What is the formula to calculate compound interest?

To calculate compound interest, the formula used is:

A = P(1 + r/n)^(nt)

Where:
A = the future value of the investment/loan, including interest
P = the principal amount (initial investment/loan amount)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years

Here's how to calculate compound interest step by step:

1. Determine the principal amount (P) and the annual interest rate (r). For example, let's say you have $10,000 as the principal amount and an annual interest rate of 5% (0.05).

2. Check how many times the interest is compounded per year (n). For instance, if it's compounded annually, then n = 1. If it's compounded semiannually, n = 2. If it's compounded quarterly, n = 4.

3. Determine the time period (t) in years. Let's assume you want to calculate the compound interest for 3 years.

4. Plug the values into the compound interest formula: A = P(1 + r/n)^(nt)
A = $10,000(1 + 0.05/1)^(1*3)

5. Simplify the equation in brackets: (1 + 0.05/1)^(1*3) becomes (1.05)^3.

6. Calculate the value of (1.05)^3: 1.05 * 1.05 * 1.05 = 1.157625.

7. Multiply the principal amount with the simplified equation: $10,000 * 1.157625 = $11,576.25.

Therefore, the future value of the investment/loan (A) after 3 years with an initial principal amount of $10,000 and an annual interest rate of 5% compounded annually, would be $11,576.25.