Compound Interest Calculator
Understanding Compound Interest
Compound interest is the interest earned on both the initial principal and the accumulated interest from previous periods. It's often described as "interest on interest," and it's a powerful tool for growing wealth over time. Unlike simple interest, which is only calculated on the principal amount, compound interest allows your investment to grow at an accelerating rate.
How It Works:
The magic of compounding lies in its exponential growth potential. When interest is calculated and added to the principal, the new, larger principal then earns interest in the next period. This cycle repeats, causing your investment to grow faster and faster.
Key Factors:
- Principal: The initial amount of money invested or borrowed.
- Interest Rate: The percentage of the principal charged as interest over a given period.
- Compounding Frequency: How often the interest is calculated and added to the principal. More frequent compounding (e.g., daily or monthly) generally leads to higher returns than less frequent compounding (e.g., annually).
- Time: The longer your money is invested, the more significant the effect of compounding becomes.
The Formula:
The future value of an investment with compound interest is calculated using the following formula:
A = P (1 + r/n)^(nt)
- 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
Example Calculation:
Let's say you invest $1,000 (Principal) at an annual interest rate of 5% (r=0.05), compounded quarterly (n=4), for 10 years (t=10).
A = 1000 * (1 + 0.05/4)^(4*10)
A = 1000 * (1 + 0.0125)^40
A = 1000 * (1.0125)^40
A = 1000 * 1.643619…
A ≈ $1,643.62
So, after 10 years, your initial investment of $1,000 would grow to approximately $1,643.62, meaning you've earned $643.62 in compound interest.
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function calculateCompoundInterest() {
var principal = parseFloat(document.getElementById("principal").value);
var annualInterestRate = parseFloat(document.getElementById("annualInterestRate").value);
var compoundingFrequency = parseInt(document.getElementById("compoundingFrequency").value);
var years = parseFloat(document.getElementById("years").value);
var resultDiv = document.getElementById("result");
if (isNaN(principal) || principal < 0 ||
isNaN(annualInterestRate) || annualInterestRate < 0 ||
isNaN(compoundingFrequency) || compoundingFrequency <= 0 ||
isNaN(years) || years < 0) {
resultDiv.innerHTML = "
Please enter valid positive numbers for all fields.";
return;
}
var ratePerPeriod = annualInterestRate / 100 / compoundingFrequency;
var numberOfPeriods = compoundingFrequency * years;
var futureValue = principal * Math.pow(1 + ratePerPeriod, numberOfPeriods);
var totalInterestEarned = futureValue – principal;
// Format numbers to two decimal places
var formattedFutureValue = futureValue.toFixed(2);
var formattedTotalInterestEarned = totalInterestEarned.toFixed(2);
resultDiv.innerHTML = "
Results:
" +
"Future Value:
$" + formattedFutureValue + "" +
"Total Compound Interest Earned:
$" + formattedTotalInterestEarned + "";
}