Compound interest is the interest calculated on the initial principal and also on the accumulated interest of previous periods. It's often referred to as "interest on interest." This powerful concept is a cornerstone of long-term investing and wealth building because it allows your money to grow exponentially over time.
How Compound Interest Works
Unlike simple interest, which is only calculated on the principal amount, compound interest adds the earned interest back to the principal. In the next period, interest is calculated on this new, larger amount. This snowball effect means your investment grows at an accelerating rate.
The formula for compound interest is:
A = P (1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for
Key Factors Influencing Compound Growth
Principal Amount: The larger your initial investment, the more potential for growth.
Interest Rate: A higher annual interest rate leads to faster compounding.
Time: The longer your money is invested, the more time it has to compound and grow. Time is arguably the most crucial factor in harnessing the power of compounding.
Compounding Frequency: Interest that is compounded more frequently (e.g., daily vs. annually) will yield slightly higher returns due to the earlier addition of interest to the principal.
Example Calculation
Let's say you invest $5,000 (Principal) with an annual interest rate of 7% (Annual Rate) for 20 years (Number of Years), and the interest is compounded quarterly (Compounding Frequency = 4).
Using the formula:
A = 5000 * (1 + 0.07/4)^(4*20)
A = 5000 * (1 + 0.0175)^(80)
A = 5000 * (1.0175)^80
A = 5000 * 3.9960...
A ≈ $19,980.09
This means your initial $5,000 investment would grow to approximately $19,980.09 after 20 years, with over $14,980 of that being earned interest!
Our calculator helps you explore these scenarios and understand the potential of your investments through the magic of compound interest.
function calculateCompoundInterest() {
var principal = parseFloat(document.getElementById("principal").value);
var annualRate = parseFloat(document.getElementById("annualRate").value);
var years = parseFloat(document.getElementById("years").value);
var compoundingFrequency = parseInt(document.getElementById("compoundingFrequency").value);
var resultDiv = document.getElementById("result");
if (isNaN(principal) || isNaN(annualRate) || isNaN(years) || isNaN(compoundingFrequency)) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (principal <= 0 || annualRate < 0 || years <= 0 || compoundingFrequency <= 0) {
resultDiv.innerHTML = "Please enter positive values for principal, years, and compounding frequency, and a non-negative interest rate.";
return;
}
var ratePerPeriod = annualRate / 100 / compoundingFrequency;
var numberOfPeriods = years * compoundingFrequency;
var futureValue = principal * Math.pow((1 + ratePerPeriod), numberOfPeriods);
var totalInterestEarned = futureValue – principal;
resultDiv.innerHTML = "