Compound interest

Definition

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. It can be expressed mathematically using exponential functions.

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. Exponential growth in compound interest is characterized by a constant relative growth rate.
3. Continuous compounding can be represented as $A = Pe^{rt}$ where $e$ is Euler's number, approximately equal to 2.71828.
4. In integration applications, compound interest problems often involve finding the integral of an exponential function to determine future values.
5. Exponential decay, conversely, involves negative growth rates and can model scenarios like depreciation or radioactive decay.

Review Questions

• What is the difference between simple and compound interest in terms of their formulas?
• How do you express continuously compounded interest using an exponential function?
• What role does Euler's number ($e$) play in the formula for continuous compounding?

Related terms

Exponential Growth: A process that increases quantity over time at a rate proportional to its current value.

Exponential Decay: A process where quantities decrease over time at a rate proportional to its current value.

$e$ (Euler's Number): An irrational number approximately equal to 2.71828 used as the base for natural logarithms and continuous compounding.