Your Projected Balance: $0.00
Total Interest Earned: $0.00
Understanding Annual Percentage Yield (APY)
The Annual Percentage Yield (APY) is a normalized representation of an interest rate that accounts for compounding. It tells you the real rate of return you will earn on an investment over a year, assuming the interest is compounded over that period. Unlike the Annual Percentage Rate (APR), which simply states the nominal interest rate, APY includes the effect of earning interest on previously earned interest. This makes APY a more accurate measure of your actual earnings, especially for savings accounts, certificates of deposit (CDs), and other interest-bearing financial products.
How APY is Calculated
The formula for APY is generally derived from the periodic interest rate and the number of compounding periods per year. However, when considering monthly contributions and a specific time frame, the calculation becomes more complex, involving future value of an annuity.
For this calculator, we first determine the monthly interest rate by dividing the annual interest rate by 12.
Monthly Interest Rate = Annual Interest Rate / 12
Then, we calculate the future value of the series of monthly contributions (an annuity) and the future value of the initial deposit separately. The total future value is the sum of these two components. The formula used is:
Future Value of Annuity: FV_annuity = P * [((1 + r)^n - 1) / r]
Where:
FV_annuity is the future value of the monthly contributions.
P is the monthly contribution amount.
r is the monthly interest rate (Annual Interest Rate / 12).
n is the total number of months.
Future Value of Initial Deposit: FV_deposit = Principal * (1 + r)^n
Where:
FV_deposit is the future value of the initial deposit.
Principal is the initial deposit amount.
r is the monthly interest rate.
n is the total number of months.
Total Future Value: Total FV = FV_annuity + FV_deposit
The total interest earned is then the Total Future Value minus the total amount deposited (initial deposit + total monthly contributions).
Total Interest = Total FV - (Principal + (Monthly Contribution * Number of Months))
When to Use This Calculator
This calculator is ideal for:
Estimating the growth of savings accounts with regular deposits.
Forecasting the returns on investment accounts that offer compounding interest monthly.
Understanding how APY impacts your earnings over different time periods.
Comparing different savings or investment scenarios by adjusting the initial deposit, monthly contribution, interest rate, and duration.
By inputting your specific financial details, you can gain a clear picture of your potential earnings and make more informed decisions about your savings and investments.
function calculateAPY() {
var principal = parseFloat(document.getElementById("principal").value);
var monthlyContribution = parseFloat(document.getElementById("monthlyContribution").value);
var annualInterestRate = parseFloat(document.getElementById("annualInterestRate").value);
var numberOfMonths = parseInt(document.getElementById("numberOfMonths").value);
var resultDiv = document.getElementById("result");
var projectedBalanceSpan = resultDiv.getElementsByTagName("span")[0];
var totalInterestSpan = resultDiv.getElementsByTagName("span")[1];
// Validate inputs
if (isNaN(principal) || principal < 0 ||
isNaN(monthlyContribution) || monthlyContribution < 0 ||
isNaN(annualInterestRate) || annualInterestRate < 0 ||
isNaN(numberOfMonths) || numberOfMonths 0) {
fvAnnuity = monthlyContribution * (Math.pow(1 + monthlyInterestRate, numberOfMonths) – 1) / monthlyInterestRate;
} else {
// Handle case where interest rate is 0
fvAnnuity = monthlyContribution * numberOfMonths;
}
totalFutureValue = fvDeposit + fvAnnuity;
var totalInterestEarned = totalFutureValue – totalDeposits;
// Format currency for display
var formattedProjectedBalance = totalFutureValue.toLocaleString(undefined, {
minimumFractionDigits: 2,
maximumFractionDigits: 2
});
var formattedTotalInterest = totalInterestEarned.toLocaleString(undefined, {
minimumFractionDigits: 2,
maximumFractionDigits: 2
});
projectedBalanceSpan.textContent = "$" + formattedProjectedBalance;
totalInterestSpan.textContent = "$" + formattedTotalInterest;
}