The formula for compound interest is:

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

Where:

• A = the future value of the investment/loan, including interest
• P = the principal investment/loan amount (the initial deposit or loan)
• r = the annual interest rate (decimal)
• n = the number of times the interest is compounded per year
• t = the number of years the money is invested or borrowed for

Example:

If you invest $1000 at an annual interest rate of 5%, compounded quarterly, for 3 years, the formula would look like this:

$A = 1000 \left(1 + \frac{0.05}{4}\right)^{4 \times 3} = 1000 \left(1 + 0.0125\right)^{12} \approx 1000 \times (1.0125)^{12} \approx 1000 \times 1.1616 \approx 1161.60$

So, after 3 years, the investment would grow to approximately $1161.60.

Would you like any further details on this? If so, I can walk you through another example or explain specific terms!

Here are some related questions you may find interesting:

1. How do you calculate compound interest for different compounding frequencies (e.g., monthly vs annually)?
2. What happens to the future value as the number of compounding periods increases?
3. How does the compound interest formula differ from the simple interest formula?
4. How can compound interest be used to compare different investment opportunities?
5. How do changes in the interest rate affect the compound interest calculation?

Tip: The more frequently interest is compounded, the more total interest you'll earn, as the interest is calculated on a growing balance more often.