Ordinary Annuity Calculator
:root {
–primary-blue: #004a99;
–success-green: #28a745;
–light-background: #f8f9fa;
–border-color: #dee2e6;
–text-color: #343a40;
–label-color: #495057;
}
body {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: var(–light-background);
color: var(–text-color);
line-height: 1.6;
margin: 0;
padding: 20px;
}
.loan-calc-container {
max-width: 700px;
margin: 30px auto;
padding: 30px;
background-color: #ffffff;
border-radius: 8px;
box-shadow: 0 4px 15px rgba(0, 0, 40, 0.1);
border: 1px solid var(–border-color);
}
h1, h2 {
color: var(–primary-blue);
text-align: center;
margin-bottom: 25px;
}
.input-group {
margin-bottom: 20px;
display: flex;
flex-direction: column;
}
.input-group label {
display: block;
margin-bottom: 8px;
font-weight: 500;
color: var(–label-color);
}
.input-group input[type="number"],
.input-group input[type="text"] {
width: 100%;
padding: 12px 15px;
border: 1px solid var(–border-color);
border-radius: 5px;
box-sizing: border-box;
font-size: 1rem;
transition: border-color 0.2s ease-in-out, box-shadow 0.2s ease-in-out;
}
.input-group input[type="number"]:focus,
.input-group input[type="text"]:focus {
border-color: var(–primary-blue);
box-shadow: 0 0 0 3px rgba(0, 74, 153, 0.2);
outline: none;
}
.input-group select {
width: 100%;
padding: 12px 15px;
border: 1px solid var(–border-color);
border-radius: 5px;
box-sizing: border-box;
font-size: 1rem;
background-color: #fff;
cursor: pointer;
}
button {
width: 100%;
padding: 14px 20px;
background-color: var(–primary-blue);
color: white;
border: none;
border-radius: 5px;
font-size: 1.1rem;
font-weight: 600;
cursor: pointer;
transition: background-color 0.2s ease-in-out, transform 0.1s ease-in-out;
margin-top: 10px;
}
button:hover {
background-color: #003366;
transform: translateY(-1px);
}
button:active {
transform: translateY(0);
}
#result {
margin-top: 30px;
padding: 25px;
background-color: var(–success-green);
color: white;
border-radius: 6px;
text-align: center;
font-size: 1.8rem;
font-weight: bold;
box-shadow: 0 2px 10px rgba(40, 167, 69, 0.3);
}
#result span {
font-size: 1.2rem;
display: block;
margin-top: 5px;
font-weight: normal;
}
.article-section {
margin-top: 40px;
background-color: #ffffff;
padding: 30px;
border-radius: 8px;
box-shadow: 0 4px 15px rgba(0, 0, 40, 0.1);
border: 1px solid var(–border-color);
}
.article-section h2 {
text-align: left;
margin-bottom: 20px;
}
.article-section p, .article-section ul, .article-section ol {
margin-bottom: 15px;
color: var(–text-color);
}
.article-section li {
margin-bottom: 8px;
}
.formula {
font-family: 'Courier New', Courier, monospace;
background-color: var(–light-background);
padding: 10px 15px;
border-radius: 4px;
overflow-x: auto;
margin-bottom: 15px;
display: block;
}
@media (max-width: 600px) {
.loan-calc-container {
margin: 15px auto;
padding: 20px;
}
h1 {
font-size: 1.8rem;
}
#result {
font-size: 1.4rem;
}
button {
font-size: 1rem;
}
}
Ordinary Annuity Calculator
What is an Ordinary Annuity?
An ordinary annuity is a financial contract where a series of equal payments are made at regular intervals for a specified period. The key characteristic of an "ordinary" annuity is that the payments are made at the *end* of each period. This distinguishes it from an annuity due, where payments are made at the *beginning* of each period.
Ordinary annuities are very common in personal finance and business. They are used in scenarios like:
- Saving for retirement through regular contributions to a pension or investment fund.
