what is compound interest and give an example

**Compound interest** refers to the interest on a loan or deposit that is calculated based on both the initial principal and the accumulated interest from previous periods. Unlike simple interest, which is calculated only on the principal, compound interest allows the interest to "compound," or grow exponentially over time.

The formula for compound interest is:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $A$ = the amount of money accumulated after $n$ years, including interest.
- $P$ = the principal (initial investment).
- $r$ = the annual interest rate (decimal).
- $n$ = the number of times that interest is compounded per year.
- $t$ = the time the money is invested or borrowed for, in years.

### Example
Suppose you invest $1,000 in a bank that offers an annual interest rate of 5%, compounded annually for 3 years.

- $P = 1000$
- $r = 0.05$
- $n = 1$ (since it's compounded annually)
- $t = 3$

Using the formula:

\[
A = 1000 \left(1 + \frac{0.05}{1}\right)^{1 \times 3} = 1000 \left(1.05\right)^3 \approx 1000 \times 1.157625 = 1157.63
\]

So, after 3 years, the investment will grow to **$1,157.63**, earning **$157.63** in interest.

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### Related Questions:
1. What is the difference between simple and compound interest?
2. How does the frequency of compounding affect the total interest earned?
3. Can compound interest work negatively in loans (like mortgages)?
4. What are some real-life applications of compound interest?
5. How does compound interest behave with continuous compounding?

### Tip:
The more frequently interest is compounded, the more interest is accrued over time.

Learn about compound interest and how it works using a real-life example. Discover how a $1000 investment grows with a 5% annual interest rate compounded over 3 years. Suitable for students in Grades 9-12, this example demonstrates the power of exponential growth and the compound interest formula.

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