• What does each variable represent in the compound interest formula $A = P(1 + \frac{r}{n})^{nt}$?
• How does increasing the frequency of compounding affect the total amount of compound interest?
• What formula do you use for continuous compounding?

Related terms

Exponential Growth:

Growth whose rate becomes ever more rapid in proportion to the growing total number or size.

Principal: The initial sum of money placed in an account or invested.

$e$ (Euler's Number): $e$ is a mathematical constant approximately equal to 2.71828, used as a base for natural logarithms and continuous compounding.