function calculateSavings() {
var P = parseFloat(document.getElementById('initialDeposit').value);
var PMT = parseFloat(document.getElementById('monthlyContribution').value);
var annualRate = parseFloat(document.getElementById('nominalRate').value) / 100;
var n = parseInt(document.getElementById('compoundingPeriod').value);
var t = parseFloat(document.getElementById('years').value);
if (isNaN(P) || isNaN(annualRate) || isNaN(t)) {
alert("Please enter valid numbers for deposit, rate, and years.");
return;
}
if (isNaN(PMT)) PMT = 0;
// 1. Calculate APY
// APY = (1 + r/n)^n – 1
var apy = (Math.pow((1 + annualRate / n), n) – 1) * 100;
// 2. Future Value of Initial Deposit
// FV = P * (1 + r/n)^(n*t)
var fvPrincipal = P * Math.pow((1 + annualRate / n), (n * t));
// 3. Future Value of Monthly Contributions
// We must adjust for monthly contributions vs compounding frequency
// Standard formula for monthly PMT with monthly compounding:
// FV = PMT * [((1 + r/12)^(12*t) – 1) / (r/12)]
var rMonthly = annualRate / 12;
var months = t * 12;
var fvContributions = 0;
if (rMonthly > 0) {
fvContributions = PMT * (Math.pow((1 + rMonthly), months) – 1) / rMonthly;
} else {
fvContributions = PMT * months;
}
var totalBalance = fvPrincipal + fvContributions;
var totalDeposits = P + (PMT * months);
var totalInterest = totalBalance – totalDeposits;
document.getElementById('resAPY').innerText = apy.toFixed(3) + "%";
document.getElementById('resTotal').innerText = "$" + totalBalance.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
document.getElementById('resDeposits').innerText = "$" + totalDeposits.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
document.getElementById('resInterest').innerText = "$" + totalInterest.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
document.getElementById('savingsResult').style.display = 'block';
}
Understanding Savings Rates and APY
When you open a high-yield savings account or a Certificate of Deposit (CD), you are often presented with two different numbers: the Interest Rate (APR) and the Annual Percentage Yield (APY). While they sound similar, understanding the difference is key to maximizing your wealth accumulation.
What is APY?
APY, or Annual Percentage Yield, represents the real rate of return on your savings taking into account the effect of compound interest. Unlike simple interest, compound interest is calculated on both the initial principal and the accumulated interest from previous periods.
The formula used in this calculator for APY is:
APY = (1 + r/n)^n – 1
r = The nominal interest rate (APR)
n = The number of compounding periods per year
Why Compounding Frequency Matters
The more frequently your interest compounds, the higher your APY will be. For example, if you have a 5% nominal interest rate:
Annual Compounding: 5.00% APY
Monthly Compounding: 5.12% APY
Daily Compounding: 5.13% APY
Over several years and with large balances, these small fractions can translate into hundreds or thousands of dollars in extra interest.
APY vs. APR: What's the Difference?
Generally, APR (Annual Percentage Rate) is used for loans and credit cards. It tells you the simple interest cost of borrowing. APY is used for savings accounts and investments. It tells you what you will actually earn after compounding is factored in. Always look for the APY when comparing savings accounts to get an "apples-to-apples" comparison.
Example Calculation
Imagine you deposit $10,000 into a high-yield savings account with a 4.00% interest rate compounded monthly, and you add $500 every month for 5 years.
Total Deposits: $40,000 ($10k initial + $30k contributions)
Effective APY: 4.074%
Total Interest Earned: Approximately $4,465
Final Balance: $44,465
By using this calculator, you can play with different contribution amounts and interest rates to see how quickly your "nest egg" can grow through the power of consistent saving and compounding interest.