Compound Interest Calculator
Understanding Compound Interest
Compound interest is often called the "eighth wonder of the world" because of its power to grow your investments over time. Unlike simple interest, which is calculated only on the initial principal amount, compound interest is calculated on the initial principal plus the accumulated interest from previous periods. This means your money works harder for you, generating earnings on your earnings.
How Compound Interest Works
The magic of compounding lies in its exponential growth. Let's break down the formula:
A = P (1 + r/n)^(nt)
Where:
- A is the future value of the investment/loan, including interest
- P is the principal investment amount (the initial deposit or loan amount)
- r is the annual interest rate (as a decimal)
- n is the number of times that interest is compounded per year
- t is the number of years the money is invested or borrowed for
Key Factors Influencing Compound Growth
- Principal Amount (P): The larger your initial investment, the more significant the impact of compounding.
- Interest Rate (r): A higher interest rate leads to faster growth. Even small differences in rates can make a big difference over long periods.
- Compounding Frequency (n): The more frequently interest is compounded (e.g., daily vs. annually), the greater the total return. This is because interest starts earning interest sooner.
- Time Period (t): This is arguably the most powerful factor. The longer your money is invested and compounds, the more dramatic the growth becomes. Patience is key to harnessing the full potential of compound interest.
Example Calculation
Let's say you invest $5,000 (P) with an annual interest rate of 7% (r = 0.07). If the interest is compounded monthly (n = 12) for 20 years (t):
A = 5000 * (1 + 0.07/12)^(12*20)
A = 5000 * (1 + 0.00583333)^240
A = 5000 * (1.00583333)^240
A = 5000 * 3.99936…
A ≈ $19,996.80
In this example, your initial $5,000 would grow to approximately $19,996.80 after 20 years, meaning you earned about $14,996.80 in interest!
Our calculator helps you explore different scenarios and visualize how your investments can grow through the power of compounding.
function calculateCompoundInterest() {
var principal = parseFloat(document.getElementById("principalAmount").value);
var rate = parseFloat(document.getElementById("annualInterestRate").value);
var frequency = parseInt(document.getElementById("compoundingFrequency").value);
var time = parseFloat(document.getElementById("timePeriod").value);
var resultDiv = document.getElementById("result");
if (isNaN(principal) || isNaN(rate) || isNaN(frequency) || isNaN(time) ||
principal < 0 || rate < 0 || frequency <= 0 || time < 0) {
resultDiv.innerHTML = "Please enter valid positive numbers for all fields.";
return;
}
var rateDecimal = rate / 100;
var compoundInterest = principal * Math.pow((1 + rateDecimal / frequency), (frequency * time));
var totalInterestEarned = compoundInterest – principal;
resultDiv.innerHTML = "
Calculation Results
" +
"
Initial Investment: $" + principal.toFixed(2) + "" +
"
Annual Interest Rate: " + rate.toFixed(2) + "%" +
"
Compounding Frequency: " + getFrequencyDescription(frequency) + "" +
"
Time Period: " + time + " years" +
"
Total Amount (Principal + Interest): $" + compoundInterest.toFixed(2) + "" +
"
Total Interest Earned: $" + totalInterestEarned.toFixed(2) + "";
}
function getFrequencyDescription(frequency) {
switch (frequency) {
case 1: return "Annually";
case 2: return "Semi-Annually";
case 4: return "Quarterly";
case 12: return "Monthly";
case 52: return "Weekly";
case 365: return "Daily";
default: return "Custom";
}
}
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