Compound interest is the interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods. It's often referred to as "interest on interest," and it's a powerful tool for wealth growth over time. The longer your money is invested and the more frequently it compounds, the greater the impact of compounding.
Key Concepts:
Principal: The initial amount of money you invest or deposit.
Annual Interest Rate: The yearly rate at which your investment grows.
Number of Years: The duration for which your investment will grow.
Compounding Frequency: How often the interest is calculated and added to the principal. Common frequencies include annually (1), semi-annually (2), quarterly (4), monthly (12), or even daily (365). A higher compounding frequency generally leads to greater returns, assuming all other factors remain constant.
The Compound Interest Formula:
The future value of an investment with compound interest is calculated using the following formula:
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
Example Calculation:
Let's say you invest $5,000 (Principal) at an annual interest rate of 7% (Annual Interest Rate) for 15 years (Number of Years), with interest compounding monthly (Compounding Frequency = 12).
Using the formula:
P = 5000
r = 0.07 (7% as a decimal)
n = 12 (monthly compounding)
t = 15
A = 5000 * (1 + 0.07/12)^(12*15)
A ≈ 5000 * (1 + 0.0058333)^(180)
A ≈ 5000 * (1.0058333)^(180)
A ≈ 5000 * 2.8339
A ≈ $14,169.50
So, your initial investment of $5,000 would grow to approximately $14,169.50 after 15 years with monthly compounding at a 7% annual interest rate.
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 = parseFloat(document.getElementById("compoundingFrequency").value);
var resultDiv = document.getElementById("result");
if (isNaN(principal) || isNaN(annualRate) || isNaN(years) || isNaN(compoundingFrequency) ||
principal <= 0 || annualRate < 0 || years <= 0 || compoundingFrequency <= 0) {
resultDiv.innerHTML = "Please enter valid positive numbers for all fields.";
return;
}
var ratePerPeriod = annualRate / 100 / compoundingFrequency;
var numberOfPeriods = compoundingFrequency * years;
var futureValue = principal * Math.pow((1 + ratePerPeriod), numberOfPeriods);
resultDiv.innerHTML = "Future Value: $" + futureValue.toFixed(2) + "" +
"Total Interest Earned: $" + (futureValue – principal).toFixed(2) + "";
}