- Making regular loan repayments (though loan calculations often use present value of annuity formulas).
- Receiving regular income from an investment or lottery winnings.
- Lease payments.
The Math Behind the Calculation
The formula used in this calculator determines the Future Value (FV) of an ordinary annuity. The future value represents the total worth of a series of future payments, including compounded interest, at a specific point in time.
The formula for the Future Value of an Ordinary Annuity is:
FV = P * [((1 + r)^n - 1) / r]
Where:
- FV is the Future Value of the annuity.
- P is the amount of each periodic payment.
- r is the periodic interest rate (expressed as a decimal).
- n is the total number of periods.
Explanation of the Formula Components:
- (1 + r)^n: This part calculates the future value of a single dollar after 'n' periods, considering the compound interest rate 'r'.
- (1 + r)^n – 1: Subtracting 1 accounts for the fact that we're dealing with payments, not a single lump sum that grows over time.
- ((1 + r)^n – 1) / r: This is the annuity factor, which multiplies the periodic payment to give the total future value, accounting for all payments and their compounded interest.
How to Use the Calculator:
- Periodic Payment Amount (P): Enter the fixed amount you will pay or receive at the end of each period.
- Periodic Interest Rate (r): Input the interest rate that applies to each period. You can enter it as a percentage (e.g., 5%) or a decimal (e.g., 0.05). The calculator will automatically convert percentages to decimals.
- Number of Periods (n): Enter the total number of payments or periods for the annuity.
- Click "Calculate Future Value" to see the total accumulated amount at the end of all periods.
Example Calculation:
Let's say you invest $200 at the end of every month for 5 years, and your investment earns an annual interest rate of 6%, compounded monthly.
- Periodic Payment Amount (P) = $200
- Annual Interest Rate = 6%
- Periods per year = 12
- Total Number of Periods (n) = 5 years * 12 months/year = 60 months
- Periodic Interest Rate (r) = 6% / 12 = 0.5% per month = 0.005
Using the formula:
FV = 200 * [((1 + 0.005)^60 - 1) / 0.005]
FV ≈ $13,878.54
This means that after 5 years, your total investment, including all contributions and compounded interest, would grow to approximately $13,878.54.
function calculateAnnuity() {
var paymentAmountInput = document.getElementById("paymentAmount");
var interestRateInput = document.getElementById("interestRate");
var numberOfPeriodsInput = document.getElementById("numberOfPeriods");
var resultDiv = document.getElementById("result");
var p = parseFloat(paymentAmountInput.value);
var r_input = interestRateInput.value.trim();
var n = parseInt(numberOfPeriodsInput.value);
// Input validation
if (isNaN(p) || p <= 0) {
resultDiv.innerHTML = "Please enter a valid payment amount.";
return;
}
if (r_input === "") {
resultDiv.innerHTML = "Please enter the interest rate.";
return;
}
if (isNaN(n) || n <= 0) {
resultDiv.innerHTML = "Please enter a valid number of periods.";
return;
}
var r;
if (r_input.endsWith('%')) {
r = parseFloat(r_input.replace('%', '')) / 100;
} else {
r = parseFloat(r_input);
}
if (isNaN(r) || r < 0) {
resultDiv.innerHTML = "Please enter a valid periodic interest rate (e.g., 5% or 0.05).";
return;
}
// Special case: if interest rate is 0, FV is simply P * n
var fv;
if (r === 0) {
fv = p * n;
} else {
// Calculate Future Value using the annuity formula
var numerator = Math.pow((1 + r), n) – 1;
var denominator = r;
fv = p * (numerator / denominator);
}
// Format the result to two decimal places
var formattedFV = fv.toFixed(2);
resultDiv.innerHTML = "$" + formattedFV.replace(/\B(?=(\d{3})+(?!\d))/g, ",") + "
Total Future Value";
}