Understanding Compound Interest
What is Compound Interest?
Compound interest is the interest on a loan or deposit that is calculated based on both the initial principal and the accumulated interest from previous periods. It is a powerful concept in finance and investments because it allows your money to grow exponentially over time.
How does Compound Interest work?
Compound interest works by reinvesting the interest earned, rather than paying it out. This means that in each period, the interest earned is added to the principal, so the principal amount grows, and more interest is earned in the next period. The formula for compound interest is:
Compound Interest Formula:
Understanding the Formula:
The formula might seem complicated, but it can be broken down into simpler parts:
- Principal (P): This is the initial amount of money you start with.
- Interest Rate (r): This is the annual interest rate, expressed as a decimal. For example, if your interest rate is 5%, you would use 0.05 in the formula.
- Number of Times Compounded (n): This is how often the interest is applied to your balance per year. Common compounding periods are annually (once a year), semi-annually (twice a year), quarterly (four times a year), monthly (twelve times a year), and daily (365 times a year).
- Time (t): This is the total time the money is invested or borrowed for, in years.
- Accumulated Amount (A): This is the total amount of money accumulated after the interest has been applied over the specified time period.
To use the formula, you first convert the annual interest rate from a percentage to a decimal by dividing by 100. Then, you divide this rate by the number of compounding periods per year. Next, you add 1 to this value, raise the result to the power of the total number of compounding periods (n multiplied by t), and finally multiply by the principal amount (P).
Converting percentage to decimal:
Interest rates are often given as a percentage. To use the formula, you need to convert the percentage to a decimal. To do this, divide the percentage by 100. For example, if the annual interest rate is 5%, convert it to decimal form by dividing 5 by 100, which equals 0.05.
Examples of Compound Interest
Let’s look at a few examples to better understand how compound interest works.
Example 1: Annual Compounding
Suppose you invest $1,000 at an annual interest rate of 5%, compounded annually for 10 years. Using the formula:
After 10 years, your investment would grow to approximately $1,628.89.
Example 2: Quarterly Compounding
Suppose you invest $1,000 at an annual interest rate of 5%, compounded quarterly for 10 years. Using the formula:
After 10 years, your investment would grow to approximately $1,643.62.