Understanding Compound Interest
Compound interest, often called "interest on interest," is a powerful tool for wealth accumulation. It works by adding the interest earned during a period to the principal amount. In the next period, interest is calculated on this new, larger principal.
The Formula
The formula for compound interest is:
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
Why it Matters
The key to compound interest is time and consistency. The longer your money is invested and the more frequently it is compounded, the greater the impact of compounding. Even small amounts can grow significantly over long periods.
Example Calculation
Let's say you invest $1000 (P) at an annual interest rate of 5% (r = 0.05), compounded monthly (n = 12), for 10 years (t).
- A = 1000 * (1 + 0.05/12)^(12*10)
- A = 1000 * (1 + 0.00416667)^120
- A = 1000 * (1.00416667)^120
- A = 1000 * 1.647009
- A ≈ $1647.01
In this example, the future value would be approximately $1647.01, meaning you earned about $647.01 in interest.
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function calculateCompoundInterest() {
var principal = parseFloat(document.getElementById("principal").value);
var annualInterestRate = parseFloat(document.getElementById("annualInterestRate").value);
var compoundingFrequency = parseFloat(document.getElementById("compoundingFrequency").value);
var timeInYears = parseFloat(document.getElementById("timeInYears").value);
if (isNaN(principal) || isNaN(annualInterestRate) || isNaN(compoundingFrequency) || isNaN(timeInYears)) {
document.getElementById("futureValue").textContent = "Invalid input";
document.getElementById("totalInterestEarned").textContent = "";
return;
}
var ratePerPeriod = annualInterestRate / 100 / compoundingFrequency;
var numberOfPeriods = compoundingFrequency * timeInYears;
var futureValue = principal * Math.pow((1 + ratePerPeriod), numberOfPeriods);
var totalInterestEarned = futureValue – principal;
document.getElementById("futureValue").textContent = "$" + futureValue.toFixed(2);
document.getElementById("totalInterestEarned").textContent = "$" + totalInterestEarned.toFixed(2);
}