Compound interest is the interest calculated on the initial principal, which also includes all the accumulated interest from previous periods. In other words, interest is earned not only on the original amount of money but also on the interest that has been added 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 $t$ years, including interest.
• $P$ = the principal amount (the initial investment or loan).
• $r$ = the annual interest rate (in decimal form, so 5% would be 0.05).
• $n$ = the number of times interest is compounded per year.
• $t$ = the time the money is invested or borrowed for, in years.

Example

If you invest $1,000 at an annual interest rate of 5%, compounded yearly for 3 years, the formula would be applied as:

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

So after 3 years, your investment would grow to approximately $1,157.63.

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Would you like further details or any clarifications?

5 Related Questions:

1. What is the difference between simple interest and compound interest?
2. How does the frequency of compounding affect the total interest earned?
3. What are some real-life examples of compound interest?
4. How can you calculate compound interest when it's compounded continuously?
5. What impact does the interest rate have on compound interest growth?

Tip:

To maximize your gains with compound interest, try to invest early and take advantage of accounts with higher compounding frequencies (monthly, daily, etc.).