Mortgage Interest Rate Calculator

Compound Interest Savings Calculator

Investment Summary

Total Balance

Total Principal

Total Interest

function calculateCompoundInterest() { var p = parseFloat(document.getElementById('initialDeposit').value); var pmt = parseFloat(document.getElementById('monthlyDeposit').value); var r = parseFloat(document.getElementById('interestRate').value) / 100; var t = parseFloat(document.getElementById('years').value); var n = parseInt(document.getElementById('frequency').value); if (isNaN(p) || isNaN(pmt) || isNaN(r) || isNaN(t)) { alert("Please enter valid numerical values."); return; } // Compound interest formula for principal: A = P(1 + r/n)^(nt) var amountFromPrincipal = p * Math.pow(1 + (r / n), n * t); // Future value of a series (contributions): PMT * [((1 + r/n)^(nt) – 1) / (r/n)] // We adjust for monthly contributions even if compounding is different var monthlyRate = r / 12; var totalMonths = t * 12; var amountFromContributions = 0; if (r > 0) { amountFromContributions = pmt * (Math.pow(1 + r/n, n * t) – 1) / (r/n) * (1 / (n/12)); // Note: This is a simplified approximation for monthly contributions compounding n times per year // For accuracy with monthly deposits: var periodicRate = r / n; var periods = n * t; var contributionPerPeriod = pmt * (12 / n); amountFromContributions = contributionPerPeriod * (Math.pow(1 + periodicRate, periods) – 1) / periodicRate; } else { amountFromContributions = pmt * 12 * t; } var totalBalance = amountFromPrincipal + amountFromContributions; var totalInvested = p + (pmt * 12 * t); var totalInterest = totalBalance – totalInvested; document.getElementById('totalBalance').innerText = "$" + totalBalance.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById('totalPrincipal').innerText = "$" + totalInvested.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById('totalInterest').innerText = "$" + totalInterest.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById('resultsArea').style.display = 'block'; }

---

Understanding the Power of Compound Interest

Compound interest is often referred to as the "eighth wonder of the world." Unlike simple interest, which is calculated only on the principal amount, compound interest is calculated on the principal plus the accumulated interest from previous periods. This creates a "snowball effect" where your money grows at an accelerating rate over time.

The Compound Interest Formula

The standard formula for compound interest including monthly contributions is:

A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) – 1) / (r/n)]

• A = The future value of the investment
• P = Initial principal balance
• r = Annual interest rate (decimal)
• n = Number of times interest is compounded per year
• t = Number of years the money is invested
• PMT = Monthly contribution amount

Example Calculation

Suppose you start with $5,000 and contribute $200 every month into an index fund with an average annual return of 8%, compounded monthly. After 20 years:

• Your total contributions would be $53,000 ($5,000 initial + $48,000 monthly).
• Your total balance would grow to approximately $141,945.
• You would have earned over $88,000 in interest alone.

Why Compounding Frequency Matters

The more frequently interest is compounded, the faster your investment grows. For instance, interest compounded daily will result in a slightly higher return than interest compounded annually on the same nominal rate. This is because your interest begins earning interest sooner. Most high-yield savings accounts compound daily or monthly, while many bonds compound semi-annually.

Tips for Maximizing Growth

1. Start Early: Time is the most critical variable. The longer your money has to compound, the more dramatic the growth becomes in the final years.
2. Be Consistent: Regular monthly contributions, even small ones, significantly increase the ending balance compared to a one-time deposit.
3. Minimize Fees: High management fees can eat into your compounding returns over decades. Look for low-cost index funds or ETFs.
4. Reinvest Dividends: Ensure that any dividends or interest earned are automatically reinvested back into the account to keep the compounding cycle moving.