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 grows at an exponential rate, unlike simple interest which grows linearly.

5 Must Know Facts For Your Next Test

1. Compound interest can be modeled using the exponential function $A = P e^{rt}$, where $P$ is the principal amount, $r$ is the annual interest rate, and $t$ is time in years.
2. The formula for compound interest with different compounding intervals is $A = P (1 + \frac{r}{n})^{nt}$, where $n$ is the number of times interest is compounded per year.
3. Continuous compounding can be represented as $A = Pe^{rt}$, taking the limit as $n$ approaches infinity.
4. In integration applications, you might need to integrate functions involving compound interest over a certain period to find total growth or decay.
5. The effective annual rate (EAR) can be calculated using compound interest to compare different compounding intervals.

Review Questions

• What is the difference between simple and compound interest?
• How does continuous compounding affect the growth of an investment compared to annual compounding?
• What does the variable $n$ represent in the compound interest formula?

Related terms

Exponential Growth:

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

Decay Rate:

The rate at which a quantity decreases over time.

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