Compound Interest Calculator
Understanding Compound Interest
Compound interest is often called the "eighth wonder of the world" because of its power to grow wealth over time. It's essentially "interest on interest." Unlike simple interest, where interest is calculated only on the initial principal amount, compound interest is calculated on the principal amount plus any accumulated interest from previous periods.
How It Works:
Imagine you invest $1,000 at an annual interest rate of 5%, compounded annually.
- Year 1: You earn 5% interest on $1,000, which is $50. Your total is now $1,050.
- Year 2: You earn 5% interest on $1,050, which is $52.50. Your total is now $1,102.50.
- Year 3: You earn 5% interest on $1,102.50, which is approximately $55.13. Your total is now $1,157.63.
As you can see, the amount of interest earned each year increases because the interest is added to the principal, and the next interest calculation is based on this larger sum. This effect snowballs over time, leading to significantly higher returns compared to simple interest.
The Formula:
The future value of an investment with compound interest can be calculated using the following formula:
FV = P (1 + r/n)^(nt)
Where:
- FV = Future Value of the investment/loan, including interest
- P = Principal investment amount (the initial deposit or loan amount)
- r = Annual interest rate (as a decimal)
- n = Number of times that interest is compounded per year
- t = Number of years the money is invested or borrowed for
Factors Affecting Compound Interest:
- Principal Amount: A larger initial investment will result in a larger future value.
- Interest Rate: Higher interest rates accelerate wealth growth dramatically.
- Time: The longer your money is invested, the more significant the compounding effect becomes. This is why starting to invest early is crucial.
- Compounding Frequency: The more frequently interest is compounded (e.g., daily vs. annually), the slightly higher the future value will be, though the difference becomes less pronounced with very high frequencies.
Our calculator helps you visualize how these factors can impact your investment's growth. Experiment with different values to see the potential of compounding!
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function calculateCompoundInterest() {
var principal = parseFloat(document.getElementById("principal").value);
var annualRate = parseFloat(document.getElementById("annualRate").value);
var time = parseFloat(document.getElementById("time").value);
var compoundingFrequency = parseInt(document.getElementById("compoundingFrequency").value);
var resultElement = document.getElementById("result");
if (isNaN(principal) || isNaN(annualRate) || isNaN(time) || isNaN(compoundingFrequency)) {
resultElement.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (principal <= 0 || annualRate < 0 || time <= 0 || compoundingFrequency <= 0) {
resultElement.innerHTML = "Please enter positive values for principal, time, and compounding frequency, and a non-negative rate.";
return;
}
var rateDecimal = annualRate / 100;
var numberOfPeriods = time * compoundingFrequency;
var futureValue = principal * Math.pow((1 + rateDecimal / compoundingFrequency), numberOfPeriods);
resultElement.innerHTML = "Future Value: $" + futureValue.toFixed(2);
}