### How to calculate compound interest?

Calculating compound interest involves considering not only the initial principal amount and the interest rate but also the effect of reinvesting the interest earned over time. Compound interest leads to exponential growth of the invested amount. The formula for calculating compound interest is:

Compound Interest (CI) = P × (1 + r/n)^(nt) – P

Where:

• P is the principal amount (initial investment).
• r is the annual interest rate (as a decimal).
• n is the number of times interest is compounded per year.
• t is the number of years.

Here’s how you can calculate compound interest step by step:

1. Gather Information:
• Determine the principal amount (the initial sum of money).
• Find the annual interest rate (as a decimal, not percentage).
• Determine the number of times interest is compounded per year (n).
• Determine the time period in years (t).
2. Convert Rate to Decimal:
• Divide the annual interest rate by 100 to convert it to a decimal.
3. Calculate the Exponential Factor:
• Calculate the exponent in the formula: (1 + r/n)^(nt).
4. Plug Values into the Formula:
• Substitute the values you gathered into the compound interest formula: Compound Interest (CI) = P × (1 + r/n)^(nt) – P
5. Calculate the Result:
• Calculate the value of the exponential factor, subtract the principal amount (P), and then multiply by the principal to get the compound interest amount.

Example: Suppose you invest \$1,000 at an annual interest rate of 6%, compounded semiannually (n = 2), for 3 years.

• Principal (P) = \$1,000
• Rate (r) = 6% (convert to decimal: 0.06)
• Compounded semiannually (n) = 2
• Time (t) = 3 years

Using the formula: Exponential factor = (1 + 0.06/2)^(2*3) ≈ 1.191016 Compound Interest (CI) = 1000 × (1.191016) – 1000 ≈ \$191.02

So, the compound interest on \$1,000 at a rate of 6%, compounded semiannually for 3 years, is approximately \$191.02.